Polynomial

دسترسی آزاد مقاله

1 - An Effective Computational Approach by Hybrid Functions Operational Matrix for Solving Mixed Kind of the Partial Integro-Differential Equations
یاسر رستمی

In the present paper, a new method is introduced for the approximate solution of two-dimensional mixed Volterra-Fredholm Partial integro-differential equations with initial conditions using twodimensional hybrid Bernstein polynomials and Block-Pulse functions. For this چکیده کامل

In the present paper, a new method is introduced for the approximate solution of two-dimensional mixed Volterra-Fredholm Partial integro-differential equations with initial conditions using twodimensional hybrid Bernstein polynomials and Block-Pulse functions. For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of hybrid functions. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations. Convergence analysis and some numerical results are presented to illustrate the effectiveness and accuracy of the method. پرونده مقاله

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2 - تعیین جواب بهینه معادله ی کوپر- اشمیت با پیاده سازی روش های بسط پایه های ژاکوپی و ایرفویل
شادان صدیق بهزادی فاطمه گروه‌ای علی رفیعی

در این مقاله، معادله ی کوپر اشمیت را به روش هم محلی با پایه های ژاکوپی و ایرفویل، حل می کنیم. این معادله PDE یکی از معادلات مهم و پرکاربرد در فیزیک و شیمی است. این معادله غیرخطی درمهندسی مکانیک به صورت پدیده موج ظاهر شده، و در فیزیک پلاسما درباره سیستم‌هایی بحث می‌کند چکیده کامل

در این مقاله، معادله ی کوپر اشمیت را به روش هم محلی با پایه های ژاکوپی و ایرفویل، حل می کنیم. این معادله PDE یکی از معادلات مهم و پرکاربرد در فیزیک و شیمی است. این معادله غیرخطی درمهندسی مکانیک به صورت پدیده موج ظاهر شده، و در فیزیک پلاسما درباره سیستم‌هایی بحث می‌کند که از ذرّات باردار مثبت و منفی تشکیل شده‌اند و می‌توانند آزادانه حرکت کنند. مقایسه سطح تولیدات گرم الکترون و سطح آن باعث انتشار هارمونیک برخی از نشانه های منشاء می شود والکترون های گرما در پلاسما، به صورت کروی تابش می شوند [1]. معادله کوپر- اشمیت نقش مهمی در پراکندگی غیر خطی موج ایفا می کند. امواج انفرادی در پراکندگی غیر خطی رسانه ها پخش می شوند. این امواج یک فرم پایدار را حفظ می کنند. به دلیل تعادل پویا وغیر خطی بودن این معادله راه حل تقریبی در بسیاری از مقالات ارائه شده است [12و13].در این مقاله با پیاده سازی روش های عددی روی معادله مورد نظر، دستگاههای غیر خطی حاصل می شود که می توان آنها را با روش های حل دستگاههای غیرخطی، مثل روش تکراری نیوتن حل کرد. وجود، یکتایی جواب و همگرایی روشها مورد بررسی قرار می گیرد و در مثالی نشان خواهیم داد که با تکرار کم به معیار توقف |u_(n+1)-u_n |/|u_n | پرونده مقاله

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3 - حل عددی معادلات دیفرانسیل معمولی منفرد غیرخطی حاصل شده دربیولوژی، ازطریق ماتریس عملیاتی چند جمله ای های زرنیکه شعاعی
محمد علی عبادی الهام السادات هاشمی زاده امیرحسین رفاهی شیخانی

هدف از این مقاله، ارائه رویکردی عددی جدید، برای حل معادلات دیفرانسیل منفرد غیر خطی که در زمینه ی بیولوژی حاصل می شوند، می باشد. این قبیل معادلات در مسائل متعدد بیولوژی نظیر انتشار اکسیژن در سلول های خونی، انتشار گرما از سر انسان و رشد تومورهای سرطانی ظاهر می شوند. در ای چکیده کامل

هدف از این مقاله، ارائه رویکردی عددی جدید، برای حل معادلات دیفرانسیل منفرد غیر خطی که در زمینه ی بیولوژی حاصل می شوند، می باشد. این قبیل معادلات در مسائل متعدد بیولوژی نظیر انتشار اکسیژن در سلول های خونی، انتشار گرما از سر انسان و رشد تومورهای سرطانی ظاهر می شوند. در این مقاله این معادلات به کمک یک روش عددی جدید بر پایه چند جمله های زرنیکه شعاعی حل می‌شوند. در روش ارائه شده برای اولین بار ماتریس های عملیاتی مشتق گیری این توابع به دست آمده و سپس بر اساس ماتریس های عملیاتی برای مشتق توابع زرنیکه شعاعی، معادله ی دیفرانسیل اصلی به یک دستگاه از معادلات غیر خطی جبری تبدیل شود که به راحتی حل پذیرند. پیاده سازی این روش ساده و جذاب است. در پایان، مثال های کاربردی برای نشان دادن پیاده سازی روش ارائه شده و مقایسه جوابهای به دست آمده از این روش با جواب های سایر روش های معروف ارائه و حل شده است، و نتایج حاصل از آن، حاکی از دقت و کارایی این روش عددی است. پرونده مقاله

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4 - گراف‌های صحیح تطابقی از مرتبه کم
سمیه خلاشی قزل احمد

در این مقاله به بررسی گرافهای صحیح تطابقی از مرتبه کم می‌پردازیم. یک گراف را صحیح تطابقی گوییم هر گاه تمام ریشه‌‌های چندجمله‌ایی تطابقی آن صحیح باشند. گراف‌های صحیح تطابقی برای اولین بار توسط اکبری و همکاران مورد مطالعه قرار گرفتند. آن‌ها تمام گراف‌های قابل ردیابی و تما چکیده کامل

در این مقاله به بررسی گرافهای صحیح تطابقی از مرتبه کم می‌پردازیم. یک گراف را صحیح تطابقی گوییم هر گاه تمام ریشه‌‌های چندجمله‌ایی تطابقی آن صحیح باشند. گراف‌های صحیح تطابقی برای اولین بار توسط اکبری و همکاران مورد مطالعه قرار گرفتند. آن‌ها تمام گراف‌های قابل ردیابی و تمام گراف‌های منظم که صحیح تطابقی هستند را شناسایی نمودند. همچنین نشان دادند هیچ گراف فاقد پنجه‌ایی وجود ندارد که صحیح تطابقی باشد. به‌علاوه ثابت کردند گراف کامل از مرتبه دو تنها گرافی است که تطابق کامل دارد و صحیح تطابقی است. در این مقاله تمام گراف‌های همبند صحیح تطابقی از مرتبه حداکثر هفت را شناسایی می‌کنیم و نشان می‌دهیم دقیقا هشت گراف صحیح تطابقی از مرتبه حداکثر هفت وجود دارد. به‌علاوه نشان می‌کنیم یک گراف همبند صحیح تطابقی از مرتبه هشت حتما دارای تطابق سه یالی بوده و سایز آن برابر چهارده است. در نهایت تمام گراف‌های همبند صحیح تطابقی با ماکزیم درجه رئوس حداکثر سه را شناسایی می‌کنیم. پرونده مقاله

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5 - حلقه های J- مک کوی Alpha- اریب
محمد وحدانی مهرآبادی شروین صاحبی

در این مقاله، برای درونریختی حلقه ای Alpha، حلقه های J -مک کوی Alpha -اریب را معرفی می کنیم که تعمیمی از حلقه های مک کوی Alpha -اریب و حلقه های J- مک کوی می باشند. برای حلقه R ، نشان می دهیم برای هر خودتوان e اگر Alpha(e)=e و R یک حلقه J -مک کوی Alpha -اریب باشد در این چکیده کامل

در این مقاله، برای درونریختی حلقه ای Alpha، حلقه های J -مک کوی Alpha -اریب را معرفی می کنیم که تعمیمی از حلقه های مک کوی Alpha -اریب و حلقه های J- مک کوی می باشند. برای حلقه R ، نشان می دهیم برای هر خودتوان e اگر Alpha(e)=e و R یک حلقه J -مک کوی Alpha -اریب باشد در این صورت eRe یک حلقه J -مک کوی Alpha-اریب است. عکس این مطلب زمانی برقرار است که R یک حلقه آبلی باشد. همچنین اگر عدد صحیح t موجود باشد که Alpha پس از t بار ترکیب همانی شودو R[x] یک حلقه J-مک کوی Alpha -اریب باشد در این صورت حلقه R نیز J -مک کوی Alpha -اریب است. عکس این مطلب وقتی برقرار است که J(R)[x] زیرمجموعه J(R[x]) باشد. بعلاوه، مثالی ارایه می کنیم که نشان می دهد خاصیت J -مک کوی Alpha -اریب بودن یک حلقه نمی تواند به ماتریس های روی حلقه انتقال یابد. اما برای هرn ، اگرR یک حلقه J -مک کوی Alpha -اریب باشد در این صورت Tn(R)نیز یک حلقه J -مک کوی Alpha -اریب می باشد. همچنین نشان دادیم اگر R یک حلقه شبه دو راست (چپ) و Alpha یک درونریختی از حلقه R باشد، در این صورت J، R -مک کوی Alpha -اریب است اما عکس این مطلب در حالت کلی برقرار نیست. پرونده مقاله

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6 - پایه‌هایی جدید برای فضاهای با پایه چندجمله‌ای
مریم محمدی مریم بحرکاظمی

پایه‌های متداول درونیابی، مونومیال‌ها یا تک جمله‌ای‌ها هستند، بنابراین ماتریس ضرایب در حل دستگاه حاصل از درونیابی چندجمله‌ای، ماتریس واندرموند خواهد بود که ماتریسی بد وضع و چگال بوده و پایداری جواب را با مشکل مواجه می‌کند. در این مقاله ما به دنبال یافتن پایه‌های دیگری ا چکیده کامل

پایه‌های متداول درونیابی، مونومیال‌ها یا تک جمله‌ای‌ها هستند، بنابراین ماتریس ضرایب در حل دستگاه حاصل از درونیابی چندجمله‌ای، ماتریس واندرموند خواهد بود که ماتریسی بد وضع و چگال بوده و پایداری جواب را با مشکل مواجه می‌کند. در این مقاله ما به دنبال یافتن پایه‌های دیگری از روی پایه‌های متداول مونومیال‌ها هستیم، به طوری که عدد وضعیت ماتریس متناظر با پایه‌های جدید کوچکتر باشد. پایه‌های معرفی شده وابسته به داده بوده و به دو دسته پایه‌های l2-متعامد یکه‌ی گسسته و L2-متعامد یکه‌ی پیوسته تقسیم می‌شوند. این پایه‌ها، پایه‌هایی هستند که اعضای آنها به ترتیب تحت ضرب داخلی فضاهای l2(X) و [1,1-]L2 دو به دو متعامد بوده، یا به عبارتی ماتریس گرام متناظر با ضرب داخلی آنها ماتریس همانی می‌باشد. دسته‌ی اول با اعمال تجزیه QR و تجزیه مقدار تکین بر روی ماتریس واندرموند و دسته‌ی دوم با اعمال تجزیه چولسکی و تجزیه مقدار تکین بر روی ماتریس گرام متناظر با مونومیال‌ها به دست می‌آیند. نتایج عددی به دست آمده بر کوچکتر بودن عدد وضعیت ماتریس‌های ارزیابی حاصل از پایه های جدید نسبت به پایه‌های متداول مونومیال و همچنین دقت بالای این پایه‌ها در درونیابی دلالت دارد. پرونده مقاله

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7 - روشی جدید برای حل معادلات دیفرانسیل فازی از مرتبه n ام با استفاده از چند جمله ای درونیاب
الهام احمدی نازنین احمدی

روشی جدید برای حل معادلات دیفرانسیل فازی از مرتبه n ام با استفاده از چند جمله ای درونیاب با توجه به اهمیت نقش معادلات دیفرانسیل فازی در علوم و مهندسی در این مقاله ما روشی عددی برای حل معادله دیفرانسیل فازی از مرتبه n ام تحت مشتق تعمیم یافته را مورد بررسی قرار می دهیم. د چکیده کامل

روشی جدید برای حل معادلات دیفرانسیل فازی از مرتبه n ام با استفاده از چند جمله ای درونیاب با توجه به اهمیت نقش معادلات دیفرانسیل فازی در علوم و مهندسی در این مقاله ما روشی عددی برای حل معادله دیفرانسیل فازی از مرتبه n ام تحت مشتق تعمیم یافته را مورد بررسی قرار می دهیم. در این روش جواب معادله دیفرانسیل فازی توسط چندجمله ای فازی که به فرم یک قطعه ای چند جمله ای است در هر زیر بازه از بازه جواب تقریب زده می شود. در حالت خاص برای حل معادله دیفرانسیل فازی از مرتبه دوم با توجه به نوع مشتق پذیری چهار حالت در نظر گرفته می شود و سپس چند جمله ای فازی برای هر حالت ساخته می شود. درجه قطعه ای چند جمله ا ی ها در هر یک از زیر بازه های جواب از درجه ۲ می باشد. این روش توسط دو مثال از معادله دیفرانسیل فازی مرتبه ۲ تحت مشتق تعمیم یافته شرح داده شده است. پرونده مقاله

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8 - حل عددی مدل ریاضی انتشار بیماریهای عفونیبر پایه چندجمله ایهای برنشتاین انتقال یافته
فرشید میرزائی سیده فاطمه حسینی سحر علیپور

معادلات انتگرال ولترا تأخیری کاربرد زیادی در شاخه های مختلف علوم از جمله زیست شناسی، بومشناسی، فیزیک و مدلسازی مسائل مهندسی و علوم طبیعی دارند. در بسیاری از موارد حل تحلیلی این معادلات بسیار دشوار است، بنابراین روشهای عددی به عنوان یک روش تقریبی سودمند برای حل معادلات ا چکیده کامل

معادلات انتگرال ولترا تأخیری کاربرد زیادی در شاخه های مختلف علوم از جمله زیست شناسی، بومشناسی، فیزیک و مدلسازی مسائل مهندسی و علوم طبیعی دارند. در بسیاری از موارد حل تحلیلی این معادلات بسیار دشوار است، بنابراین روشهای عددی به عنوان یک روش تقریبی سودمند برای حل معادلات انتگرال ولترا تأخیری مورد توجه بسیاری از محققین قرار گرفته است. در این مقاله حل عددی معادله انتگرال ولترا- همرشتاین تاخیری با استفاده از روش تقریب کمترین مربعات و بر پایه n برنشتاین انتقال یافته lمورد بحث قرار می گیرد. این معادله یک مدل ریاضی برای انتشار بیماریهای عفونی معینی میباشد که بطور فصلی و با سرعت ثابت تغییر میکند. روش کمترین مربعات مدلی برای برازش داده ها است که در آن مجموع اختلاف بین داده مشاهده شده و مقداری که از مدل بدست می آید کمینه میشود. در این مقاله چندجملهایهای برنشتاین انتقال یافته معرفی شده و سپس تقریب تابعی دلخواه با استفاده از این چندجمله ایها ارائه میگردد. همچنین معادله انتگرال ولترا-همرشتاین تأخیری معرفی میشود و جزئیات روش کمترین مربعات و روش حل مدل ریاضی با روش پیشنهادی بیان میگردد. در پایان دقت و کارایی روش پیشنهادی را با حل دومثال عددی و مقایسه نتایج آنها با دیگر روشهای موجود نشان میدهیم. پرونده مقاله

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9 - تقریب ضرایب برای رده ای از توابع دو-تک ارزمرومورفیک
صفا صالحیان احمد معتمدنژاد

رده Σ را خانواده توابع مرومورفیک f به فرم f(z)=z+b_0+∑_(n=1)^∞▒b_n/z^n در نظر می گیریم که بر دامنهΔ={z∈C:1

رده Σ را خانواده توابع مرومورفیک f به فرم f(z)=z+b_0+∑_(n=1)^∞▒b_n/z^n در نظر می گیریم که بر دامنهΔ={z∈C:1 پرونده مقاله

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10 - یک روش عددی براساس چندجمله ایهای چلیشکوف برای حل معادلات دیفرانسیل – انتگرال از مرتبه کسری
رضا دهقان

در این مقاله، بسط تقریبی چلیشکوف برای حل معادلات دیفرانسیل- انتگرال ولترای از مرتبه ی کسری که مشتق کسری آن از نوع کپوتو است، ارائه شده است. با استفاده از خواص چند جمله ایهای چلیشکوف و فرمول انتگرال گیری عددی، حل معادلات دیفرانسیل- انتگرال کسری به حل دستگاه معادلات جبری چکیده کامل

در این مقاله، بسط تقریبی چلیشکوف برای حل معادلات دیفرانسیل- انتگرال ولترای از مرتبه ی کسری که مشتق کسری آن از نوع کپوتو است، ارائه شده است. با استفاده از خواص چند جمله ایهای چلیشکوف و فرمول انتگرال گیری عددی، حل معادلات دیفرانسیل- انتگرال کسری به حل دستگاه معادلات جبری تقلیل یافته است. سپس با حل دستگاه معادلات جبری، جواب معادله دیفرانسیل انتگرال کسری به صورت تابعی بر حسب چند جمله ایهای چلیشکوف نمایش داده می شود. دقت جواب و تحلیل خطا مورد بررسی قرار گرفته است و از آنجا که میزان دقت نتایج بدست آمده برای معادلات دیفرانسیل انتگرال کسری به تعداد چندجمله ایهای چلیشکوف انتخاب شده وابسته است لذا با افزایش تعداد چند جمله ایهای چلیشکوف می توان گام به گام به دقت مطلوب دست یافت. تمامی محاسبات توسط نرم افزار متلب انجام شده است. همچنین، نتایج عددی روش چند جمله ایهای چلیشکوف با نتایج برخی از روش های موجود به جهت اعتبار، دقت و کارآیی تکنیک مورد بررسی و مقایسه قرار گرفته است. پرونده مقاله

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11 - مشخصه‌سازی خانواده‌های α- حلال با کران چند جمله ای
مینا شاه علی سیده مرضیه قویدل

چکیده نظریه خانواده های α-حلال، بعنوان یک توسیع از تئوری نیم گروههای پیوسته قوی و خانواده عملگرهای کسینوسی با هدف مطالعه ی معادلات تحولی کسری با مشتق کاپوتو از مرتبه α گسترش زیادی پیدا کرده است. یکی از مسائل مهم در نظریه نیم گروه های پیوسته قوی، همچنین خانوا چکیده کامل

چکیده نظریه خانواده های α-حلال، بعنوان یک توسیع از تئوری نیم گروههای پیوسته قوی و خانواده عملگرهای کسینوسی با هدف مطالعه ی معادلات تحولی کسری با مشتق کاپوتو از مرتبه α گسترش زیادی پیدا کرده است. یکی از مسائل مهم در نظریه نیم گروه های پیوسته قوی، همچنین خانواده های کسینوسی بحث پیدا کردن کران های متفاوتی برای این خانواده ها (بر حسب مولد آنها) است. در این مقاله، خانواده‌های α-حلال با کران چندجمله‌ای مورد مطالعه قرار می گیرند. در واقع شرایطی روی حلال یک عملگر با دامنه‌ی چگال بیان می‌کنیم که یک خانواده ‌α-حلال چند جمله‌ای کراندار تولید کند. همچنین ثابت می‌کنیم که این شرایط در فضای هیلبرت لازم نیز هستند. با توجه به اینکه خانواده‌های حلال توسیع نیم‌گروه‌های پیوسته قوی هستند، نتایج به‌دست آمده تعمیمی از قضایای اثبات شده توسط آیزنر برای نیم گروههای چند جمله ای کراندار می‌باشد. از طرفی، چون جوابهای معادلات تحولی کسری بر حسب خانواده های α-حلال بیان می شود لذا توسط این نتایج، همزمان در مورد وجود و پایداری جواب های این مسئله ها بحث می شود. پرونده مقاله

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12 - حل عددی مدل کسری عفونت HIV در سلولهای CD4+T
محمد رضا دوستدار طیبه دمرچلی علیرضا وحیدی

در این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی م چکیده کامل

در این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی مناسب حل نمود. همچنین، در بحث آنالیز خطا، کران بالای خطا ارائه شده است. کارایی و دقت روش، با استفاده از یک نمونه عددی برای برخی مشتقات صحیح و کسری بررسی و برخی مقایسه ها و نتایج گزارش شده است. در این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی مناسب حل نمود. همچنین، در بحث آنالیز خطا، کران بالای خطا ارائه شده است. کارایی و دقت روش، با استفاده از یک نمونه عددی برای برخی مشتقات صحیح و کسری بررسی و برخی مقایسه ها و نتایج گزارش شده است. پرونده مقاله

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13 - جفت های متمایز عناصر جبری
آزاده نیک سرشت

10.30495/jnrm.2022.60572.2086

فرض کنید v یک ارزیاب هنسلی روی میدان K و v ̃ توسیع منحصربه&lrm;‌فرد آن به بستار جبری K ̃ از K باشد. عنصر α∈K ̃K دارای جفت متمایز است هرگاه مجموعه M(α,K) متناظر آن (تعریف‌شده با ضابطه زیر) دارای عضو ماکسیمم باشدM(α,K)={v ̃(α-β)┤β in چکیده کامل

فرض کنید v یک ارزیاب هنسلی روی میدان K و v ̃ توسیع منحصربه&lrm;‌فرد آن به بستار جبری K ̃ از K باشد. عنصر α∈K ̃K دارای جفت متمایز است هرگاه مجموعه M(α,K) متناظر آن (تعریف‌شده با ضابطه زیر) دارای عضو ماکسیمم باشدM(α,K)={v ̃(α-β)┤β in K ̃,[K(β) ∶K]<[K(α) ∶K]}.در این‌صورت یک جفت (α,β)از عناصر K ̃ یک جفت متمایز برای α است هرگاه β عضوی از کوچکترین درجه روی K باشد به‌طوری‌که deg⁡α>deg⁡β و v ̃(α-β)=supM(α,K). در این مقاله ابتدا نتایجی در مورد جفت‌های متمایز برای عناصر جبری از درجه دلخواه روی میدان‌های ارزیاب هنسلی ارائه می‌دهیم. سپس با توجه به اهمیت عناصر جبری از درجه اول در توسیع‌های میدان‌های ارزیاب، توجه خود را روی چنین عناصری معطوف می‌کنیم. خصوصاً برای α∈K ̃ از درجه یک عدد اول روی K، یک شرط لازم و کافی برای وجود ماکسیمم مجموعه متناظر M(α,K) با استفاده از چندجمله‌ای مینیمال α روی K ارائه می‌دهیم. پرونده مقاله

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14 - روشی عددی برای حل معادلات انتگرال دو بعدی فردهلم خطی به کمک پایه‌های چندجمله‌ای بوبکر
فرشاد مهدی فر علی خانی

در این مقاله، روش هم‌محلی جدیدی، بر مبنای چندجمله‌ای‌های بوبکر، برای جواب‌های تقریبی رده‌ای از معادلات انتگرال دو بعدی فردهلم خطی نوع دوم معرفی کرده‌ایم. خصوصیات توابع بوبکر دوبعدی بکار گرفته شده است. ماتریس اساسی انتگرال‌گیری به وسیله‌ی نقاط هم‌محلی برای کاهش فرم جواب چکیده کامل

در این مقاله، روش هم‌محلی جدیدی، بر مبنای چندجمله‌ای‌های بوبکر، برای جواب‌های تقریبی رده‌ای از معادلات انتگرال دو بعدی فردهلم خطی نوع دوم معرفی کرده‌ایم. خصوصیات توابع بوبکر دوبعدی بکار گرفته شده است. ماتریس اساسی انتگرال‌گیری به وسیله‌ی نقاط هم‌محلی برای کاهش فرم جواب معادله‌ی انتگرالی به فرم جوابی از دستگاه معادلات جبری مورد استفاده قرار گرفته است. دقت جواب و تحلیل خطا به طور کاملاً دقیق و ساختاری مورد مطالعه قرار گرفته شده و تاکید شده است که روش پیشنهادی برای انواع معادلات انتگرال دو بعدی فردهلم خطی با هسته‌ی پیوسته از نوع چندجمله‌ای کاملاً دقیق و بدون خطا می‌باشد. از طرف دیگر، کمک گرفتن از نرم‌افزار ریاضی مِیپل باعث شده جوابِ ضرایب چند جمله ای بوبکر بسیار آسان محاسبه شود. همچنین، نتایج روش حاضر را با نتایج سایر روش‌های موجود به جهت ارائه اعتبار، دقت و کارایی تکنیک مورد بررسی و مقایسه قرار داده‌ایم. پرونده مقاله

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15 - ماتریس عملیاتی جدید برای حل یک کلاس از مسائل کنترل بهینه با مشتق کسری ریمان- لیوویل اصلاح شده جمیره
محسن علی پور پریسا الله‌قلی

در این مقاله، ما روش طیفی را برمبنای چندجملهایهای برنشتاین برای حل یک کلاس از مسائل کنترل بهینه با مشتق کسری ریمانلیوویل اصلاح شده جمیره به کار میبریم. در مرحله اول، پایه دوگان و ماتریس عملیاتی حاصلضرب را براساس پایه برنشتاین معرفی مینمائیم. سپس ماتر چکیده کامل

در این مقاله، ما روش طیفی را برمبنای چندجملهایهای برنشتاین برای حل یک کلاس از مسائل کنترل بهینه با مشتق کسری ریمانلیوویل اصلاح شده جمیره به کار میبریم. در مرحله اول، پایه دوگان و ماتریس عملیاتی حاصلضرب را براساس پایه برنشتاین معرفی مینمائیم. سپس ماتریس عملیاتی برنشتاین را برای مشتقات کسری ریمانلیوویل اصلاح شده جمیره بدست میآوریم که تا کنون انجام نشده است. با استفاده از تقریب توابع براساس پایه برنشاین و ماتریسهای عملیاتی ذکر شده، مسئله کنترل بهینه با مشتق کسری ریمانلیوویل اصلاح شده جمیره به یک سیستم معادلات جبری کاهش مییابد که با استفاده از روش تکراری نیوتن به سادگی قابل حل میباشد. روش مطرح شده را برای حل دو مسئله بکار میگیریم. نتایج عددی نشان میدهد که جوابهای تقریبی حاصل، از دقت بالایی برخوردار هستند. برخی مقایسهها با روش دیگر تضمین میکند که نتایج منطقی میباشند. همچنین همانطور که انتظار میرفت، وقتی مرتبه مشتق کسری به عدد 1 میل نماید، جوابهای بدست آمده به جوابهای کلاسیک میل مینماید. پرونده مقاله

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16 - یک الگوریتم نقطه درونی شدنی برای مسائل مکمل خطی ترکیبی بر روی مخروط‌های متقارن
مریم زنگی‌آبادی حسین منصوری محمد پیرحاجی

در این مقاله، یک روش نقطه درونی شدنی برای حل مسائل مکمل خطی ترکیبی متقارن که یک کلاس کلی و جامع از مسائل مکمل خطی می‌یاشند ارائه خواهیم میشود. جهتهای جستجوگر نیوتن با استفاده از روش نسترو تاد متقارنسازی خواهند شد و با بکارگیری جبر جردن اقلیدسی & چکیده کامل

در این مقاله، یک روش نقطه درونی شدنی برای حل مسائل مکمل خطی ترکیبی متقارن که یک کلاس کلی و جامع از مسائل مکمل خطی می‌یاشند ارائه خواهیم میشود. جهتهای جستجوگر نیوتن با استفاده از روش نسترو تاد متقارنسازی خواهند شد و با بکارگیری جبر جردن اقلیدسی  همگرایی الگوریتم ارائه شده در این مقاله اثبات میشود. نشان داده میشود که پیچیدگی الگوریتم پیشنهادی منطبق بر بهترین کران پیچیدگی بدست آمده بوسیله روش‌های نقطه درونی شدنی برای حل مسائل بهینهسازی است.   پرونده مقاله

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17 - یک روش نقطه درونی نشدنی با گام کامل NT با پیچیدگی (O(n برای حاصل‌ضرب دکارتی P_*(k) –HLCP روی مخروط‌های متقارن با استفاده از تحدب نمایی
بهروز خیرفام معصومه حقیقی

در این مقاله،  با استفاده از خاصیت تحدب نمایی یک تابع مانع، یک روش نقطه درونی نشدنی را برای مساله حاصل‌ضرب دکارتی مکملی خطی افقی روی مخروط‌های متقارن  ارایه میدهیم. در این روش، از گام‌های کامل نسترو-تاد استفاده کرده و نشان میدهیم که الگوریتم منظور شد چکیده کامل

در این مقاله،  با استفاده از خاصیت تحدب نمایی یک تابع مانع، یک روش نقطه درونی نشدنی را برای مساله حاصل‌ضرب دکارتی مکملی خطی افقی روی مخروط‌های متقارن  ارایه میدهیم. در این روش، از گام‌های کامل نسترو-تاد استفاده کرده و نشان میدهیم که الگوریتم منظور شده خوش تعریف است. کران تکرار الگوریتم با بهترین کران تکرار شناخته شده برای مسایل حاصل‌ضرب دکارتی مکملی خطی افقی روی مخروطهای متقارن  منطبق است. هزینه اجرای یک تکرار  عملیات حسابی است. پرونده مقاله

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18 - حل عددی مسائل اشتورم-لیوویل با توابع کاردینال چبیشف
محمد شهریاری بهزاد نعمتی سرای فیروز پاشائی

در این مقاله، هدف اصلی ارائه‌ی یک روش عددی نوین برای تقریب مقادیر ویژه و توابع ویژه‌ی در حل مسأله‌ی اشتورم-لیوویل منظم است. به عنوان یک هدف راهبردی، ساختار توابع کاردینال چبیشف مبتنی بر چندجملهایهای چبیشف نوع اول بیان و بررسی میشود. شیوه‌ی محوری کار، تقلی چکیده کامل

در این مقاله، هدف اصلی ارائه‌ی یک روش عددی نوین برای تقریب مقادیر ویژه و توابع ویژه‌ی در حل مسأله‌ی اشتورم-لیوویل منظم است. به عنوان یک هدف راهبردی، ساختار توابع کاردینال چبیشف مبتنی بر چندجملهایهای چبیشف نوع اول بیان و بررسی میشود. شیوه‌ی محوری کار، تقلیل مسأله‌ی اشتورم-لیوویل به یک دستگاه معادلات جبری است که نیازمند به کارگیری ماتریس عملیاتی مشتق خواهد بود. حل دستگاه معادلات جبری منجر به تقریب عددی مقادیر ویژه و توابع ویژه مسأله اصلی میگردد. ارائه‌ی مثال‌های عددی عملکرد روش و اهمیت آن را نمایان‌تر می‌سازد. پرونده مقاله

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19 - انتگرال‌گیری عددی وزن‌دار با نقاط دوجمله‌ای
محمد مسجدجامعی محمدرضا بیکی

در این مقاله کلاس جدیدی از قوانین انتگرال‌گیری عددی &lrm;&lrm;وزن‌دار به&lrm;&lrm; شکل  ----------------------------------------------- ارائه شده که در آن  یک تابع وزن مثبت&rlm;،  نقاط درونیابی،  ضرایب وزنی و نهایتاً  جمله‌ی خطا می‌باشد. شکل کلی چکیده کامل

در این مقاله کلاس جدیدی از قوانین انتگرال‌گیری عددی &lrm;&lrm;وزن‌دار به&lrm;&lrm; شکل  ----------------------------------------------- ارائه شده که در آن  یک تابع وزن مثبت&rlm;،  نقاط درونیابی،  ضرایب وزنی و نهایتاً  جمله‌ی خطا می‌باشد. شکل کلی نقاط درونیاب به صورت در نظر گرفته شده که در آن   و با استفاده از قضیه‌ی -دوجمله‌ای فرم‌های صریحی برای وزن‌های   به‌دست می‌آوریم. &lrm;در ادامه به آنالیز خطای فرمول &lrm;معرفی&lrm;&lrm;&lrm;&lrm; شده پرداخته و کاربرد آن را در قالب چند مثال عددی شرح می‌دهیم. پرونده مقاله

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20 - A new approach to the numerical solution of dual fully fuzzy polynomial equations
M. Otadi

پرونده مقاله

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21 - Using Multiquadric Quasi-Interpolation for Solving Kawahara Equation
R. Ezzati

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22 - Extended ‎A‎artificial Neural Networks Approach and Fractional Volterra ‎I‎ntegro-Differential Equation‎s
A. Jafarian R. Saneifard

10.30495/ijim.2023.15261.817

In current research, an architecture of hybrid articial neural networks has been employed to solve a special kind of fuzzy systems. The proposed four-layer fuzzied recurrent network can approximate real solution of the present fuzzy system to any desired degree of acc چکیده کامل

In current research, an architecture of hybrid articial neural networks has been employed to solve a special kind of fuzzy systems. The proposed four-layer fuzzied recurrent network can approximate real solution of the present fuzzy system to any desired degree of accuracy. To do this, a back-propagation learning rule based on the gradient descent method is designed to estimate the unknowns. Finally, some numerical experiments with comparison are presented to show the effectiveness of the recurrent back-propagation method.In current research, an architecture of hybrid articial neural networks has been employed to solve a special kind of fuzzy systems. The proposed four-layer fuzzied recurrent network can approximate real solution of the present fuzzy system to any desired degree of accuracy. To do this, a back-propagation learning rule based on the gradient descent method is designed to estimate the unknowns. Finally, some numerical experiments with comparison are presented to show the effectiveness of the recurrent back-propagation method. پرونده مقاله

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23 - A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials
M. Mohamadi E. Babolian S. Yousefi

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrice چکیده کامل

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied. پرونده مقاله

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24 - Solving the First-Order Linear Matrix Differential Equations Using Bernstein Matrix Approach
Z. Lorkojouri N. Mikaeilvand E. Babolian

This paper uses a new framework for solving a class of linear matrix differential equations. For doing so, the operational matrix of the derivative based on the shifted Bernstein polynomials together with the collocation method are exploited to decrease the principal pr چکیده کامل

This paper uses a new framework for solving a class of linear matrix differential equations. For doing so, the operational matrix of the derivative based on the shifted Bernstein polynomials together with the collocation method are exploited to decrease the principal problem to system of linear matrix equations. An error estimation of this method is provided. Numerical experiments are reported to show the applicably and efficiency of the propounded method. پرونده مقاله

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25 - A Numerical Method For Solving Physiology Problems By Shifted Chebyshev Operational Matrix
E. Hashemizadeh F. Mahmoodi

In this study, a numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed. The methodology is based on the shifted Chebyshev polynomials operational matrix of derivative and collocation. To assess the ac چکیده کامل

In this study, a numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed. The methodology is based on the shifted Chebyshev polynomials operational matrix of derivative and collocation. To assess the accuracy of the method, five numerical problems, such as the human head, Oxygen diffusion and Bessel differential equation, were solved. The numerical results were compared with other existed methods in tables for verification. پرونده مقاله

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26 - Application of Laguerre Polynomials for Solving Infinite Boundary Integro-Differential Equations
A. Riahifar M. Matinfar

In this study&lrm;, &lrm;an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials&lrm;. &lrm;Properties of these polynomials and operational matrix o چکیده کامل

In this study&lrm;, &lrm;an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials&lrm;. &lrm;Properties of these polynomials and operational matrix of integration are first presented&lrm;. &lrm;These properties are then used to transform the integral equation to a matrix equation which corresponds to a linear system of algebraic equations with unknown Laguerre coefficients&lrm;. &lrm;We prove the convergence analysis of method applied to the solution integro-differential equations&lrm;. &lrm;Finally&lrm;, &lrm;numerical examples illustrate the efficiency and accuracy of the method. پرونده مقاله

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27 - An ‎E‎ffective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument
M. Khaleghi E. Babolian S. Abbasbandy

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergen چکیده کامل

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some numerical examples. پرونده مقاله

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28 - Bernstein ‎M‎ulti-Scaling Operational Matrix Method for Nonlinear Matrix Differential Models of Second-‎Order‎
M. Mohamadi E. Babolian S. A. Yousefi

In The current paper presents an idea for solving a class of linear matrix differential equations of second order. To perform so, the operational matrix of the integration based on the Bernstein multi-scaling polynomials are used to reduce the main problem to system of چکیده کامل

In The current paper presents an idea for solving a class of linear matrix differential equations of second order. To perform so, the operational matrix of the integration based on the Bernstein multi-scaling polynomials are used to reduce the main problem to system of matrix equations. Numerical experiments illustrate the applicably and efficiency of the propounded &lrm;technique.&lrm; پرونده مقاله

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29 - An Efficient Numerical Method for a Class of Boundary Value Problems, Based on Shifted Jacobi-Gauss Collocation Scheme
M. Maleki Miyane S. Abbasbandy

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomi چکیده کامل

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the proposed method. پرونده مقاله

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30 - A Method for Numerical Solution of Third-Kind Volterra Integral Equations Using Krall-Laguerre Polynomials
P. Jami E. Hashemizadeh

10.30495/ijim.2022.19201

The numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper w چکیده کامل

The numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper we propose a new method for numerical solution of linear integral equations of third kind. The proposed method is based on the approximation of the unknown function with Krall-Laguerre polynomials. This method has a simple computation with a quite acceptable approximate solution. Moreover, we obtain an estimate of the error bound for suggested method. Two examples are also presented to show the efficiency of the proposed method. پرونده مقاله

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31 - Numerical Solution of Interval Volterra-Fredholm-Hammerstein Integral Equations via Interval Legendre Wavelets ‎Method‎
N. khorrami A. Salimi Shamloo B. Parsa Moghaddam

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is define چکیده کامل

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examples show the effectiveness and efficiency of the approach. پرونده مقاله

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32 - Numerical ‎S‎olution of a SIR Fractional Model of the Distribution of Computer Viruses Using Dickson Polynomials
D. Shirani M. Tavassoli &lrm;Kajani&lrm; S. Salahshour

&lrm;In this paper, a numerical method is presented using a Dickson-based collocations method to solve a fractional model of computer virus propagation. The model presented in this paper is a system of differential equations of fraction. By using the Dickson-based collo چکیده کامل

&lrm;In this paper, a numerical method is presented using a Dickson-based collocations method to solve a fractional model of computer virus propagation. The model presented in this paper is a system of differential equations of fraction. By using the Dickson-based collocation method and using Chebyshev's spatial points, we transform the system of deficit differential equations into a system of algebraic equations. In this way, an approximate solution can be found for the proposed model. By introducing the error functions for the expressed fractional model, the accuracy and convergence of the obtained solutions are investigated. Some of the approximate results obtained using this method is displayed in the numerical results &lrm;section.&lrm; پرونده مقاله

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33 - Computing Some Topological Indices of the Molecular Graphs of Benzyl Ether with $C_{60}H$ Core and Benzyl Ether with Porphyrin Core
B. Solaymani SH. Heidarian F. Khaksar Haghani

In this paper, the first, second and third Zagreb indices, the first and second multiplicative Zagreb indices, the F-index and F-polynomial of benzyl ether dendrimer with C60H core and benzyl ether dendrimer with porphyrin core are calculated. In addition, the first and چکیده کامل

In this paper, the first, second and third Zagreb indices, the first and second multiplicative Zagreb indices, the F-index and F-polynomial of benzyl ether dendrimer with C60H core and benzyl ether dendrimer with porphyrin core are calculated. In addition, the first and second Zagreb coindices, the first and second multiplicative Zagreb coindices of these graphs are computed as well. Finally, the multiplicative Zagreb index of these graphs is computed through the link of graphs. پرونده مقاله

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34 - A New Efficient Method for Solving System of Fuzzy Volterra Integral Equations Based on Fibonacci ‎Polynomials
T. Sheverini M. Paripour N. Karamikabir

10.30495/ijim.2022.19394

Here, based on the Fibonacci polynomials, a new collocation method is presented in order to solve the system of linear fuzzy Volterra integral equations of the second kind. By using this method, these systems are reduced to a linear system of algebraic equations that ar چکیده کامل

Here, based on the Fibonacci polynomials, a new collocation method is presented in order to solve the system of linear fuzzy Volterra integral equations of the second kind. By using this method, these systems are reduced to a linear system of algebraic equations that are easily solvable. Also, the existence of the solution and error analysis of the proposed method are discussed. Finally, in order to show the importance and application of the proposed method, we have used several illustrative examples. The method is computationally very attractive and gives very accurate results. Easy implementation and simple operations are the essential features of the Fibonacci polynomials. پرونده مقاله

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35 - Numerical solution of general nonlinear Fredholm-Volterra integral equations using Chebyshev ‎approximation
F. Fattahzadeh

A numerical method for solving nonlinear Fredholm-Volterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use t چکیده کامل

A numerical method for solving nonlinear Fredholm-Volterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been imated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has lowest operation count in contrast to other early methods which use operational matrices (with huge number of operations) or involve intermediate numerical techniques for evaluating intermediate integrals which presented in integral equation or solve special case of nonlinear integral equations. Also rate of convergence are given. The numerical examples show the applicability and accuracy of the &lrm;method.&lrm; پرونده مقاله

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36 - Bernoulli operational matrix method for system of linear Volterra integral ‎equations
E. Hashemizadeh&lrm; M. Mohsenyzadeh

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elast چکیده کامل

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridization of Bernoulli polynomials and Block-Pulse functions which are orthonormal and have compact support on $[0, 1]$. By these orthonormal bases we drove new operational matrix which was a sparse matrix. By use of this new operational matrix we reduces the system of integral equations to a system of linear algebraic equations that can be solved easily by any usual numerical method. The numerical results obtained by the presented method have been compared with some existed methods and they have been in good agreement with the analytical solutions and other methods that prove the profit and efficiency of the proposed &lrm;method.&lrm; پرونده مقاله

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37 - A New Iterative Method For Solving Fuzzy Integral ‎Equations
R. Ezzati S. Ziari S. M. &lrm;Sadatrasoul&lrm;

In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed m چکیده کامل

In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed method is given and the numerical examples illustrate that the proposed iterative algorithm are &lrm;valid.&lrm; پرونده مقاله

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38 - The Ritz-Galerkin method for MHD Couette flow of non-Newtonian fluid
Z. Barikbin R. Ellahi S. Abbasbandy

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein polynomials together with the Ritz-Galer چکیده کامل

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution of algebraic equations. پرونده مقاله

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39 - Numerical Solution of Fredholm Integro-differential Equations By Using Hybrid Function Operational Matrix of ‎Differentiation‎
R. Jafri R. Ezzati K. &lrm;Maleknejad&lrm;

In this paper&lrm;, &lrm;first&lrm;, &lrm;a numerical method is presented for solving a class of linear Fredholm integro-differential equation&lrm;. &lrm;The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pu چکیده کامل

In this paper&lrm;, &lrm;first&lrm;, &lrm;a numerical method is presented for solving a class of linear Fredholm integro-differential equation&lrm;. &lrm;The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions&lrm;. &lrm;The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to the algebraic equations&lrm;. &lrm;Finally&lrm;, &lrm;show the efficiency of the proposed method is indicated by some numerical &lrm;examples.&lrm; پرونده مقاله

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40 - Application of the exact operational matrices for solving the Emden-Fowler equations, arising in ‎Astrophysics‎
S. A. Hossayni&lrm; J. A. Rad K. Parand S. Abbasbandy

The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; b چکیده کامل

The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the excellence of this new method. So, we chose Emden-Fowler type differential equations and solved them utilizing this method. To confirm the accuracy of the new method and to show the preeminence of EOMs over OOMs, the norm 1 of the residual and error function for both methods are evaluated for multiple $m$ values, where $m$ is the degree of the Bernstein polynomials. We report the results by some plots to illustrate the error convergence of both methods to zero and also to show the primacy of the new method versus OOMs. The obtained results demonstrate the increased accuracy of the new &lrm;method.&lrm; پرونده مقاله

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41 - Injection into Orbit Optimization using Orthogonal Polynomials
Sedigheh Shahmirzaee Jeshvaghany Farshad Pazooki Alireza Basohbat Novinzaddeh

In this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. The method was based on orthogonalpolynomial approximation. This method consisted of reducing the optimal control problem to a چکیده کامل

In this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. The method was based on orthogonalpolynomial approximation. This method consisted of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as Chebyshev or Legendre polynomials with undetermined coefficients. The main characteristic of this technique was that it converted the differential expressions arising from the system dynamics and the performance index into some nonlinear algebraic equations, thereby greatly simplifying the problem solution. Our research effort focused on applying a Chebyshev series expansion to optimize the trajectory profile of a point-mass Satellite Launch Vehicle (SLV). This paper is divided as follows: first, the Chebyshev and Legender series expansion to optimization are introduced. Then, the flight mechanics model of the point-mass SLV is given. Next, our optimization problem is described and optimization results are presented and discussed. پرونده مقاله

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42 - حل عددی معادلات دیفرانسیل پانتوگراف کسری غیرخطی با شرایط مرزی با استفاده از چندجمله‌ای‌های ژاکوبی
سمیه نعمتی فائزه باکوئی

در این پژوهش، یک روش عددی بر پایه‌ی چندجمله‌ای‌های ژاکوبی برای حل معادلات دیفرانسیل پانتوگراف کسری غیر‌خطی با شرایط مرزی معرفی می‌شود. ابتدا، معادله‌ دیفرانسیل به‌صورت یک معادله‌ انتگرال ولترا-فردهلم معادل بیان می‌شود. سپس، چندجمله‌ای‌های ژاکوبی و فرمول انتگرال‌گیری گاو چکیده کامل

در این پژوهش، یک روش عددی بر پایه‌ی چندجمله‌ای‌های ژاکوبی برای حل معادلات دیفرانسیل پانتوگراف کسری غیر‌خطی با شرایط مرزی معرفی می‌شود. ابتدا، معادله‌ دیفرانسیل به‌صورت یک معادله‌ انتگرال ولترا-فردهلم معادل بیان می‌شود. سپس، چندجمله‌ای‌های ژاکوبی و فرمول انتگرال‌گیری گاوس-ژاکوبی به‌همراه نقاط هم‌محلی نیوتن-کاتس برای تبدیل معادله‌ انتگرال حاصل به دستگاهی از معادلات جبری غیر‌خطی استفاده می‌شود. در آخر، با در نظر گرفتن چند مثال و محاسبه خطاهای L^"2" و L^∞، کارایی و دقت روش پیشنهادی نشان داده می‌شود.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - پرونده مقاله

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43 - Rubber/Carbon Nanotube Nanocomposite with Hyperelastic Matrix
M Motamedi M Moosavi Mashhadi

Anelastomeris apolymerwith the property ofviscoelasticity,generally having notably lowYoung's modulusand highyield straincompared with other materials. Elastomers, in particular rubbers, are used in a wide variety of products ranging from rubber hoses, isolation bearing چکیده کامل

Anelastomeris apolymerwith the property ofviscoelasticity,generally having notably lowYoung's modulusand highyield straincompared with other materials. Elastomers, in particular rubbers, are used in a wide variety of products ranging from rubber hoses, isolation bearings, and shock absorbers to tires. Rubber has good properties and is thermal and electrical resistant. We used carbon nanotube in rubber and modeled this composite with ABAQUS software. Because of hyperelastic behavior of rubber we had to use a strain energy function for nanocomposites modeling. A sample of rubber was tested and gained uniaxial, biaxial and planar test data and then the data used to get a good strain energy function. Mooney-Rivlin form, Neo-Hookean form, Ogden form, Polynomial form, reduced polynomial form, Van der Waals form etc, are some methods to get strain function energy. Modulus of elasticity and Poisson ratio and some other mechanical properties gained for a representative volume element (RVE) of composite in this work. We also considered rubber as an elastic material and gained mechanical properties of composite and then compared result for elastic and hyperelastic rubber matrix together. پرونده مقاله

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44 - New Method for Large Deflection Analysis of an Elliptic Plate Weakened by an Eccentric Circular Hole
Sh Dastjerdi L Yazdanparast

The bending analysis of moderately thick elliptic plates weakened by an eccentric circular hole has been investigated in this article. The nonlinear governing equations have been presented by considering the von-Karman assumptions and the first-order shear deformation t چکیده کامل

The bending analysis of moderately thick elliptic plates weakened by an eccentric circular hole has been investigated in this article. The nonlinear governing equations have been presented by considering the von-Karman assumptions and the first-order shear deformation theory in cylindrical coordinates system. Semi-analytical polynomial method (SAPM) which had been presented by the author before has been used. By applying SAPM method, the nonlinear partial differential equations have been transformed to the nonlinear algebraic equations system. Then, the nonlinear algebraic equations have been solved by using Newton–Raphson method. The obtained results of this study have been compared with the results of other references and the accuracy of the results has been shown. The effect of some important parameters on the results such as the location of the circular hole, the ratio of major to minor radiuses of elliptical plate, the size of circular hole and boundary conditions have been studied. It is concluded that applying the presented method is very convenient and efficient. So, it can be used for analyzing the mechanical behavior of elliptical plates, instead of relatively complicated formulations in elliptic coordinates system. پرونده مقاله

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45 - Nonlocal Bending Analysis of Bilayer Annular/Circular Nano Plates Based on First Order Shear Deformation Theory
Sh Dastjerdi M Jabbarzadeh

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Sh چکیده کامل

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) which is a highly accurate numerical method and a new semi-analytical polynomial method (SAPM). The ordinary differential equations (ODE’s) are converted to the nonlinear algebraic equations applying DQM or SAPM. Then, the Newton–Raphson iterative scheme is applied. The obtained results of DQM and SAPM are compared. It is concluded that although, the SAPM’s formulation is considerably simple in comparison with DQM, however, the results of two methods are so close to each other. The results are validated with available researches. The effects of small scale parameter, the value of van der Waals interaction between the layers, different values of elastic foundation and loading, the comparison between the local and nonlocal deflections and linear to nonlinear analysis are investigated. پرونده مقاله

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46 - Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and Second Kind
Ahmad Shahsavaran M. M. Shamivand

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interva چکیده کامل

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which leads to approximating the unknown function and it's derivatives in terms of Chebyshev polynomials of the first kind. The proposed method, transforms the Abel's integral equations of the first and second kind into a system of linear algebraic equations which can be solved by Gaussian elimination algorithm. Finally, some numerical examples are included to clarify the accuracy and applicability of the presented method which indicate that proposed method is computationally very attractive. In thispaper, all numerical computations were carried out on a PC executing some programs written in maple software. پرونده مقاله

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47 - A novel method to solve fuzzy Volterra integral equations using collocation method
Nouredin Parandin Mohsen Darabi

Fuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introd چکیده کامل

Fuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introduced. Some properties of these polynomials are consideredto implement a collocation method in order to approximate the solution of Fuzzy Volterra integral equations ofthe second kind. The existence and uniqueness of the solution also convergence and error analysis of proposedmethod are proved thoroughly. The results showed the calculations of the method are simple and low cost. پرونده مقاله

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48 - On the computation of characteristic polynomials and spectra of balanced rooted trees
Abbas Heydari

A generalized Bethe tree is a rooted unweighted tree in whichthe vertices in each of its levels have equal degree. In this paperwe derive an explicit formula for the characteristic polynomialsof the adjacency and Laplacian matrices of unweighted rootedtree which obtaine چکیده کامل

A generalized Bethe tree is a rooted unweighted tree in whichthe vertices in each of its levels have equal degree. In this paperwe derive an explicit formula for the characteristic polynomialsof the adjacency and Laplacian matrices of unweighted rootedtree which obtained from the union of the generalized Bethe treesjoined at their respective root vertices by using of rooted productof graphs. پرونده مقاله

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49 - Using Constrained Optimization to Find Real Roots of Polynomial(RRP)
Hossein Jafari Mohammad Ehsanifar

The roots of a polynomial have many applications in various sciences. If the polynomial under study has a degree of 4 or more, it will be impossible to find its roots through the coefficients. In this situation, most researchers use numerical methods to find the roots. چکیده کامل

The roots of a polynomial have many applications in various sciences. If the polynomial under study has a degree of 4 or more, it will be impossible to find its roots through the coefficients. In this situation, most researchers use numerical methods to find the roots. The purpose of this research is to introduce a relatively simple method for calculating the real roots of a polynomial. In fact, the proposed approach emphasizes the ability of operation research science in the area of finding roots. In the end, some numerical examples are solved with the help of lingo software to better understand the proposed method. The results indicated that the proposed method is remarkably effective in finding the roots of a polynomial. پرونده مقاله

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50 - Approximation of the n-th Root of a Fuzzy Number by Polynomial Form Fuzzy Numbers
Majid Amirfakhrian

In this paper we introduce the root of a fuzzy number, and we present aniterative method to nd it, numerically. We present an algorithm to generatea sequence that can be converged to n-th root of a fuzzy number.

In this paper we introduce the root of a fuzzy number, and we present aniterative method to nd it, numerically. We present an algorithm to generatea sequence that can be converged to n-th root of a fuzzy number. پرونده مقاله

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51 - Interpolation of the tabular functions with fuzzy input and fuzzy output
Mehran Chehlabi

In this paper, rst a design is proposed for representing fuzzy polynomials withinput fuzzy and output fuzzy. Then, we sketch a constructive proof for existenceof such polynomial which can be fuzzy interpolation polynomial in a set given ofdiscrete points rather than a چکیده کامل

In this paper, rst a design is proposed for representing fuzzy polynomials withinput fuzzy and output fuzzy. Then, we sketch a constructive proof for existenceof such polynomial which can be fuzzy interpolation polynomial in a set given ofdiscrete points rather than a fuzzy function. Finally, to illustrate some numericalexamples are solved. پرونده مقاله

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52 - The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear differential equations with variable coefficients
Z Kalateh Bojdi S Ahmadi-Asl A Aminataei

In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which e چکیده کامل

In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof the original expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierential equationsto solve a system of linear algebraic equations, thus greatly simplify the problem. In addition, severalnumerical experiments are given to demonstrate the validity and applicability of the method. پرونده مقاله

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53 - Optimization of the Black-Scholes Equation with the Numerical Method of Local Expansion to Minimize Risk Coverage
Amirreza Keyghobadi Shadan Behzadi Fatemeh Gervei

10.22034/amfa.2020.579396.1140

In this paper, we present an efficient and accurate method for calculating the Black-Scholes differential equations and solve the Black-Scholes equations using Jacoby and Airfoil orthogonal bases, with the collocation method. The Black-Scholes equation is a partial diff چکیده کامل

In this paper, we present an efficient and accurate method for calculating the Black-Scholes differential equations and solve the Black-Scholes equations using Jacoby and Airfoil orthogonal bases, with the collocation method. The Black-Scholes equation is a partial differential equation, which describes the price of choice in terms of time and the collocation method is a method of deter-mining coefficients. Then we show the computational results and examine the performance of the method for the two options, the price of basic assets and its issues. These results show that the Jacoby method is more efficient in solving the Black Scholes equation, and the method error is less and the convergence rate is higher. In this paper, by applying numerical methods to the desired equation, nonlinear devices can be solved by nonlinear solution methods, such as Newton's iterative method. The existence, uniqueness of the solution, and convergence of the methods are examined, and we will show in an example that by repeating then |u n+1-u n |/|u n | <ε can be reached and this indicates the accuracy of the response to these methods. پرونده مقاله

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54 - Remote Sensing and Land Use Extraction for Kernel Functions Analysis by Support Vector Machines with ASTER Multispectral Imagery
E. Akbari N. Amiri H. Azizi

Land use is being considered as an element in determining land change studies, environmental planning and natural resource applications. The Earth’s surface Study by remote sensing has many benefits such as, continuous acquisition of data, broad regional coverage, چکیده کامل

Land use is being considered as an element in determining land change studies, environmental planning and natural resource applications. The Earth’s surface Study by remote sensing has many benefits such as, continuous acquisition of data, broad regional coverage, cost effective data, map accurate data, and large archives of historical data. To study land use / cover, remote sensing as an efficient technology, is always desired by experts. In this case, classification could be considered as one of the most important methods of extracting information from digital satellite images. Selecting the best classification method and applying the proper values for parameters extremely influence the trust level of extracted land use maps. This research is an applied study which attempts to introduce Support Vector Machines (SVM) classification method, a recent development from the machine learning community. Moreover, we prove its potential for structure–activity relationship analysis on Aster multispectral data of central county of Kabodar-Ahang region in Hamedan, Iran. Accuracy of SVMs method is varied by the type of kernel functions and its parameters. The purpose of this research is to find the accuracy of Land use extraction by SVM method by Polynomial and radial basis functions kernel with their estimated optimum parameters in addition to compare the results with Maximum Likelihood method. Most of the scientists imply that Maximum Likelihood method is suitable for classification. Therefore, we try to compare SVM with ML method and to deliberate the efficiency of this new method in classification progress on Aster multispectral data. The accuracy of SVM method by Polynomial and radial basis functions kernel with optimum parameters and ML classification methods achieved 93.18%, 91.77% and 88.35 % respectively as an overall accuracy. By comparing the accuracy of these methods, SVM method by Polynomial kernel was evaluated as suitable. Therefore, we can suggest using SVM method especially with the use of Polynomial kernel to determine land use. In general, the results of this research are very practical in natural resources conservation planning and studies. Also, this study verifies the effectiveness and robustness of SVMs in the classification of remotely sensed images. پرونده مقاله

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55 - Stability of the Classification of Returns to Scale FDH Models in the Presence of Undesirable Data
Leila Jalaei Dariush Akbarian

This paper deals with the estimation of returns to scale (RTS) in free disposal hull (FDH) models for undesirable data and provides some stability intervals for preserving the RTS classification. It has been shown that the proposed stability intervals can be obtained vi چکیده کامل

This paper deals with the estimation of returns to scale (RTS) in free disposal hull (FDH) models for undesirable data and provides some stability intervals for preserving the RTS classification. It has been shown that the proposed stability intervals can be obtained via a polynomial-time algorithm based on the calculation of certain ratios of inputs and outputs, without solving any mathematical programming problem. The results of the study have been proved via some lemmas and theorems for undesirable data and have been illustrated by numerical example. پرونده مقاله

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56 - تعیین ضریب شدت تنش در ورق با ترک میانی با استفاده از روش هم هندسی براساس عملگر بیزییر تحت بارگذاری کوپله حرارتی و مکانیکی
محمد مهدی شهیب پیمان یوسفی

در این تحقیق، هدف تعیین ضریب شدت تنش در یک ورق ترک دار تحت بارگذاری حرارتی و مکانیکی است. برای این منظور به کمک کدنویسی در نرم افزارمتلب یک ورق با ترک میانی به روش هم هندسی بر اساس عملگر بیزییر، مدل سازی و المان بندی گردید. در این روش توابع پایه نربز با استفاده از عمل چکیده کامل

در این تحقیق، هدف تعیین ضریب شدت تنش در یک ورق ترک دار تحت بارگذاری حرارتی و مکانیکی است. برای این منظور به کمک کدنویسی در نرم افزارمتلب یک ورق با ترک میانی به روش هم هندسی بر اساس عملگر بیزییر، مدل سازی و المان بندی گردید. در این روش توابع پایه نربز با استفاده از عملگر بیزییر به صورت یک ترکیب خطی از چندجمله ای های برنشتاین تولید می شوند. استفاده از این عملگر موجب تولید المان های بیزییر با پیوستگی Co شده که چندجمله ای های برنشتاین بر روی این المان ها تعریف می شوند. جهت مدل سازی ترک از روش هم هندسی توسعه یافته استفاده شد. در این روش به کمک تعریف تابع مجموعه تراز مناسب، نقاط کنترلی که در طول ترک و نوک ترک وجود دارند شناسایی و استخراج شده اند. با غنی سازی نقاط کنترلی استخراج شده با توابع غنی ساز مناسب و اعمال شرایط مرزی، فرآیند تحلیل انجام شده و کرنش ها و تنش ها محاسبه گردیدند. در نهایت مقدار ضریب شدت تنش مد اول بر اساس روش انتگرال اندرکنش به دست آمد. برای بررسی صحت نتایج به دست آمده، تحلیل مشابهی به روش اجزا محدود انجام شد و نتایج حاصل از هر دو روش مقایسه شد. پرونده مقاله

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57 - Time series modeling of Alborzs crustal velocity by using artificial neural networks
Tohid malekzadeh Dilmaghani

Artifitial neural network (ANN) is an information processing system that is formed by a large number of simple processing elements, known as artificial nerves. It is formed by a number of nodes and weights connecting the nodes. Using the trained data, the designed ANN c چکیده کامل

Artifitial neural network (ANN) is an information processing system that is formed by a large number of simple processing elements, known as artificial nerves. It is formed by a number of nodes and weights connecting the nodes. Using the trained data, the designed ANN can be adjusted in an iterative procedure to determine optimal parameters of ANN. Then for an unknown input, we can compute corresponding output using the trained ANN. There are many methods for training the network and modifications of the weights. One of the most famous and simplest methods is a back-propagation algorithm that trains the network in two stages: Feed-forward and feed-backward. In the feed-forward process, the input parameters are moved to the output layer. In this stage, the output parameters the next stage is done In this study, a 3-layer perceptron neural network was used with 28 neurons in a hidden layer for modeling the eastern component (VE) and 27 neurons in a hidden layer for modeling the northern component (VN) velocity field of the earth's crust in Iran. The minimum relative error obtained from this evaluation for the eastern component was -3.57% and for the northern component was +0.16%: also the maximum relative error for the eastern component was +38.1 % and for the northern component was +95.3%. In this study, a polynomial of degree 5 with 18 coefficients was used to model the east and north components for the evaluation of artificial neural networks in estimating the velocity rate of geodetic points. A comparison of the relative error from the polynomial model and the relative error from the neural network illustrated the superiority of the neural model with respect to the polynomial model in this region. پرونده مقاله

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58 - Application of optimization algorithm to nonlinear fractional optimal control problems
Asma Moradikashkooli Hamid Haj Seyyed Javadi Sam Jabbehdari

10.22094/jcr.2023.1996770.1317

In this study, an optimization algorithm based on the generalized Laguerre polynomials (GLPs) as the basis functions and the Lagrange multipliers is presented to obtain approximate solution of nonlinear fractional optimal control problems. The Caputo fractional derivati چکیده کامل

In this study, an optimization algorithm based on the generalized Laguerre polynomials (GLPs) as the basis functions and the Lagrange multipliers is presented to obtain approximate solution of nonlinear fractional optimal control problems. The Caputo fractional derivatives of GLPs is constructed. The operational matrices of the Caputo and ordinary derivatives are introduced. The established scheme transforms obtaining the solution of such problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions. The method is very accurate and is computationally very attractive. Examples are included to provide the capacity of the proposal method. پرونده مقاله

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59 - Phase-II Monitoring of AR (1) Autocorrelated Polynomial Profiles
Mehdi Keramatpour سید تقی اخوان نیاکی Amirhossein Amiri

In some statistical process control applications, quality of a process or product can be characterized by a relationship between a response and one or more independent variables, which is typically referred to a profile. In this paper, polynomial profiles are considered چکیده کامل

In some statistical process control applications, quality of a process or product can be characterized by a relationship between a response and one or more independent variables, which is typically referred to a profile. In this paper, polynomial profiles are considered to monitor processes in which there is a first order autoregressive relation between the error terms in each profile. A remedial measure is first proposed to eliminate the effect of autocorrelation in phase-ІІ monitoring of autocorrelated profiles. Then, three methods are employed to monitor polynomial profiles where their performances are compared using the average run length criterion. پرونده مقاله

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60 - Trajectory Planning Using High Order Polynomials under Acceleration Constraint
Hossein Barghi Jond Vasif V. Nabiyev Rifat Benveniste

10.22094/joie.2016.255

The trajectory planning, which is known as a movement from starting to end point by satisfying the constraints along the path is an essential part of robot motion planning. A common way to create trajectories is to deal with polynomials which have independent coefficien چکیده کامل

The trajectory planning, which is known as a movement from starting to end point by satisfying the constraints along the path is an essential part of robot motion planning. A common way to create trajectories is to deal with polynomials which have independent coefficients. This paper presents a trajectory formulation as well as a procedure to arrange the suitable trajectories for applications. Created trajectories aimed to be used for safe and smooth navigation in mobile robots. First, a trajectory problem is formulized by considering a border on the robotâ€™s acceleration as the constraint. Also, initial and final conditions for the robotâ€™s velocity along the straight path are settled. To investigate that suggested trajectories perform motions with continuous velocity and smooth acceleration, three trajectory problems are formulated using 3rd, 4th and 5th degree of polynomials. The high-degree polynomials are used because of providing of smoothness, but there is complexity in the calculation of additional coefficients. To reduce the complexity of finding the high-degree polynomial coefficients, the acceleration constraint is simplified and this process is based on a certain scenarios. Afterwards, the coefficients of the used polynomials are found by taking into account the acceleration constraint and velocity conditions. Additionally, to compare the obtained solutions through proposed scenarios, the polynomials` coefficients are solved numerically by Genetic Algorithm (GA). The computer simulation of motions shows that as well as acceleration constraint, the velocity conditions at the beginning and at the end of motion are fulfilled. پرونده مقاله

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61 - تحلیل زمانی مکانی سالانه توفانهای تندری استان تهران
محمود احمدی یوسف قویدل رحیمی محدثه جانثاری

توفانهای تندری از مهمترین بلایای طبیعیاند که همه ساله علاوه بر نابودی بخشی ازمحصولهای کشاورزی سبب تلفات انسانی زیادی در سراسر دنیا میشوند. هدف از اینپژوهش شناسایی ویژگیهای آماری مربوط به توزیع مکانی و زمانی پدیده اقلیمی توفانهایتندری میباشد. با استفاده از دادههای مربوط چکیده کامل

توفانهای تندری از مهمترین بلایای طبیعیاند که همه ساله علاوه بر نابودی بخشی ازمحصولهای کشاورزی سبب تلفات انسانی زیادی در سراسر دنیا میشوند. هدف از اینپژوهش شناسایی ویژگیهای آماری مربوط به توزیع مکانی و زمانی پدیده اقلیمی توفانهایتندری میباشد. با استفاده از دادههای مربوط به فراوانی وقوع توفانهای تندری در استانتهران )با تأکید بر هفت ایستگاه سینوپتیک در مناطقی با توپوگرافی و طول و عرض جغرافیاییمتفاوت( ویژگیهای زمانی و مکانی توفانهای تندری مورد مطالعه و تحلیل قرار داده شدهاست. در این پژوهش بر حسب مورد از روشهای همبستگی و تحلیل رگرسیون، تجزیه مؤلفهروند سریهای زمانی )تحلیل روند خطی و پلی نومیال(، تحلیل خوشهای سلسله مراتبی وارد،توزیع احتمال وقوع و دوره بازگشت با توزیع احتمال 42 درصد، آزمون ناپارامتری من کندال 1 وروش IDW5 5002 ( برای طبقه بندی سالانه وقوع توفانهای – در دوره زمانی 15 ساله) 1442تندری استفاده شده است. نتایج نشان داد بیشترین فراوانی وقوع توفان تندری متعلّق به سال5009 و کمترین فراوانی وقوع در سال 5000 بوده است؛ همچنین ایستگاه مهرآباد بیشترین وایستگاه چیتگر کمترین نوسانها را در طول دوره آماری دارا بودهاند. بر اساس دندروگرامسالانه حاصل از روش سلسله مراتبی تحلیل خوشهای وارد به سه خوشه دسته بندی شدند.مدلهای نوسانی زمانی و روند خطی و پلی نومیال توفانهای تندری سالانه درهمه ایستگاههابجز چیتگر و ژئوفیزیک وقوع توفانهای تندی دارای روندی افزایشی است. نقشههای توزیعمکانی و مطالعات الگوهای مکانی که با استفاده از روش IDW ترسیم شدهاند نیز نشان دادآبعلی و فیروزکوه) POLL ) 3 دارای بیشترین و ژئوفیزیک دارای کمترین فراوانی وقوع توفانتندری در بین ایستگاهها در بازه زمانی مورد مطالعه بودند. پرونده مقاله

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62 - Multiple-input single-output nonlinear system identification using Bezier- Bernstein polynomials with noise cancellation
Mohammad Jahani Moghaddam

This article deals with an identification method for the fractional multiple-input single-output ‎model. It is considered the Hammerstein model to separate dynamic linear and static nonlinear ‎behaviors. Which Bezier-Bernstein polynomials are used to approximate the non چکیده کامل

This article deals with an identification method for the fractional multiple-input single-output ‎model. It is considered the Hammerstein model to separate dynamic linear and static nonlinear ‎behaviors. Which Bezier-Bernstein polynomials are used to approximate the nonlinear functions ‎and the fractional order transfer function is applied to estimate the linear part. A hybrid ‎identification method based on a modified evolutionary algorithm and a recursive classic method ‎is presented. As an advantage, this method can also correctly identify the system in the presence ‎of output noise. A photovoltaic experimental system and a numerical example are used to ‎illustrate the efficiency and performance of the proposed scheme.‎ پرونده مقاله

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63 - بررسی پایداری دینامیکی ریزشبکه‌ی اینورتری با در نظر گرفتن مجموعه‌ی بارهای دینامیکی و استاتیکی
سعید زمانیان سجاد سعدی رضا غفارپور آرام مهدویان

عملکرد مناسب و پایدار هر سیستم الکتریکی تا حد زیادی مرتبط با شناخت طراحان از ماهیت آن سیستم است؛ بنابراین لزوم ارائه ی مدلی دقیق و مبتنی بر رفتار واقعی سیستم از اهمیت فوق العاده ای برخوردار است. درزمینه‌ی ریزشبکه های اینورتری با توجه به نبود گشتاور همگام ساز کافی فرآیند چکیده کامل

عملکرد مناسب و پایدار هر سیستم الکتریکی تا حد زیادی مرتبط با شناخت طراحان از ماهیت آن سیستم است؛ بنابراین لزوم ارائه ی مدلی دقیق و مبتنی بر رفتار واقعی سیستم از اهمیت فوق العاده ای برخوردار است. درزمینه‌ی ریزشبکه های اینورتری با توجه به نبود گشتاور همگام ساز کافی فرآیند طراحی باید با حداکثر دقت انجام پذیرد. به این منظور ابتدا باید مدل دینامیکی کاملی از ریزشبکه به دست آورد. یکی از مهم ترین بخش های ریزشبکه های اینورتری بخش بار است، به این دلیل که رفتار بار در خروجی بخش تولید توان، بر تمامی ارکان سیستم تأثیرگذار است؛ بنابراین تمرکز مقاله ی حاضر بر بررسی تأثیر مدل سازی بار در فرآیند طراحی سیستم خواهد بود.ابتدا با ارائه ی معادلات اجزای ریزشبکه مدل فضای حالت آن به‌دست‌ آمده و در حضور مدل بار استاتیکی پایداری سیستم بررسی خواهد شد. سپس با قرار دادن مجموعه ی بارهای مدل دینامیکی بازیابی نمایی و استاتیکی چندجمله ای، صحت نتایج حاصل از طراحی مبتنی بر مدل استاتیکی مورد تحقیق قرار می‌گیرد. در این مسیر روش مکان ریشه ها و مشاهده ی عملکرد ریزشبکه معیار پایداری سیستم خواهد بود. به‌منظور دست یابی به اهداف پایدارسازی و بهبود عملکرد سیستم، ضرایب مشارکت متغیرهای حالت استخراج و پارامترهای تأثیرگذار مورد مطالعه قرار خواهند گرفت. پرونده مقاله

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64 - The Relation Between some Polynomials and the Wiener Index of Fuzzy Graphs
Seyed Sadegh Salehi Amiri

10.30495/fomj.2023.1990256.1102

In this paper, the distance between two vertices in a fuzzy graph is defined in a new way. In addition, some new degree-based fuzzy graph polynomials are introduced. By using this definition, fuzzy graph polynomials, and a special lower triangular matrix, the Wiener ind چکیده کامل

In this paper, the distance between two vertices in a fuzzy graph is defined in a new way. In addition, some new degree-based fuzzy graph polynomials are introduced. By using this definition, fuzzy graph polynomials, and a special lower triangular matrix, the Wiener index and the generalized Wiener index of a fuzzy graph are computed, which coincide with the Wiener index and the generalized Wiener index in the crisp graph. The result is used to compute the Wiener index of the sum, products, and composition of two fuzzy graphs. پرونده مقاله

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65 - An Efficient Approach based on Wu’s Method for Solving Fully Fuzzy Polynomial Equations System
Hamed Farahani Mohammad Javad Ebadi Seyed Ahmad Edalatpanah

10.30495/fomj.2023.1987443.1088

This article introduces a productive algebraic approach to identifying positive solutions for a system of fully fuzzy polynomial equations (FFPEs). To achieve this, the FFPEs system is transformed into a comparable system of crisp polynomial equations. The Wu's alg چکیده کامل

This article introduces a productive algebraic approach to identifying positive solutions for a system of fully fuzzy polynomial equations (FFPEs). To achieve this, the FFPEs system is transformed into a comparable system of crisp polynomial equations. The Wu's algorithm is then employed to solve the set of crisp polynomial equations as the solution method. This algorithm results in the solution of characteristic sets that are readily solvable. A key benefit of the proposed method is that all the solutions are obtained simultaneously. The article concludes by presenting some practical examples to demonstrate the efficacy of the proposed method. پرونده مقاله

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66 - Shifted Chebyshev Approach for the Solution of Delay Fredholm and Volterra Integro-Differential Equations via Perturbed Galerkin Method
Kazeem Issa Jafar Biazar Babatunde Yisa

The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodiﬀerential equations. The application of the proposed method is also extended to the solutions of integro-diﬀerential diﬀeren چکیده کامل

The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodiﬀerential equations. The application of the proposed method is also extended to the solutions of integro-diﬀerential diﬀerence equations. The method is validated using some selected problems from the literature. In all the problems that are considered, the new proposed approach performs better than many other methods. پرونده مقاله

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67 - Solution of optimal control problems using shifted chebyshev polynomial
هاجر علیمراد

This paper suggests a new and efficient method for solving linear quadratic optimal control problems. A shifted chebyshev matrix approach is implemented for solving this problem. In this method, the problem of optimal control changes into a problem of non-linear program چکیده کامل

This paper suggests a new and efficient method for solving linear quadratic optimal control problems. A shifted chebyshev matrix approach is implemented for solving this problem. In this method, the problem of optimal control changes into a problem of non-linear programming which can be solved easily. The corresponding nonlinear programming problem will be solved using Matlab software to find the unknown coefficients which are related to the approximate solution. Numerical examples are also given in order to compare this new method with another one. پرونده مقاله

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68 - Numerical solution of Fredholm and Volterra integral equations using the normalized Müntz−Legendre polynomials
فرشته صائمی حمیده ابراهیمی محمود شفیعی

The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operationa چکیده کامل

The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operational matrices, a system of algebraic equations is derived that can be readily handled through the use of the Newton scheme. The stability, error bound, and convergence analysis of the method are discussed in detail by preparing some theorems. Several illustrative examples are provided formally to show the efficiency of the proposed method. پرونده مقاله

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69 - Numerical solution of integro-differential equations via pertubed-Gegenbauer, Jacobi polynomials and Galerkin method
Kazeem Issa Kazeem Aliu Kazeem Arokoola Kazeem Micah

In this paper, we proposed perturbed Galerkin method for solving integro-differential equations via shifted Gegenbauer and shifted Jacobi polynomials as approximating polynomials. We use Galerkin method to transform the perturbed integro-differential equation to system چکیده کامل

In this paper, we proposed perturbed Galerkin method for solving integro-differential equations via shifted Gegenbauer and shifted Jacobi polynomials as approximating polynomials. We use Galerkin method to transform the perturbed integro-differential equation to system of linear algebraic equations and obtained N + 1 linear equations with N +m+2 unknowns. Moreover, with m+1 boundary conditions we obtained N +m+2 algebraic equations which was then solved to obtain the approximate solutions at various values of α and β depending on the orthogonal polynomials, that’s shifted Gegenbauer or shifted Jacobi polynomials. The proposed method was implemented on some selected problems in the literature to validate the effectiveness and the accuracy of the proposed method. پرونده مقاله

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70 - Canonical representation for approximating solution of fuzzy polynomial equations
م. صالح نزاد س. عباس بندی م. مصلح م. اوتادی

In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based چکیده کامل

In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness. پرونده مقاله

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71 - A method to obtain the best uniform polynomial approximation for the family of rational function
م.ع فریبرزی عراقی ف. فروزانفر

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1on any non symmetric interval [d,e]. Using the obtained approxim چکیده کامل

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1for both cases b2-4ac L 0and b2-4ac G 0. پرونده مقاله

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72 - Analysis of Test Day Milk Yield by Random Regression Models and Evaluation of Persistency in Iranian Dairy Cows
M. Elahi Torshizi A.A. Aslamenejad M.R. Nassiri H. Farhangfar J. Solkner M. Kovac G. Meszaros S. Malovrh

Variace / covariance components of 227118 first lactaiom test-day milk yield records belonged to 31258 Iranian Holstein cows were estimated using nine random regression models. Afterwards, different measures of persistency based on estimation breeding value were evaluat چکیده کامل

Variace / covariance components of 227118 first lactaiom test-day milk yield records belonged to 31258 Iranian Holstein cows were estimated using nine random regression models. Afterwards, different measures of persistency based on estimation breeding value were evaluated. Three functions were used to adjust fixed lactation curve: Ali and Schaeffer (AS), quadratic (LE3) and cubic (LE4) order of Legendre polynomial but for random effects, unequal order of Legendre polynomials (LE3, LE4, LE5 and Ali and Schaffer) functions were evaluated. Heterogeneous residual variance considered during days in milk and evaluation of models was based on eigenvalues and associated eigenvectors and residual variance. Model with Ali and Schaeffer function for fixed part and LE3 and LE4 for additive and permanent environmental effects was selected as the best model for random regression analysis in first parity dairy cows. The highest and lowest heritability were observed in the middle (0.29) and beginning (0.08) of lactation, respectively. Persistency measurement proposed by Cobuci (PSY1) (difference between estimation breeding value between 290 and 90 days) was preferential for using in further genetic evaluations for persistency in milk yield of Iranian Holstein cows. پرونده مقاله

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73 - The Precision Approach of the Lactation Curve in Sirohi Goats Using Non-Linear Models
L. Gautam H. Ashraf Waiz

Lactation knowledge enables total milk yield prediction from single and multiple lactation test days. The objective of this study was to compare different non-linear lactation curve models and to select the best fit model for evaluation of the Sirohi goat's milk product چکیده کامل

Lactation knowledge enables total milk yield prediction from single and multiple lactation test days. The objective of this study was to compare different non-linear lactation curve models and to select the best fit model for evaluation of the Sirohi goat's milk production curve. Data retrieved fortnightly test day milk yield (FTDMY) in the various days (15, 30, 45, 60, 75, 90, 105, 120, 135 and 150) at 22.630 fortnightly test day milk yield of 2,263 Sirohi does in different lactations at All India Coordinated Research project area period from 2004 to 2016. Gamma, inverse quadratic polynomial, exponential, mixed log, and polynomial regression were evaluated to describe the lactation curve. The mean FTDMY increased from 0.811 ± 0.004 kg on Td1 (15th day of lactation) to 1.025 ± 0.005 kg on Td3 (45th day of lactation) and then decreased to 0.379 ± 0.001 kg on Td10 (150th day of lactation), with a coefficient of variation ranging from 20.40% to 28.68%. The polynomial regression function had the best adjusted R2 value of 99.4% and the smallest root mean square error of 0.003 kg., with expected peak yield, persistency, and total milk yield were 1.03 kg, 60.8%, and 115.73%, respectively. Out of the five lactation curve models examined, the polynomial regression function produced an outstanding model for predicting fortnightly test day milk output in Sirohi goats, with a relatively strong R2 and a low root mean square error (RMSE). پرونده مقاله

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74 - Exploring the Use of Random Regression Models withLegendre Polynomials to Analyze Clutch Sizein Iranian Native Fowl
ع. عبادی تبریزی م. طهمورث‌پور ع. نجاتی جوارمی

Random regression models (RRM) have become common for the analysis of longitudinal data or repeated records on individual over time. The goal of this paper was to explore the use of random regression models with orthogonal / Legendre polynomials (RRL) to analyze new rep چکیده کامل

Random regression models (RRM) have become common for the analysis of longitudinal data or repeated records on individual over time. The goal of this paper was to explore the use of random regression models with orthogonal / Legendre polynomials (RRL) to analyze new repeated measures called clutch size (CS) as a meristic trait for Iranian native fowl. Legendre polynomial functions of increasing order 0 (no covariate) to 4 were fitted to the age at sexual maturity (ASM) and 1 to 10 to the additive genetic and permanent environmental effects. Days in production (clutch) were used as time variables. Homogeneity of residual variance through the time was assumed. Analyses were carried out within restricted maximum likelihood algorithm (REML) using WOMBAT software. Adequacy of models was checked by Bayesian information criterion (BIC). The resulted BICs suggested a model composed of the second order polynomial for ASM and 8th order polynomial for additive genetic and permanent environmental effect was the most suitable for adjusting the present records. The highest phenotypic and permanent environmental variance of CS was at the beginning of the production period. Additive genetic variance was fairly consistent during 210 and 265 days of age (d 210-d265). Estimates of heritability for CS ranged from 0.033 to 0.199 for d 161 and d 242 in the first cycle of egg production, respectively. The ratio of animal permanent environmental variance to phenotypic variance was in the range of 0.01 and 0.264. The estimated ranges for additive genetic and permanent environmental correlations were -0.18 to 0.99 and -0.5 to 0.99, respectively and were high between the adjacent ages and they tended to decrease at nonadjacent ages. پرونده مقاله

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75 - Genetic Analysis of Milk Yield in Iranian Holstein Cattle by the Test Day Model
ی. نادری N. امام جمعه کاشان ر. واعظ ترشیزی م. امین افشار

Using monthly test day records the genetic parameters of Iranian Holstein cattle in first lactation were studied. Data of 277400 test-day milk records from 65320 cows and 2210 sires were analyzed by an animal random regression model using restricted maximum likelihood m چکیده کامل

Using monthly test day records the genetic parameters of Iranian Holstein cattle in first lactation were studied. Data of 277400 test-day milk records from 65320 cows and 2210 sires were analyzed by an animal random regression model using restricted maximum likelihood methodology. The model included herd-test-date, interaction between year-season of calving, days in milk (linear and quadratic) and dam age (linear and quadratic) as fixed effects and random regression coefficients for additive genetic and permanent environmental effects. The average of 305 days milk yield was 9760 (±1324) kilogram. Differences of milk yield among provinces were significant (P<0.05). The average of heritability estimates of milk was 0.50. The genetic correlations between adjacent test-day records were high and decreased with increase in interval between tests. پرونده مقاله

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76 - Presenting an Imperceptible Steganographic Algorithm through Genetic Algorithm and Mix Column Transform
Mahsa Amini Kaleibar Saeid Taghavi Afshord

Due to growth and development of data communications, the need for fast and secure transmission of information is very important. In order to address this problem, especially over the internet, some of the security systems such as cryptography and steganography can be u چکیده کامل

Due to growth and development of data communications, the need for fast and secure transmission of information is very important. In order to address this problem, especially over the internet, some of the security systems such as cryptography and steganography can be used. Steganography is a way for secure and confidential communication. In this paper, an algorithm for color image steganography through mix column transform and the genetic algorithm is presented, which is a distinct type of the transform. The proposed method divides the image into blocks and the mix column transform of each block is obtained. Then, the genetic algorithm is applied to determine the best permutation for inserting the secret message. By using the genetic algorithm, bits of the message is embedded in the least significant bits of the image. Experimental results show that, not only the visual quality of the stego image is improved, but also the embedding time of the image and the capacity are increased. پرونده مقاله

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77 - Symbolic computation of the Duggal transform
D. Pappas V. Katsikis I. Stanimirovic

Following the results of \cite{Med}, regarding the Aluthge transform of polynomial matrices, the symboliccomputation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. چکیده کامل

Following the results of \cite{Med}, regarding the Aluthge transform of polynomial matrices, the symboliccomputation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical characteristics. The introduced algorithm is proven and illustrated in numerical examples.We also represent symbolically the Duggal transform of rank-one matricesusing cross products of vectors and show that the Duggal transform of such matrices can be givenexplicitly by a closed formula and is equal to its Aluthge transform. پرونده مقاله

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78 - On the energy of non-commuting graphs
M. Ghorbani Z. Gharavi-Alkhansari

For given non-abelian group G, the non-commuting (NC)-graph $\Gamma(G)$ is agraph with the vertex set $G$\ $Z(G)$ and two distinct vertices $x, y\in V(\Gamma)$ areadjacent whenever $xy \neq yx$. The aim of this paper is to compute the spectra ofsome well-known NC-graphs چکیده کامل

For given non-abelian group G, the non-commuting (NC)-graph $\Gamma(G)$ is agraph with the vertex set $G$\ $Z(G)$ and two distinct vertices $x, y\in V(\Gamma)$ areadjacent whenever $xy \neq yx$. The aim of this paper is to compute the spectra ofsome well-known NC-graphs. پرونده مقاله

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79 - Numerical solution of a system of fuzzy polynomial equations by modified Adomian decomposition method
M. Mosleh

In this paper, we present some efficient numericalalgorithm for solving system of fuzzy polynomial equations based on Newton'smethod. The modified Adomian decomposition method is applied toconstruct the numerical algorithms. Some numerical illustrationsare given to show چکیده کامل

In this paper, we present some efficient numericalalgorithm for solving system of fuzzy polynomial equations based on Newton'smethod. The modified Adomian decomposition method is applied toconstruct the numerical algorithms. Some numerical illustrationsare given to show the efficiency of algorithms. پرونده مقاله

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80 - Ring endomorphisms with nil-shifting property
C. A. K. Ahmed R. T. M. Salim

Cohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,b\in R.$ The reversible property is an important role in noncommutative ring theory&lrm;. &lrm;Recently&lrm;, &lrm;Abdul-Jabbar et al&lrm;. &lrm;studied the reversible ring property on nilpo چکیده کامل

Cohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,b\in R.$ The reversible property is an important role in noncommutative ring theory&lrm;. &lrm;Recently&lrm;, &lrm;Abdul-Jabbar et al&lrm;. &lrm;studied the reversible ring property on nilpotent elements&lrm;, &lrm;introducing&lrm;the concept of commutativity of nilpotent elements at zero (simply&lrm;, &lrm;a CNZ ring)&lrm;. &lrm;In this paper&lrm;, &lrm;we extend the CNZ property of a ring as follows&lrm;: &lrm;Let $R$ be a ring and $\alpha$ an endomorphism of $R$&lrm;, &lrm;we say that $ R $ is right (resp.&lrm;, &lrm;left) $\alpha$-nil-shifting ring if whenever $ a\alpha(b) = 0 $ (resp.&lrm;, &lrm;$\alpha(a)b = 0$) for nilpotents $a,b$ in $R$&lrm;, &lrm;$ b\alpha(a) = 0 $ (resp.&lrm;, &lrm;$ \alpha(b)a= 0) $&lrm;. &lrm;The characterization of $\alpha$-nil-shifting rings and their related properties are investigated&lrm;. پرونده مقاله

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81 - A Chebyshev functions method for solving linear and nonlinear fractional differential equations based on Hilfer fractional derivative
M. H. Derakhshan A. Aminataei

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we needan efficient and accurate computational method for the solution of fractional differential equa چکیده کامل

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we needan efficient and accurate computational method for the solution of fractional differential equations.This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential equations with constant coefficients subject to initial conditions based on the fractional order Chebyshev functions that this function is defined as follows:\begin{equation*}\overline{T}_{i+1}^{\alpha}(x)=(4x^{\alpha}-2)\overline{T}_{i}^{\alpha}(x)\overline{T}_{i-1}^{\alpha}(x),\,i=0,1,2,\ldots,\end{equation*}where $\overline{T}_{i+1}^{\alpha}(x)$ can be defined by introducing the change of variable $x^{\alpha},\,\alpha>0$, on the shifted Chebyshevpolynomials of the first kind. This new method is an adaptation of collocationmethod in terms of truncated fractional order Chebyshev Series. To do this method, a new operational matrix of fractional order differential in the Hilfer sense for the fractional order Chebyshev functions is derived. By using this method we reduces such problems to those ofsolving a system of algebraic equations thus greatly simplifying the problem. At the end of this paper, several numerical experiments are given to demonstrate the efficiency and accuracy of the proposed method. پرونده مقاله

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82 - Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind
M. Paripour Z. Shojaei S. Abdolahi

In this paper, the Bernstein polynomials are used to approximate the solutionsof linear integral equations with multiple time lags (IEMTL) through expansion methods(collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated چکیده کامل

In this paper, the Bernstein polynomials are used to approximate the solutionsof linear integral equations with multiple time lags (IEMTL) through expansion methods(collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact andapproximated results obtained from these methods is carried out. پرونده مقاله

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83 - Numerical solution of Fredholm integral-differential equations on unbounded domain
M. Matinfar A. Riahifar

In this study, a new and efficient approach is presented for numerical solution ofFredholm integro-differential equations (FIDEs) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized Laguerrepolynomials(G چکیده کامل

In this study, a new and efficient approach is presented for numerical solution ofFredholm integro-differential equations (FIDEs) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized Laguerrepolynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultilized to reduce the (FIDEs) to the solution ofa system of linear algebraic equations with unknown generalized Laguerre coefficients. Inaddition, two examples are given to demonstrate the validity, efficiency and applicability ofthe technique. پرونده مقاله

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84 - Operational matrices with respect to Hermite polynomials and their applications in solving linear differential equations with variable coefficients
Z. Kalateh Bojdi S. Ahmadi-Asl A. Aminataei

In this paper, a new and efficient approach is applied for numerical approximationof the linear differential equations with variable coeffcients based on operational matriceswith respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoeffc چکیده کامل

In this paper, a new and efficient approach is applied for numerical approximationof the linear differential equations with variable coeffcients based on operational matriceswith respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoeffcients for the moments of derivatives of any differentiable function in terms of theoriginal expansion coefficients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear differentialequations to solve a system of linear algebraic equations, thus greatly simplifying the problem.In addition, two experiments are given to demonstrate the validity and applicability of the method. پرونده مقاله

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85 - Higher rank numerical ranges of rectangular matrix polynomials
Gh. Aghamollaei M. Zahraei

In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated.Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higherrank چکیده کامل

In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated.Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higherrank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural generalization of the standard higher rank numericalranges. پرونده مقاله

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86 - Some properties of band matrix and its application to the numerical solution one-dimensional Bratu's problem
R. Jalilian Y. Jalilian H. Jalilian

A Class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional Bratu's problem are presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some b چکیده کامل

A Class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional Bratu's problem are presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Associated boundary formulas are developed. Convergence analysis of these methods is discussed. Numerical results are given to illustrate the efficiency of methods. پرونده مقاله

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87 - Numerical Solution of Nonlinear System of Ordinary Differential Equations by the Newton-Taylor Polynomial and Extrapolation with Application from a Corona Virus Model
Bahman Babayar-Razlighi

10.30495/ijm2c.2021.685126

In this paper, we consider a nonlinear non autonomous system of differential equations. We linearize this system by the Newton's method and obtain a sequence of linear systems of ODE. We are going to solve this system on [0,Nl] , for some positive integer N and a positi چکیده کامل

In this paper, we consider a nonlinear non autonomous system of differential equations. We linearize this system by the Newton's method and obtain a sequence of linear systems of ODE. We are going to solve this system on [0,Nl] , for some positive integer N and a positive real l>0 . For this purpose, in the first step we solve the problem on [0,l]. By knowing the solution on [0,l], we solve the problem on [l,2l] and obtain the solution on [0,2l]. We continue this procedure until [0,Nl]. In each partial interval [(k-1)l,kl], first of all, we solve the problem by the extrapolation method and obtain an initial guess for the Newton-Taylor polynomial solutions. These procedures cause that the errors don’t propagate. The sequence of linear systems in Newton's method are solved by a famous method called Taylor polynomial solutions, which have a good accuracy for linear systems of ODE. Finally, we give a mathematical model of the novel corona virus disease and illustrate accuracy and applicability of the method by some examples from this model and compare them by similar work, that simulate the numerical solutions. پرونده مقاله

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88 - Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations
Khadijeh Sadri Zainab Ayati

&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product&lrm;. &lrm;The main aim is to generalize the Jacobi integral and product operationa چکیده کامل

&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;&lrm;This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product&lrm;. &lrm;The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations&lrm; which appear in various fields of science such as physics and engineering. &lrm;The Operational matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations&lrm;. &lrm; Indeed, to solve the system of integro-differential equations, a fast algorithm is used for simplifying the problem under study. &lrm;The method is applied to solve system of linear and nonlinear Fredholm and Volterra integro-differential equations&lrm;. &lrm;Illustrative examples are included to demonstrate the validity and efficiency of the presented method&lrm;. It is further found that the absolute errors are almost constant in the studied interval. &lrm;Also&lrm;, &lrm;several theorems related to the convergence of the proposed method&lrm;, &lrm;will be presented&lrm;&lrm;.&lrm; پرونده مقاله

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89 - On a modication of the Chebyshev collocation method for solving fractional diffiusion equation
Hosein jalebbonab Hojatollah Adibi

In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .T چکیده کامل

In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency of the proposed method. پرونده مقاله

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90 - Approximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method
Sara Davaeifar Jalil Rashidinia

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Us چکیده کامل

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the given conditions, to a system of nonlinear algebraic equations. By solving such arising non linear system, the Bernstein coefficients can be determined to obtain the finite Bernstein series approach. Numerical examples are tested and the resultes are incorporated to demonstrate the validity and applicability of the approach. Comparisons with a number of conventional methods are made in order to verify the nature of accuracy and the applicability of the proposed approach. Keywords: Systems of nonlinear Volterra integro-differential equations; The Bernstein polyno- mials and series; Collocation points. 2010 AMS Subject Classication: 34A12, 34A34, 45D05, 45G15, 45J05, 65R20. پرونده مقاله

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91 - Determination of a Matrix Function in the Form of f(A)=g(q(A)) Where g(x) Is a Transcendental Function and q(x) Is a Polynomial Function of Large Degree Using the Minimal Polynomial
Esmat Nikbakht

Matrix functions are used in many areas of linear algebra and arise in numerical applications in science and engineering. In this paper, we introduce an effective approach for determining matrix function f(A)=g(q(A)) of a square matrix A, where q is a polynomial functio چکیده کامل

Matrix functions are used in many areas of linear algebra and arise in numerical applications in science and engineering. In this paper, we introduce an effective approach for determining matrix function f(A)=g(q(A)) of a square matrix A, where q is a polynomial function from a degree of m and also function g can be a transcendental function. Computing a matrix function f(A) will be time- consuming and difficult if m is large. We propose a new technique which is based on the minimal polynomial and characteristic polynomial of the given matrix A, which causes, to reduce the degree of polynomial function significantly. The new approach has been tested on several problems to show the efficiency of the presented method. Finally, the application of this method in state space and matrix quantum mechanics is highlighted. پرونده مقاله

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92 - Solving Differential Equations by Using a Combination of the First Kind Chebyshev Polynomials and Adomian Decomposition Method
hasan barzegar kelishami

In this paper, we are going to solve a class of ordinary diﬀerential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the ﬁrst kind, then we solve the ordinary diﬀerential equations by usi چکیده کامل

In this paper, we are going to solve a class of ordinary diﬀerential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the ﬁrst kind, then we solve the ordinary diﬀerential equations by using the Adomian decomposition method پرونده مقاله

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93 - On Extension of Generalized Laguerre Polynomials of Two Variable
Ahmed Al-Gonah

In this paper, we introduce a new extension of generalized Laguerre polynomials of two variable by using the extended Beta function. Some properties of these extension polynomials such as generating functions, integral representation, recurrencerelations and summation f چکیده کامل

In this paper, we introduce a new extension of generalized Laguerre polynomials of two variable by using the extended Beta function. Some properties of these extension polynomials such as generating functions, integral representation, recurrencerelations and summation formulae are obtained. پرونده مقاله

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94 - Structure of an Adaptive with Memory Method with Efficiency Index 2
Vali Torkashvand

The current research develops derivative-free family with memory methods with 100% improvement in the order of convergence. They have three parameters. The parameters are approximated and increase the convergence order from 4 to 6, 7, 7.5 and 8, respectively. Additional چکیده کامل

The current research develops derivative-free family with memory methods with 100% improvement in the order of convergence. They have three parameters. The parameters are approximated and increase the convergence order from 4 to 6, 7, 7.5 and 8, respectively. Additionally, the new self-accelerating parameters are constructed by a new way. They have the properties of simple structures and they are calculated easily. The parameters do not increase the computational cost of the iterative methods. Numerical examples of the new schemes are given to support the theoretical results. پرونده مقاله

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95 - Numerical Solution Two-Dimensional Volterra-Fredholm Integral Equations of the Second Kind with Block-Pulse Functions Based on Legendre Polynomials
Jafar Khazaian Nouredin Parandin Farajollah Mohammadi Yaghoobi Nasrin Karami Kabir

10.30495/ijm2c.2022.688969

In this paper, we present a new numerical technique based on Block-pulse functions to solve two-dimensional Volterra-Fredholm integral equations of the second kind. To produce Block-pulse functions, the orthogonal Legendre polynomials is used. Furthermore, operational m چکیده کامل

In this paper, we present a new numerical technique based on Block-pulse functions to solve two-dimensional Volterra-Fredholm integral equations of the second kind. To produce Block-pulse functions, the orthogonal Legendre polynomials is used. Furthermore, operational matrix is applied to convert two-dimensional Volterra-Fredholm integral equations to a linear algebraic system. The convergence analysis of the new method is discussed. Finally, some numerical examples are given to confirm the applicability and efficiency of the new method for solving two-dimensional Volterra-Fredholm integral equations of the second kind. پرونده مقاله

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96 - A Numerical Solution for 2D-Nonlinear Fredholm Integral Equations Based on Hybrid Functions Basis
Maryam Mohammadi A. Zakeri Majid Karami Narges Taheri Raheleh Nouraei

10.30495/ijm2c.2023.1960582.1254

This work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and sol چکیده کامل

This work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and solved by Newton's iterative method along with the numerical integration and collocation methods. Also, the convergence theorem for this algorithm is proved. Finally, some numerical examples are given to show the effectiveness and simplicity of the proposed method. پرونده مقاله

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97 - NON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS
Reza Jalilian J. Rashidinia K. Farjian H. Jalilian

A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of s چکیده کامل

A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence analysis of these methods is discussed. Numerical results are given to illustrate the eciency of methods and compared with the methods in [28-32]. پرونده مقاله

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98 - MEAN VALUE INTERPOLATION ON SPHERES
Kh. Rahsepar Fard

In this paper we consider multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have concentric spheres. Indeed, we consider the problem in three variables when it is not correct.

In this paper we consider multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have concentric spheres. Indeed, we consider the problem in three variables when it is not correct. پرونده مقاله

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99 - APPLICATION OF FUZZY EXPANSION METHODS FOR SOLVING FUZZY FREDHOLM- VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND
Sh. S. Fallah Jelodar T. Allahviranloo S. Abbasbandy

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods. پرونده مقاله

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100 - NON-POLYNOMIAL SPLINE SOLUTIONS FOR SPECIAL NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS
R. Jalilian

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions o چکیده کامل

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications of method, and to compare the computedresults with other known methods. پرونده مقاله

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101 - INTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS
M. Amirfakhrian H. Nouriani

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are present چکیده کامل

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented. پرونده مقاله

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102 - A STRONG COMPUTATIONAL METHOD FOR SOLVING OF SYSTEM OF INFINITE BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS
M. Matinfar Abbas Riahifar H. Abdollahi

The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coeffi چکیده کامل

The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coefficients. Properties of these polynomials and operational matrix of integration are rst presented. Finally, two examples illustrate the simplicity and the effectiveness of the proposed method have been presented. پرونده مقاله

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103 - Comparing Different Methodologies Used To Ensure the Security of RFID Credit Card: A Comparative Analysis
Rohit Sharma Anuj Kumar Agarwal P.K Singh

The use of Radio Frequency Identification (RFID) advancement is turning out to be rapidly transversely over an extensive variety of business undertakings. Engineers apply the development not simply in customary applications, for instance, asset or stock after, also in s چکیده کامل

The use of Radio Frequency Identification (RFID) advancement is turning out to be rapidly transversely over an extensive variety of business undertakings. Engineers apply the development not simply in customary applications, for instance, asset or stock after, also in security organizations, electronic travel papers and RFID-embedded card. In any case, RFID development moreover brings different worries up as to assurance, security and law prerequisite. In an indistinguishable route from different advances, ease Radio Frequency Identification (RFID) systems will get the chance to be inescapable in our regular daily existences when secured to standard customer things as "sharp stamps". While yielding unprecedented effectiveness gets, RFID structures may make new perils to the security and insurance of individuals or affiliations. For securing RFID trade, part of plan have presented. Here in this paper , first I give a near investigation on RFID Mastercard and its efforts to establish safety then will think about some of these plans those are utilized to guarantee the security of RFID charge card. In which, first proposing a model that utilize the random bit generator for creating the confutation for adversary and second discuss a model using polynomial sequence and Euclidean parameters during the data transmission in RFID. پرونده مقاله

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104 - کنترل بهینه پویایی مشتری از روش یادگیری ماشین با هسته چندجمله‌ای
سید حمید عمادی ابوالفضل صادقیان مژده ربانی حسن دهقان دهنوی

در این پژوهش، یک مدل از کنترل بهینه برای پویایی مشتریان براساس سیاست‌های بازاریابی به عنوان یک سیستم غیر خودکار از معادلات دیفرانسیل مورد بررسی قرار می‌گیرد. هدف اصلی مدل پیگیری و تحلیل رفتار تغییرات همزمان مشتریان منظم، ارجاعی و بالقوه شرکت از زمان شروع تا به اکنون ا چکیده کامل

در این پژوهش، یک مدل از کنترل بهینه برای پویایی مشتریان براساس سیاست‌های بازاریابی به عنوان یک سیستم غیر خودکار از معادلات دیفرانسیل مورد بررسی قرار می‌گیرد. هدف اصلی مدل پیگیری و تحلیل رفتار تغییرات همزمان مشتریان منظم، ارجاعی و بالقوه شرکت از زمان شروع تا به اکنون است. پیاده‌سازی یک سیاست بازاریابی موثر برای بهینه‌سازی این تغییرات و افزایش تعداد مشتریان از اهمیت ویژه‌ای برخوردار است. در راستای این هدف، یک الگوریتم جدید یادگیری ماشین نظارتی را برای شبیه‌سازی عددی مسئله ارائه شده است. الگوریتم پیشنهادی از هسته‌های چندجمله‌ای استفاده می‌کند. هسته‌های چندجمله‌ای این امکان را فراهم می‌آورند که تابعی پیچیده از داده‌ها را به گونه‌ای شبیه‌سازی کنند که به درک بهتر پویایی مشتریان کمک کند. رگرسیون بردار پشتیبان کمترین مربعات، یک روش بهینه‌سازی ساده برای استراتژی‌های بازاریابی ارائه می‌دهند که با این رویکرد، می‌توان استراتژی‌های بازاریابی را بدون پرداختن به جزئیات مربوط به هر مشتری بهینه کرد و به جای آن تمرکز را بر اثر کلی این استراتژی‌ها بر روی مجموعه مشتریان گذاشت. این تحقیق نشان می‌دهد که چگونه تکنیک‌های یادگیری ماشین می‌توانند در حل مسائل پیچیده مدیریت و بازاریابی کمک‌کننده باشند. با گذر زمان، تعداد مشتریان منظم افزایش می‌یابد و افراد مشتریان بالقوه کاهش می‌یابند. اما، تعداد مشتریان ارجاعی نشان دهنده یک رشد سریع در ابتدای دوره زمانی و وجود یک الگوی افزایشی نوسانی در ادامه زمان است. پرونده مقاله

فهرست مقالات Polynomial

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