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Bernoulli Polynomials Method for Solving Integral Equations with Singular Kernel
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هناك دائما حاجة إلى طريقة فعالة لتوليد حل عددي أكثر دقة للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة لأن الطرق العددية لها محدودة. في هذه الدراسة ، تم حل المعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة باستخدام طريقة متعددة حدود برنولي. الهدف الرئيسي من هذه الدراسة هو ايجاد حل تقريبي لمثل هذه المشاكل في شكل متعددة الحدود في سلسلة من الخطوات المباشرة. أيضا ، تم افتراض أن مقام النواة لن يكون صفرا أبدا أو أن يكون له قيمة عقدية بسبب اختيارالعقد المحددة لمتغيري النواة الوحيدين. مع متعددات حدود برنولي من الدرجة 4 و 8 كمثال على ذلك، يوفر النهج الحالي حلا قريبا جدا من الحل الدقيق في أمثلة الاختبار. بينما. يثبت الحجم المتواضع جدا للأخطاء في أمثلة الاختبار فعالية الاستراتيجية الحالية. أيضا ، فإن السهولة التي يمكن بها تنفيذ برنامج الكمبيوتر تجعل هذه التقنية فعالة للغاية. هدف آخر هو تحديد كفاءة الطريقة المقترحة من خلال مقارنتها بأساليب مختلفة. يظهر أن الحل التقريبي للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة يتقارب بشدة مع الحل المضبوط للمعادلات باستخدام متعددة حدود برنولي وهو متفوق على تلك الموجودة في الأساليب الأخرى المذكورة. هذا يضمن الأصالة والدقة العالية للطريقة المقترحة. كذلك تمت مناقشة تقارب الحل. تم تنفيذ البرامج باستخدام برنامج ال MATLAB النسخة 2018a .

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Publication Date
Tue Jun 30 2015
Journal Name
Al-khwarizmi Engineering Journal
Integral Sliding Mode Control Design for Electronic Throttle Valve System
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Abstract

 One of the major components in an automobile engine is the throttle valve part. It is used to keep up with emissions and fuel efficiency low. Design a control system to the throttle valve is newly common requirement trend in automotive technology. The non-smoothness nonlinearity in throttle valve model are due to the friction model and the nonlinear spring, the uncertainty in system parameters and non-satisfying the matching condition are the main obstacles when designing a throttle plate controller.

In this work, the theory of the Integral Sliding Mode Control (ISMC) is utilized to design a robust controller for the Electronic Throttle Valve (ETV) system. From the first in

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Publication Date
Tue May 01 2018
Journal Name
Journal Of Engineering
Design of an Optimal Integral Backstepping Controller for a Quadcopter
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In this paper, an Integral Backstepping Controller (IBC) is designed and optimized for full control, of rotational and translational dynamics, of an unmanned Quadcopter (QC). Before designing the controller, a mathematical model for the QC is developed in a form appropriate for the IBC design. Due to the underactuated property of the QC, it is possible to control the QC Cartesian positions (X, Y, and Z) and the yaw angle through ordering the desired values for them. As for the pitch and roll angles, they are generated by the position controllers. Backstepping Controller (BC) is a practical nonlinear control scheme based on Lyapunov design approach, which can, therefore, guarantee the convergence of the position tracking

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Publication Date
Fri Mar 31 2017
Journal Name
Al-khwarizmi Engineering Journal
Design an Integral Sliding Mode Controller for a Nonlinear System
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The goal of this paper is to design a robust controller for controlling a pendulum
system. The control of nonlinear systems is a common problem that is facing the researchers in control systems design. The Sliding Mode Controller (SMC) is the best solution for controlling a nonlinear system. The classical SMC consists from two phases. The first phase is the reaching phase and the second is the sliding phase. The SMC suffers from the chattering phenomenon which is considered as a severe problem and undesirable property. It is a zigzag motion along the switching surface. In this paper, the chattering is reduced by using a saturation function instead of sign function. In spite of SMC is a good method for controlling a nonlinear system b

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Publication Date
Tue Jan 01 2019
Journal Name
Baghdad Science Journal
Hazard Rate Estimation Using Varying Kernel Function for Censored Data Type I Article Sidebar
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n this research, several estimators concerning the estimation are introduced. These estimators are closely related to the hazard function by using one of the nonparametric methods namely the kernel function for censored data type with varying bandwidth and kernel boundary. Two types of bandwidth are used: local bandwidth and global bandwidth. Moreover, four types of boundary kernel are used namely: Rectangle, Epanechnikov, Biquadratic and Triquadratic and the proposed function was employed with all kernel functions. Two different simulation techniques are also used for two experiments to compare these estimators. In most of the cases, the results have proved that the local bandwidth is the best for all the types of the kernel boundary func

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Publication Date
Sun Jan 01 2017
Journal Name
Ieee Access
On Computational Aspects of Tchebichef Polynomials for Higher Polynomial Order
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Publication Date
Wed Dec 01 2021
Journal Name
Baghdad Science Journal
Analytical Solutions for Advanced Functional Differential Equations with Discontinuous Forcing Terms and Studying Their Dynamical Properties
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This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the nth order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

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Publication Date
Thu Jan 01 2026
Journal Name
Journal Of Interdisciplinary Mathematics
Sufficient conditions for the oscillation of solutions of third-order neutral difference equations with alternating coefficients
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This study deals with 3rd-order difference equations with alternating coefficients (NDEAC) with a focus on studying the oscillatory properties of their solutions. An additional sufficient condition can be derived to ensure continuity for the oscillatory solution in equations. An applied example is presented to illustrate the theoretical result obtained.

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Publication Date
Sat Sep 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
New Approach for Solving Multi – Objective Problems
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  There are many researches deals with constructing an efficient solutions for real problem having Multi - objective confronted with each others. In this paper we construct a decision for Multi – objectives based on building a mathematical model formulating a unique objective function by combining the confronted objectives functions. Also we are presented some theories concerning this problem. Areal application problem has been presented to show the efficiency of the performance of our model and the method. Finally we obtained some results by randomly generating some problems.

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Publication Date
Thu May 21 2026
Journal Name
Aip Conference Proceedings
Iterative technique for solving alcohol consumption model
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Publication Date
Mon Jun 22 2020
Journal Name
Baghdad Science Journal
Splitting the One-Dimensional Wave Equation. Part I: Solving by Finite-Difference Method and Separation Variables
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In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error

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