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Solving Linear Volterra – Fredholm Integral Equation of the Second Type Using Linear Programming Method
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In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.

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Publication Date
Sat Jan 31 2026
Journal Name
International Journal Of Intelligent Engineering And Systems
Low-complexity Deep Learning for Joint Channel-type Identification and SNR Estimation in MIMO-OFDM Using CNN–BRNN with LUT Labels
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Channel estimation (CE) is essential for wireless links but becomes progressively onerous as Fifth Generation (5G) Multi-Input Multi-Output (MIMO) systems and extensive fading expand the search space and increase latency. This study redefines CE support as the process of learning to deduce channel type and signal-tonoise ratio (SNR) directly from per-tone Orthogonal Frequency-Division Multiplexing (OFDM) observations,with blind channel state information (CSI). We trained a dual deep model that combined Convolutional Neural Networks (CNNs) with Bidirectional Recurrent Neural Networks (BRNNs). We used a lookup table (LUT) label for channel type (class indices instead of per-tap values) and ordinal supervision for SNR (0–20 dB,5-dB steps). T

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Publication Date
Mon Jan 01 2024
Journal Name
Applied And Computational Mathematics
Reliable computational methods for solving Jeffery-Hamel flow problem based on polynomial function spaces
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Publication Date
Fri Jul 19 2024
Journal Name
An International Journal Of Optimization And Control: Theories & Applications (ijocta)
Design optimal neural network based on new LM training algorithm for solving 3D - PDEs
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In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

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Publication Date
Wed May 13 2020
Journal Name
Nonlinear Engineering
Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences
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Abstract<p>In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using <italic>Mathematica</italic>® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To ill</p> ... Show More
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Publication Date
Wed May 13 2020
Journal Name
Nonlinear Engineering
Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences
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Abstract<p>In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using <italic>Mathematica</italic>® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To ill</p> ... Show More
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Publication Date
Wed Aug 30 2023
Journal Name
Iraqi Journal Of Science
Computational methods for solving nonlinear ordinary differential equations arising in engineering and applied sciences
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In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the met

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Publication Date
Wed Jun 30 2010
Journal Name
Al-kindy College Medical Journal
Frozen Shoulder in Type 2 Diabetes Mellitus
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Background: Frozen shoulder affects 2-5% of the
general population, and around 10-30% of diabetic
patients. It affect mainly the non-dominant shoulder,
and has more incidence in patients with poor
glycemic control.
Objective: To detect the incidence of frozen
shoulder in type 2 diabetic patients attending the
Specialized Center for Endocrinology and Diabetes
in Baghdad.Patients and methods: One hundred
patients with frozen shoulder were included in the
study from a total number of 580 type 2 diabetics
over a period of six months. 70 patients were
females and 30 patient were males. All were
investigated for fasting blood
glucose and HbA1c.
Results: The non-dominant shoulder was
involved in

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Publication Date
Tue Sep 01 2020
Journal Name
Baghdad Science Journal
Modified Weighted Pareto Distribution Type I (MWPDTI)
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In this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period  The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and  the hazard function are found. The behaviour of probability density function for MWPDTI distrib

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Publication Date
Tue Jun 15 2021
Journal Name
Al-academy
The Utilization of Arabic Calligraphy to Inspire Modern Arabic Type Designs: ربا حسن أبو حسنة
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Arabic calligraphy is one of the greatest achievements of Islamic art. The visual form of Arabic calligraphy is the primary means of presenting ideas and messages for expressive communication in Arabic typefaces. Emerging computer technology with calligraphy is essential for effective visual designs; however, traditional typefaces are insufficient in number and quality to fulfill the requirements of the current Saudi industry. Thus, this research investigates the processes followed by graphic designers to create modern Arabic type designs inspired by Arabic calligraphy, and presents the characteristics of Arabic calligraphy. The research implemented a mixed experimental and descriptive method, exploring 10 typefaces designed by professio

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Publication Date
Tue Nov 30 2021
Journal Name
Indian Journal Of Forensic Medicine & Toxicology
The role of vitamin D3 in improving lipid profile in type 2 diabetes patients with
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