In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

For poets to pay a great attention to the Islamic figures and their symbolism in Islam come as a prominent phenomenon in our literature . As there is an impact of them on the brilliant history commemorated by littérateurs . As a matter of fact ، the chronicle of Imam Ali Ibin Abi Talib (peace be upon him) falls in the orbit of the focus Ibn Abi Al-Hadid Al-Mu'tazili steers to in his poems . The current research study is to trace the portrayal of Imam Ali (peace be upon them) in the poetry of Ibn Abi Al-Hadid Al-Mu'tazili ، Seventh Alwiite Poems ، as there is no a study tacking such a conjecture before. In the article there are two axes : the introduction comes as first axis portraying Imam Ali Ibn Abi Talib (peace be upon him) in the wa

Many of accurate inertial guided missilc systems need to use more complex mathematical calculations and require a high speed processing to ensure the real-time opreation. This will give rise to the need of developing an effcint

Biomass has been extensively investigated, because of its presence as clean energy source. Tars and particulates formation problems are still the major challenges in development especially in the implementation of gasification technologies into nowadays energy supply systems. Laser Induced Fluorescence spectroscopy (LIF) method is incorporated for determining aromatic and Polycyclic Aromatic Hydrocarbons (PAH) produced at high temperature gasification technology. The effect of tars deposition when the gases are cooled has been highly reduced by introducing a new concept of measurement cell. The samples of PAH components have been prepared with the standard constrictions of measured PAHs by using gas chromatograph (GC). OPO laser with tun

In this paper, we characterize normal composition operators induced by holomorphic self-map , when and .Moreover, we study other related classes of operators, and then we generalize these results to polynomials of degree n.

This study aimed to identify the degree of frustration and guilt among addicts who hurt themselves with drug,  and to know the addicts perspective  who are in treatment clinics and rehabilitation centers  in Palestine, in order to achieve this goal aDeterminationThe study population has been identified , this study population consisted of ' (82) addict, the researcher used the descriptive analytical method which is appropriate for  this  study, so the researcher questioned the addicts who are in treatment clinics and rehabilitation centers  in Palestine and analyze their  responses  in light of some of the variables.

The study results showed that drug addicts who ar

This paper is concerned with introducing and studying the M-space by using the mixed degree systems which are the core concept in this paper. The necessary and sufficient condition for the equivalence of two reflexive M-spaces is super imposed. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are introduced. From an M-space, a unique supratopological space is introduced. Furthermore, the m-continuous (m-open and m-closed) functions are defined and the fundamental theorem of the m-continuity is provided. Finally, the m-homeomorphism is defined and some of its properties are investigated.

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