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

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

There are many different methods for analysis of two-way reinforced concrete slabs. The most efficient methods depend on using certain factors given in different codes of reinforced concrete design. The other ways of analysis of two-way slabs are the direct design method and the equivalent frame method. But these methods usually need a long time for analysis of the slabs.

In this paper, a new simple method has been developed to analyze the two-way slabs by using simple empirical formulae, and the results of final analysis of some examples have been compared with other different methods given in different codes of practice.

The comparison proof that this simple proposed method gives good results and it can be used in analy

The nonlinear optical properties response of nematic liquid crystal (6CHBT) and the impact of doping with two kinds of nanoparticles; Fe₃O₄ magnetic nanoparticles and SbSI ferroelectric nanoparticles have been studied using the non-linear dynamic method through z-scan measurement technique. This was achieved utilizing CW He-Ne laser. The pure LC and magnetic LC nanoparticle composite samples had a maximum absorption while the ferroelectric LC nanoparticle composite had a minimum absorption of the incident light. The nonlinear refractive index was positive for the pure LC and the rod-like ferronematic LC composite samples, while it was negative for the ferroelectric LC composite. The studying of the nonlinear optical

Abstract:
Al-Hamraa palace considers one of the most important urban traces
that the Arab left behind in Andalus .Muhammed bin Al—Ahmer put its fist
stones then it was finished later by his thrown hirer .The poems of (ibn-
Zumrek)were graved on the palaces doors ,halls, and lion cages with all the
proud and dignity those poems contain.
This search identifies this palace first, then studies the contents of the
poems on Walls ,then the Urban features, and description of the palace sites
,buildings materials ,pillars ,decorations, and the geometrical
Vocabularies in the poems such as spaces , direction ,distance ,and
height.
Then the search describes the technical engineering of words
coordination, the

In this paper, author’s study sub diffusion bio heat transfer model and developed explicit finite difference scheme for time fractional sub diffusion bio heat transfer equation by using caputo fabrizio fractional derivative. Also discussed conditional stability and convergence of developed scheme. Furthermore numerical solution of time fractional sub diffusion bio heat transfer equation is obtained and it is represented graphically by Python.

Abstract:

Robust statistics Known as, resistance to errors caused by deviation from the stability hypotheses of the statistical operations (Reasonable, Approximately Met, Asymptotically Unbiased, Reasonably Small Bias, Efficient ) in the data selected in a wide range of probability distributions whether they follow a normal distribution or a mixture of other distributions deviations different standard .

power spectrum function lead to, President role in the analysis of Stationary random processes, form stable random variables organized according to time, may be discrete random variables or continuous. It can be described by measuring its total capacity as function in frequency.

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