This study emphasizes the infinite-boundary integro-differential equation. To examine the approximate solution of the problem, two modified optimization algorithms are proposed based on generalized Laguerre functions. In the first technique, the proposed method is applied to the original problem by approximating the solution using the truncated generalized Laguerre polynomial of the unknown function, optimizing coefficients through error minimization, and transforming the integro-differential equation into an algebraic equation. In contrast, the second approach incorporates a penalty term into the objective function to effectively enforce boundary and integral constraints. This technique reduces the original problem to a mathematical optimi

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

The confirming of security and confidentiality of multimedia data is a serious challenge through the growing dependence on digital communication. This paper offers a new image cryptography based on the Chebyshev chaos polynomials map, via employing the randomness characteristic of chaos concept to improve security. The suggested method includes block shuffling, dynamic offset chaos key production, inter-layer XOR, and block 90 degree rotations to disorder the correlations intrinsic in image. The method is aimed for efficiency and scalability, accomplishing  complexity order for n-pixels over specific cipher rounds. The experiment outcomes depict great resistant to cryptanalysis attacks, containing statistical, differential and brut

The subject of multi- ethnics is one of the most important subjects in the study of political
geography, as multi- ethnics and its consequent problems are global geopolitical phenomena
that started early and reached its peak with the beginning of the twentieth century, because of
major changes in the political landscape that resulted by wars and led to the collapse of many
empires and major powers, a matter which led to put new political maps according to certain
considerations of the colonial powers, especially in Africa and Asia. All these things led to
the most serious challenges based on ethnic and sectarian conflict and led to the development
of geopolitical problems. Among the examples what most countries in th

Adsorption techniques are widely used to remove organics pollutants from waste water particularly, when using low cost adsorbent available in Iraq. Al-Khriet powder which was found in legs of Typha Domingensis is used as bio sorbent for removing phenolic compounds from aqueous solution. The influence of adsorbent dosage and contact time on removal percentage and adsorb ate amount of phenol and 4- nitro phenol onto Al-Khriet were studied. The highest adsorption capacity was for 4-nitrophenol 91.5% than for phenol 82% with 50 mg/L concentration, 0.5 gm. dosage of adsorbent and pH 6 under a batch condition. The experimental data were tested using different isotherm models. The results show that Freundlich model resulted in the best fit also

The use of biopolymer material Chitosan impregnated granular activated carbon CHGAC as adsorbent in the removal of lead ions  pb.2+   from aqueous solution was studied using batch adsorption mode. The prepared CHGAC was characterized by Scanning Electronic Microscopy (SEM) and atomic-absorption  pectrophotometer. The adsorption of lead ions onto Chitosan-impregnated granular activated carbon was examined as a function of adsorbent weight, pH and
contact time in Batch system. Langmuir and Freundlich models were employed to analyze the resulting experimental data demonstrated that better fitted by Langmuir isotherm model than Freundlich model, with good correlation coefficient. The maximum adsorption capacity calculated f

The ability of Cr (VI) removal from aqueous solution using date palm fibers (leef) was investigated .The effects of pH, contact time, sorbets concentration and initial  metal ions concentration on the biosorption were investigated.

The residual concentration of Cr (VI) in solution was determined colorimetrically using spectrophotometer at wave length 540 nm .The biosorption was pH-dependent, the optimum pH was 7 and adsorption isotherms obtained fitted well with Langmuir isotherms .The Langmuir equation obtained was Ce/Cs = 79.99 Ce-77.39, the correlation factor was 0.908.These results indicate that date palm fibers (leef) has a potential effect for the uptake of Cr (VI) from industrial waste water.

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.