In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

The paper is concerned with posterior analysis of five exponentiated (Weibull, Exponential, Inverted Weibull, Pareto, Gumbel) distrebutions. The expressions for Bayes estimators of the shape parameters have been derived under four different prior distributions assuming four different loss functions. The posterior predictive distributions have been obtained, and the comparison between estimators made by using the mean squared errors through generated different sample sizes by using simulation technique. In general, the performance of estimators under Chi-square prior using squared error loss function is the best.

This study aimed at the investigation of abnormal liver and renal functions by biochemical manifestations of underlying metabolic abnormalities in relation to hyperglycemia in non-insulin-dependent diabetic patients. The study comprised 118 diabetic patients (56 males, 62 females) and 60 age-matched healthy non-diabetic controls (30 males, 30 females). All subjects were tested for serum levels of liver enzymatic indicators, which include aspartate transaminase (AST), alanine transaminase (ALT), and alkaline phosphatase (ALP), as well as non enzymatic parameters, including total bilirubin and total proteins.Also, serum levels of renal function markers, including microalbumin, creatinine, urea, and uric acid were measured.

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     In this paper, the class of meromorphic multivalent functions of the form by using fractional differ-integral operators is introduced. We get Coefficients estimates, radii of convexity and star likeness. Also closure theorems and distortion theorem for the class ,  is calculaed.

     This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for the new generalized beta function, including, Mellin transform, differential formulas, integral representations, and essential summation relations. Furthermore, crucial statistical application has been realized for the new generalized beta function.  

Graph  is a tool that can be used to simplify and solve network problems. Domination is a typical network problem that graph theory is well suited for. A subset of nodes in any network is called dominating if every node is contained in this subset, or is connected to a node in it via an edge. Because of the importance of domination in different areas, variant types of domination have been introduced according to the purpose they are used for. In this paper, two domination parameters the first is the restrained and the second is secure domination have been chosn. The secure domination, and some types of restrained domination in one type of trees is called complete ary tree  are determined.

Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.

In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions. 

Biological image edge detection preserving the important structural properties in an image. Detecting accurate edges are very important for analyzing the basic properties associated with a biological image. Gradient operator plays very important role in edge detection. In this paper the images had been using are color biological images taken from microbiology laboratory at the biological department college of science Al-MustansiriyhUniversity and the effect of gradient operation have applied on around 10 different biological color images but view only two. In our proposed approach comparative of various gradient of biological image include (gradient of image, gradient of image using first order derivative edge detection (Soble,Prewitt,Ro