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In this short paper the monotonicity of functions involving the Beta function is considered to be study by using a similar method given in (2) and (4).

This paper provides an efficient algorithm to generate three dimensional objects from simple uncomplicated 2D environment, lead to reduce processor effort, limit of using complex mathematical operations. Most of the previous researches used the idea of ​​drawing by vanishing point to generate 3D objects from 2D environment, But the algorithm designed in this paper provides an idea of ​​how to draw three-dimensional shapes from two-dimensional drawings when applying Cohen Sutherland Line clipping algorithm, so that a basic two-dimensional shape is inserted from a set of points connected with each other must be within vision borders with a vanishing point outside of vision that is connected with all points of basic shape to consist a group of lines with partial intersections. So that any point has specific limited vision border which represents one of its coordinates of depth vertex, finally 3d object is generated when all clipping processes are completed to obtain other coordinates for all points.

The paper tackled a survey of two optimization methods to study spanning tree problem by modifying the spanning tree problem to generate all of possible solutions in undirected tree graph with simulated annealing algorithm and ant colony optimization algorithm. These algorithms are two of the optimization methods to find optimal solution from many of solutions in search space. A program is written in MATLAB 6.5 language to simulate these two algorithms with spanning tree problem. The experimental results in this paper show the effectiveness and easy implementation of each algorithm to find optimal solution, and to perform significantly better than the manual method.

If P and Q are convex subsets in ) X ( C , and 0 ) x ( q > in X for all Q q ∈ . If the approximation family is the set { } Q q , P p : q p T ∈ ∈ = An Infinitesimal approximation of ) X ( C f ∈ an element in T established in [4],[5]. A characterization of an infinitesimal approximation, necessary and sufficient conditions for the unique infinitesimal approximation are obtained. 1Introduction: In this paper the problem of obtaining an infinitesimal approximation with a necessary and sufficient conditions for the uniqueness of infinitesimal approximation are considered and studied. The following definitions and statements of nonstandard analysis will be needed throughout this papers [3],[4],[6]. The axioms of IST given by Nelson E. [3] are the axioms of ZFC together with three additional axioms, which are called the transfer principle (T), the idealization principle (I), and the standardization principle (S) are stated by the following

Let G be a k0-connected graph ,and let ,,be the w- width, distance between the two vertices u,v in G. The w-Wiener polynomial of the width distance of G is defined by: Ww(G;x) is obtained in this paper for some special graphs G such as a cycle , a wheel, a theta graph , a straight hexagonal chain , and Wagner graph .The diameter with respect to the width distance – w, and the Wiener index for each such special graphs are also obtained in this paper.

Dates are a great food that meets many human needs, and the government should encourage and intensify efforts to support the expansion of palm cultivation and development and focus on its production in our country as a means of food security in the future. In addition, palm trees have an important economic role in improving the country's economy. In this paper, a sharp decline in the quality of production will be highlighted. So, the aim of the study is to know the most important types of palm trees that affect the production of tigers for the year 2019 if the study includes 11 governorates, and the multiple linear regression method has been applied in selecting the most important types affecting the production.. and the types of palm trees did not appear Halawi and Khattawi and Khadari any effect on Dates production in the aforementioned year, although these types are considered to be one of the desirable first-class varieties in the Iraqi market, and for export in particular, in a manner that supports the country's economy.

In this paper, we used the homotopy analysis method to ordinary differential equations of type boundary value problems with a parameter representing turning points."To show the high accuracy of the solution results, we compare the numerical results applying the standard homotopy analysis method with the integral equation and the numerical solution of the Simpson and Trapezoidal rules."Also, we give the estimated order of convergence (local) and the global estimated order of convergence along the interval.

Let R be a commutative ring with identity. We associate a graph . In this paper, we find Hosoya polynomial and Wiener index of Zn , with n= pm or n= pmq, where p and q are distinct prime numbers and m is an integer with m 2.

In 2005 Wang investigated the zero divisor graphs of degrees 5,6,9 and 10. In 2012 Shuker and Mohammad investigated the zero divisor graphs of degrees 7 and 8. In this paper, we consider zero divisor graphs of commutative rings of degrees 11, 12 and 13.

In this paper, we have investigated a new class of conjugate gradient algorithms for unconstrained non-linear optimization which are based on the quadratic model. Some theoretical results are investigated which are sufficient descent and ensure the local convergence of the new proposed algorithms. Numerical results show that the proposed algorithms are effective by comparing with the Polak and Ribiere algorithm.

In this paper we study the statistical properties of one of a non-linear autoregressive model with hyperbolic triangle function(polynomial with hyperbolic cosinefunction)by using the local linearization approximation method to find the stability of the model (singular point and its stability conditions and the stability of limit cycle).Where we started by the model of lower order (first and second and third order) and generalized the idea, and we tried to apply these theory results by using some of examples to explain one of important truth that says (if the model has unstable singular point, then it, maybe, has a stable limit cycle).

In this paper, a high zero-sum weighting is applied to evaluate the nullity of a dendrimer graph for some special graphs such as cycles, paths, complete graphs, complete bipartite graphs and star graphs. Finally, we introduce and prove a sharp lower and a sharp upper bound for the nullity of the coalescence graph of two graphs.

In this paper, we study the moment of a non linear – autoregressive polynomial model of first order, also we analysis the stability of this model and find the singular point as well as the limit cycle by using the linear approximation technique.

In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for . We have found that the two schemes are unconditionally stable when , while the consistent scheme is stable under the conditions and when . Also, the lumped scheme is stable under the conditions and when .

This paper studies the bifurcations in dynamics of a family of semi-triangular maps . We will prove that this family has a series of Saddle-node bifurcations and a period doubling bifurcation. Also, we show that for some value of the parameter the functions will be chaotic.

In this paper, we derived a new conjugacy coefficient of conjugate gradient method which is based on non-linear function using inexact line searches. This method satisfied sufficient descent condition and the converges globally is provided. The numerical results indicate that the new approach yields very effective depending on number of iterations and number of functions evaluation .

In this paper, we apply He's variational iteration method (VIM) and the Adomian decomposition method (ADM) to approximate the solution of Duffing-Van Der Pol equation (DVP). In VIM, a correction functional is constructed by a general Lagrange multiplier which can be identified via a variational theory. The VIM yields an approximate solution in the form of a quickly convergent series. Comparisons of the two series solutions with the classical Runge-Kutta order four RK45 method show that the VIM is a powerful method for the solution of nonlinear equations. The convergent of He's variational iteration method to this equation is also considered.

In 2005 J. T Wang investigated the zero divisor graphs of degrees 5 and 6. In this paper, we consider the zero divisor graphs of a commutative rings of degrees 7 and 8.

In this paper we study the conditions under which the zero solution iscenter of Gravity in the semi-liner case for certain third order differential equation of the form: We have: The characteristic equation of the above differential equation has complex roots of the form : , and the other root has the following property .

In this paper we used non parametric density estimator (Kernel Estimator) to estimate probability density function for Image data of Hand Gesture and warping Hand Gesture and we see the curve for Kernel Estimator and combine the curve between Kernel Estimator and normal Distribution. Programs written using the language Matlab (R2009a) .

The objective of this paper is to speed the solution of linear Boundary Value Problem (LPVPs) by parallel Programming by using cs_tools where the solution methods is the linear superposition Algorithm.

For a wheel and a cycle the composite graphs ⊠ is constructed from the union of and and adding the edges and , where is an edge of and is an edge of . The n – diameter , the n – Hosoya polynomial and the n – Wiener index of ⊠ are obtained in this paper.

In this paper, we use Romberg algorithm, to find an approximation solution for a system of nonlinear Fredholm integral equations of the second kind. A comparison between this approximations and exact solutions for four numerical examples are given, depending on the least-square error and running computer time. Our numerical results are obtained by MATLAB 7.0 program and for a system of rank 2×2, 3×3 on Personal Computer P4.

In this paper, the parabolic partial differential equations in three-dimensions are solved by two types of finite differences, such as, Alternating Direction Explicit (ADE) method and Alternating Direction Implicit (ADI) method. By the comparison of the numerical results for the previous two methods with the Exact solution, we observe that the results of Alternating Direction Implicit (ADI) method is better and nearest to the exact solution compared with the results of Alternating Direction Explicit (ADE) method. we also studied the numerical stability of both methods by Von-Neumann Method.

In this paper, the approximate solution of a reaction-diffusion system with fast reversible reaction is obtained by using Adomian decomposition method (ADM) and variational iteration method (VIM) which are two powerful methods that were recently developed. The VIM requires the evaluation of the Lagrange multiplier, whereas ADM requires the evaluation of the Adomian polynomials. The behavior of the approximate solutions and the effects of different values of t are shown graphically.

The detour distance between two distinct vertices and of a connected graph is the length of a longest path in. The detour index of is defined by, and the detour polynomial of is . The detour indices and detour polynomials of some ladder graphs are obtained in this paper.

In this paper, we study rings whose simple right R-module are GP-injective. We prove that ring whose simple right R-module is GP-injective it will be right -weakly regular ring. Also, proved that if R is N duo ring or R is NCI ring whose simple right R-module is GP-injective is S-weakly regular ring.

The aim of this paper to found that the stability and bifurcation of Chen System by using a new method which called - discriminate method as will as we found the stability at the second critical point by another method, and we showed that the new method depended on the roots to determent the stability and bifurcation of this system while the previous methods depended on the parameters , also we showed the method which used to find the stability at the second critical point depended on the critical value and parameter . Finally, we get the same previous results but easily method.

In this paper a new class of Quasi-Newton update for solving unconstrained nonlinear optimization problem is proposed. In this work we suggested a new formula for the variable metric update with a new quasi-Newton condition used for the symmetric rank two formula. Finally, a numerical study is reported in which the performance of this new algorithm is compared to that of various members of the unmodified family. Numerical experiments indicate that this new algorithm is effective and superior to the standard BFGS and DFP algorithms, with respect to the number of functions evaluations (NOF) and number of iterations (NOI).

The basis number b(G) ,of a graph G is defined to be the least positive integer k such that G has a k-fold basis for it’s cycle space. In this research paper,we have studied the basis number of some special graphs for Mycielski’s graph .It is proved that

In This paper we suggest one of the models for non-linear Autoregressive by using local linear approximation method, then we studied the conditions of stationarity of the model specifically the conditions of stationarity the non-zero singular point of the model. And the conditions for stationarity to limit cycle stationarity. Conditions are applied in the aforementioned theories on data represent the monthly average wind speed in model of Baghdad city. The samples are classified by using one of non-linear Autoregressive model the findings are the value of non-zero fixed point and the conditions of suggested stationarity model .

Let I be a right ideal of R, then R / I is a right N–flat if and only if for each a Î I, there exists b Î I and a positive integer n such that an ≠ 0 and an = ban. In this paper, we first give and develop various properties of right N-flat rings, by which, many of the known results are extended. Also, we study the relations between such rings and regular, p-biregular ring.

This paper investigates an interleaved algorithm which combines between the extended conjugate gradient with the hybrid method of Touati-Storey . This combined algorithm is based on the exact line search to solve a number of non-linear test functions with different dimensions. Experimental results indicate that the modified algorithm is more efficient than the original Sloboda algorithm.

In this paper, we deal with non-linear functional fractional differential equation with initial condition in space. We will study the existence, uniqueness and stability of the solution of fractional differential equation.

In this paper, we give an existence results for the fractional mixed Volterra -Fredholm integrodifferential equation with Integral Boundary Conditions. First, we use the Banach contraction principle to prove the existence and the uniqueness of the solution for the boundary value problem. Second, we study the existence of the solutions for the boundary value problem. using Krasnoselskii’s fixed point theorem.

The object of this paper obtains the existence, uniqueness and upper bounds for errors of six degree splines interpolating the lacunary data (0, 2, 4). We also show that the changes of the boundary conditions and the class of spline functions has a main role in minimizing the upper bounds for error in lacunary interpolation problem. For this reason, in the construction of our spline function which interpolates the lacunary data (0, 2, 4). We changed the boundary condition and the class of spline functions which are given by [4] from first derivative to third derivative and the class of spline function from to .

Independence of observations is one of the standard assumption in analysis of Variance (ANOVA) table. Where the error terms in the model are independent, identically distributed normal variables with null means and homogeneous variances. In this paper investigate the effect of dependence of observations in ANOVA for unbalanced 2-way nested fixed model and developing a method for adjusting it. When the error terms are correlated and focus on the effects of departures from independence assumptions on hypothesis testing by determining the expect mean squares for errors as well as treatments for this model and correcting the F statistics for testing the factor effect. The model considered is one in which all measurements have same variance, and the covariance matrix enjoy a structure defined as follows: every pair of measurements comes from: i) The same experimental observation and the same experimental unit; ii) Different experimental observation, but in the same experimental unit; ii) Different experimental unit; has covariance and respectively.

This paper has studied the numerical solution for Sine-Gordon system in one dimensions using finite difference methods. We have used Explicit method and Crank-Nicholson method.A comparison between results of the two methods has been done and we obtained that Crank-Nicholson method is more accurate than the Explicit method but the Explicit method is easer . We also studied the stability analysis for each method by using Fourier(Von-Neumann) method and obtained that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the condition and .

This paper deals with the existence and uniqueness of the solution for a boundary value problem of fractional order integro-differential equation, when using Banach fixed point theorem and Shafer’s fixed point theorem. This investigation based on the well known Riemann-Liouville fractional differential operator.

In this paper, a homomorphic framework is used for the enhancement and retrieval of speckled image. The log function at the starting of the structure is used to transform the speckled image (with multiplication noise) to a noisy image (with additive noise). This image is then applied to classical contourlet transform to decompose the noisy image into approximation and details. To retrieve the image without speckle noise, some suitable threshold level is chosen. In the reconstruction part, inverse contourlet transform is performed with an exponential function to compensate for the log one. The proposed technique is compared with other techniques. The result of comparison reflects the proposed technique superiority.

In this paper a new extended generalized conjugate gradient algorithm is proposed for unconstrained optimization, which is considered as anew inverse hyperbolic model .In order to improve the rate of convergence of the new technique, a new hybrid technique between the standard F/R CG-method and Sloboda CG-method using quadratic and non- quadratic models is proposed by using exact and inexact line searches. This method is more efficient and robust when applied on number of well-known nonlinear test function.

DNA Sequence Alignment is an important problem in computational biology and is useful for comparing genomes and finding genes, for determining evolutionary linkage of different biological sequences. Dynamic Programming Problems is discussed and applied to solve this problem. This paper is concerned with computing DNA Sequence Alignment firstly by formulating a Binary Integer Programming model to compute the string sequence in Edit Distance Problem then re-formulating this model to be suitable to compute this alignment. By this model we gave a good role for Operations Researches field to prove it's efficient to solve problems of molecule of life. The suggested model is applied to solve an example in Edit Distance Problem then used again after re-formulating it for an example in DNA Sequence Alignment Problem.

In this paper we have applied the Differential Transform Method (DTM) for solving eighth-order boundary value problems. The analytical and numerical results of the equations have been obtained in terms of convergent series with the easily computable components. Three examples are considered for the numerical illustrate and implementation of this method. Numerical Comparisons with respect to the analytical solutions have been considered . It is observed that the method is an alternative and efficient for finding the approximate solutions of the boundary values problems.

The aim of this paper is to find the stability of unified chaotic system through studying different systems. The unified chaotic system is divided into three systems by depending on the values of , when , the unified chaotic system becomes Lorenz system; when; it becomes L system, when ; the unified chaotic system becomes Chen system. Investigations the stability analysis of these systems leads to the stability of the unified chaotic system.

In this paper a new low-storage VM-algorithm for constrained optimization is investigated both theoretically and experimentally. The new algorithm is based on both the well-known Fletcher's low storage algorithm which generates columns Z spanned on the gradient vectors g 1, g 2, ... g n and the idea of both Buckley and LeNir of combined variable storage- conjugate gradient method. The well-known SUMT algorithm is adapted to implement the new idea. The new algorithm is very robust compared with the standard low-storage Fletcher algorithm and the standard SUMT algorithm which was designed for solving constrained problems, of the numerical results of application very promising . 1. Interior point method (Barrier function): In the interior penalty function method, the Barrier term is defined to keep the solution from leaving the feasible region. It is impossible to directly handle equality constraints in this method. Thus the original problem for this method is defined as follows

The n-Wiener polynomials of straight hexagonal chains and the Cartesian product of a complete graph Kr and a cycle Cr are obtained in this paper. The n-diameter and the n-Wiener index of each such graphs are also determined.

In this paper, We solved the system of differential-algebraic equation (DAEs) of index one numerically with Heun's method and operational matrices of Haar wavelet method, When we compared the results of the two methods with the exact solution, show that the operational matrices of Haar wavelet method is more efficiency and it's numerical results near to the exact solution more than the Heun's method, and the solution accuracy of this method is increasing and the error decreases when the number of mesh points and size of matrices increase.

In this paper we study idempotent elements, we give some new properties of idempotent elements and provide some exam we also study central idempotent elements and orthogonal idempotent elements and give some new properties of such idempotent. Finally we study special ring which satisfies the property 1 + = n n x x for all x in R and n is a positive integer, we represent such ring in termes of idempotent and nilpotent elements.

In this paper, we study rings whose principal right ideals are left pure. Also we shall introduce the concept of a fuzzy bi-ideal in a ring, and give some properties of such fuzzy ideals. We also give a characterization of whose principal right ideal are left pure, fuzzy duo ring in terms of fuzzy deals.

This paper involves the combination between the conjugate pair and hybrid conjugate gradient methods. The new combined algorithm is based on exact line search and it is examined by using different nonlinear test functions in various dimensions. Experimental results indicate that the updated algorithm is more effective than of the two original algorithms.