Broyden update is one of the one-rank updates which solves the unconstrained optimization problem but this update does not guarantee the positive definite and the symmetric property of Hessian matrix.

In this paper the guarantee of positive definite and symmetric property for the Hessian matrix will be established by updating the vector  which represents the difference between the next gradient and the current gradient of the objective function assumed to be twice continuous and differentiable .Numerical results are reported to compare the proposed method with the Broyden method under standard problems.

In this paper, new concepts which are called: left derivations and generalized left derivations in nearrings have been defined. Furthermore, the commutativity of the 3-prime near-ring which involves some
algebraic identities on generalized left derivation has been studied.

    The main aim of this research is to present and to study several basic characteristics of the idea of FI-extending semimodules. The semimodule  is said to be an FI-extending semimodule if each fully invariant subsemimodule of  is essential in direct summand of . The behavior of the FI-extending semimodule with respect to direct summands as well as the direct sum is considered. In addition, the relationship between the singularity and FI-extending semimodule has been studied and investigated. Finally  extending propertywhich is stronger than FI extending,  that  has some results related to FI-extending and singularity is also investigated.

Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where      0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta

            In this paper, the Normality set  will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of  .

In this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given.  For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.

 The present work focuses on the changing of the structural characteristics of the grown materials through different material characterization methods. Semiconductor CdS_xSe _1-x nano crystallines have been synthesized by chemical vapor depostion. (X- ray Diffraction; XRD), (Field Emission Scanning Electron Microscopy; FESEM), measured the characterization of Semiconductor CdS_xSe_1-x nano crystallines. The optical properties of semiconductor CdS_xSe_1-x nanocrystallines have been studied by the photoluminescence (PL) (He-Cd pulsed ultraviolet laser at 325nm excitation wavelength) at room temperature. The results showed the change rule of photoluminsence peak at different S

Semi-parametric models analysis is one of the most interesting subjects in recent studies due to give an efficient model estimation. The problem when the response variable has one of two values either 0 ( no response) or one – with response which is called the logistic regression model.

We compare two methods Bayesian and . Then the results were compared using MSe criteria.

A simulation had been used to study the empirical behavior for the Logistic model , with  different sample sizes and variances. The results using represent that the Bayesian method is better than the   at small samples sizes.

         Continuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous functions in topology. The present authors continued the study on continuous functions by utilizing the concept of gpα-closed sets in topology and introduced the concepts of weakly, subweakly and almost continuous functions. Further, the properties of these functions are established.

 The transfer function model the basic concepts in the time series. This model is used in the case of multivariate time series. As for the design of this model, it depends on the available data in the time series and other information in the series so when the representation of the transfer function model depends on the representation of the data In this research, the transfer function has been estimated using the style nonparametric represented in two method  local linear regression and cubic smoothing spline method The method of semi-parametric represented use semiparametric single index model, With four proposals, , That the goal of this research is comparing the capabilities of the above mentioned m