Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

The study presents the modification of the Broyden-Flecher-Goldfarb-Shanno (BFGS) update (H-Version) based on the determinant property of inverse of Hessian matrix (second derivative of the objective function), via updating of the vector s ( the difference between the next solution and the current solution), such that the determinant of the next inverse of Hessian matrix is equal to the determinant of the current inverse of Hessian matrix at every iteration. Moreover, the sequence of inverse of Hessian matrix generated by the method would never  approach a near-singular matrix, such that the program would never break before the minimum value of the objective function is obtained. Moreover, the new modification of BFGS update (H-vers

     The focus of this article is to add a new class of rank one of  modified Quasi-Newton techniques to solve the problem of unconstrained optimization by updating the inverse Hessian matrix with an update of rank 1, where a diagonal matrix is the first component of the next inverse Hessian approximation, The inverse Hessian matrix is  generated by the method proposed which is symmetric and it satisfies the condition of modified quasi-Newton, so the global convergence is retained. In addition, it is positive definite that  guarantees the existence of the minimizer at every iteration of the objective function. We use  the program MATLAB to solve an algorithm function to introduce the feasibility of

In this paper, we proposed a modified Hestenes-Stiefel (HS) conjugate
gradient method. This achieves a high order accuracy in approximating the second
order curvature information of the objective function by utilizing the modified
secant condition which is proposed by Babaie-Kafaki [1], also we derive a nonquadratic
conjugate gradient model. The important property of the suggestion
method that is satisfy the descent property and global convergence independent of
the accuracy of the line search. In addition, we prove the global convergence under
some suitable conditions, and we reported the numerical results under these
conditions.

The Turks used the Ottoman Turkish language from the thirteenth century to the twentieth century.  During this period and under the influence of Islamic civilization, a large number of words and structures were used from the Arabic and Persian languages, Therefore, many Arabic grammatical structures were used in the Ottoman Turkish language, such as the definite article simply because it was widely used.

The paper is concerned with the use of the Arabic definite article in the Ottoman Turkish language, and the aim of this contrastive study is to find out the similarities and differences between the two languages ​​in terms of meaning and structure. Since linguistic studies depend on the practical side or applied approach, two

Endothelin-I (ET-I) is one of the potent vasoconstrictors secreted from endothelial cells when needed. Many studies revealed the elevation of serum ET-I with human diabetes and microangiopathies. Since insulin resistance is a case of mixed diabetic and pre-diabetic cases, many risk factors beyond obesity and inflammation are proposed. The current study aims to demonstrate the association between serum ET-I and asymmetric dimethylarginine (ADMA) and insulin resistance in type 2 diabetes mellitus (T2DM). Sera of 73 subjects were enrolled currently (control= 35 subjects, and 38 with T2DM for more than 7 years), aged (40-60) years old, with distinct body mass index (BMI) ≤ 25 for control volunteers and (BMI) ≥ 25 for obesity and diabetes

In this paper, we present a concept of nC- symmetric operator as  follows: Let A be a bounded linear operator on separable complex Hilbert space , the operator A is said to be nC-symmetric if there exists a positive number n (n  such that CAⁿ = A*^ⁿ C (Aⁿ = C A*^ⁿ C). We provide an example and study the basic properties of this class of operators. Finally, we attempt to describe the relation between nC-symmetric operator and some other operators such as Fredholm and self-adjoint operators.

Due to the intensity of competition between economic units that run the trade in durable goods had to pay a lot of these companies to follow the new selling methods aimed at attracting customers to be able to increase its sales and thereby increase their profits ,  these methods are installment sales, which had been in great demand by the customers with limited income, who provides them with the possibility of possession and use of such goods and to postpone the full amount of the payment to the seller, This transaction sales have grown even became installment sales system at the present time of the common types of sales transactions and deployed a lot in our environment and in many sectors of the market, and in some cases m

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.