A 2p times continuously differentiable complex-valued mapping \(F=u+i v\) in a domain \( \mathcal D \subset \mathbb C\) is polyharmonic if \(F\) satisfies the polyharmonic equation \(\underbrace{\Delta\cdot\cdot\cdot\Delta}_\text{p} F= 0\), where \(p \in \mathbb N^{+}\) and \(\Delta\) represents the complex Laplacian operator. The main aim of this paper is to introduce a subclasses of polyharmonic mappings. Coefficient conditions, distortion bounds, extreme points, of the subclasses are obtained.

Molodtsov [D. Molodtsov, Global optimization, control, and games, III, Comput. Math. Appl., \({\bf 37}\) (1999), 19--31] studied the concept of soft sets. The concept of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we give some basic relations about different classes of soft sets and soft closure operator. The purpose of this paper is to introduce soft extremally disconnected spaces via soft sets. Furthermore, some relations of soft sets and soft closure via soft extremally disconnected spaces have been investigated.

In this paper, we introduce and investigate a new class of generalized convex functions, called generalized log-convex function. We establish some new Hermite-Hadamard integral inequalities via generalized log-convex functions. Our results represent refinement and improvement of the previously known results. Several special cases are also discussed. The concepts and techniques of this paper may stimulate further research in this field.

This article considers an inverse eigenvalue problem for centrosymmetric matrices under a central principal submatrix constraint and the corresponding optimal approximation problem. We first discuss the specified structure of centrosymmetric matrices and their central principal submatrices. Then we give some necessary and sufficient conditions for the solvability of the inverse eigenvalue problem, and we derive an expression for its general solution. Finally, we obtain an expression for the solution to the corresponding optimal approximation problem.

With the development of large-scale data, the increasingly users need to store the data in the distributed storage system due to the fact that the signal computer can not hold the massive data. However, the users can not control the data access rules. So the transparent security management of Large-scale data in distributed networks is a challenge. To solve this issue, a distributed security storage model is proposed. This security storage model can deal with the high concurrency and the complexity of large-scale data management in the distributed environment. The detailed designed of the transparent security storage system is provided based on the security storage model. This system allows the users manage their data and provides confidentiality protection, integrity protection, and access permission control. Experiments exhibit that the distributed storage model can improve the data security with I/O performance loss less than 5%.

In this paper, we investigate regularization method via a proximal point algorithm for solving treating sum of two accretive operators and fixed point problems. Strong convergence theorems are established in the framework of Banach spaces. Also we apply our result to variational inequalities and equilibrium problems. Furthermore, an illustrative numerical example is presented.

Block methods for the numerical solution of ordinary differential equations (ODEs) are quite prominent in recent literature and second order initial value problems (IVPs) which falls in the family of ODEs is also a well explored area for the application of block methods. The introduction of hybrid block method methods for the solution of second order IVPs has gained good grounds in literature as the presence of off-grid points in the block method has increased the accuracy of the hybrid block methods. However, recent studies still continue to introduce new block methods that will perform more favourably than previously existing when compared in terms of error. Hence, a hybrid block method of order six is presented in this article to compete with previously existing methods of the same order and higher order. The methodology adopted in this article presents a new approach for developing the hybrid block method which is simple to implement and less computationally tiresome. The numerical results show this new \(4\)-step \(5\)-point hybrid block method performing better than previously existing methods.

A quadratic stochastic operator (QSO) describes the time evolution of different species in biology. The main problem with regard to a nonlinear operator is to study its behavior. This subject has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. In this paper we introduce a new subclass of \(\xi^{(as)}\)-QSO defined on 2D simplex. first we classify this subclass into 18 non-conjugate classes. Furthermore, we investigate the behavior of one class.