Search

The main purpose of the article is to identify key ways for the development of electronic commerce within the framework of compliance with the norms and rules of financial law in Jordan. The object of the study is the e-commerce system and its activities in the legal field of Jordan. The scientific task is to determine the strategy for the development of e-commerce within the legal framework of Jordan, taking into account the specifics of the region. The research methodology involves the use of the hierarchy analysis method in constructing a hierarchical model, determining the sums of the elements of the columns of square inversely symmetric matrices, and checking the consistency of the results. As a result, we have determined the optimal strategy for the development of e-commerce within the framework of compliance with the norms and rules of financial law. The scientific novelty of the article lies in the proposed methodological approach to determining the strategy for the development of e-commerce in Jordan within the framework of compliance with the norms and rules of financial law. The study is limited by taking into account the specifics of e-commerce and Jordanian financial law. Prospects for further research should be devoted to the specifics of the development of ecommerce in the framework of compliance with the norms and rules of financial law in other countries of the world in order to attract international experience. [ABSTRACT FROM AUTHOR]

For each integer n ≥ 3 we define a specific symmetric integer matrix of size φ (n) / 2 . We then explicitly describe all positive and negative integer powers, as well as fractional powers, of each of these matrices; their eigenvalues also appear and play an important role. All this is based on an orthogonality relation for odd Dirichlet characters which, in turn, leads to a diagonalization. In the course of this article, various other number-theoretic objects make their appearance, including the Euler and Jordan totient functions, Möbius inversion, and the divisor function. [ABSTRACT FROM AUTHOR]

For a class of second-order cone nonlinear complementarity problems, abbreviated as SOCNCPs, we establish the modulus-based matrix splitting relaxation iteration methods, which are obtained by reformulating equivalently SOCNCP as an implicit fixed-point equation based on Jordan algebra associated with the second-order cone. The global convergence theorems are given under suitable choices of the involved splitting matrix and parameter matrices. When the splitting matrix is symmetric positive definite, the strategy choice of the parameters is discussed. Numerical experiments have shown that the modulus-based iteration methods are effective for solving SOCNCPs. [ABSTRACT FROM AUTHOR]

In the present paper, the notion of (additive) local multiplier on the ring of matrices over an arbitrary unital associative ring is introduced and investigated. It is proved that every local left multiplier on the matrix ring over a division ring is a left multiplier. Also, in the present paper, the notion of (additive) local Jordan multiplier on a Jordan ring of symmetric matrices is introduced and investigated. It is proved that every local Jordan multiplier on the Jordan ring of symmetric matrices over the field of rational numbers is a Jordan multiplier. Also corollaries of these results are proved. [ABSTRACT FROM AUTHOR]