Some Properties of Multiplication Modules

Let M be an R-module. The module M is called multiplication if for anysubmodule N of M we have N = IM, where I is an ideal of R. In this paperwe state some basic properties of multiplication modules

Some Properties of Entire Functions Associated with L-entire Functions on C(I)

In this paper, let C(I) denote the Banach algebra of all continuous complex-valued functions defined on a close interval I in the set of real numbers, R. The functions having derivatives in the Lorch sense on the whole Banach algebra C(I) are considered and they are called L-entire functions [1, 3]. For each L-entire function on C(I), entire complex functions are associated and the relationship between their orders is studied. Even more, the possibility of locating the solutions of the equation F(f) = 0 from the location of zeros of the associated family of entire functions with F is analyzed too

Some Properties of Green's Matrix of Nonlinear Boundary Value Problem of First Order Differential

This paper discusses Green's matrix of nonlinear boundary value problem of first-order differential system with rectangular coeffisients, especially about its properties. In this case, the differential equation of the form  with boundary conditions of the form   and  which  is a real  matrix with  whose entries are continuous on  and . ,  are nonsingular matrices such that  and  are constant vectors. To get the Green's matrix and the assosiated generalized Green's matrix, we change the boundary condition problem into an equivalent  differential equation by using the properties of the  Moore-Penrose generalized inverse, then  its solution is found by using method of variation of parameters. The last we prove  that the defined matrices  satisfy the properties of green's function. The result is the corresponding the Green's matrix and the assosiated generalized Green's matrix have the property of Green's functions with the jump-discontinuity

Some properties of evolution algebras

The paper is devoted to the study of finite dimensional complex evolu- tion algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criteria of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent n−dimensional complex evolution algebras the possible maximal nilpotency index is 1 + 2n−1 . The criteria of planarity for finite graphs is formulated by means of evolution algebras defined by graphs.Junta de Andalucía FQM-14

Some properties of WKB series

We investigate some properties of the WKB series for arbitrary analytic potentials and then specifically for potentials $x^N$ ($N$ even), where more explicit formulae for the WKB terms are derived. Our main new results are: (i) We find the explicit functional form for the general WKB terms $\sigma_k'$, where one has only to solve a general recursion relation for the rational coefficients. (ii) We give a systematic algorithm for a dramatic simplification of the integrated WKB terms $\oint \sigma_k'dx$ that enter the energy eigenvalue equation. (iii) We derive almost explicit formulae for the WKB terms for the energy eigenvalues of the homogeneous power law potentials $V(x) = x^N$, where $N$ is even. In particular, we obtain effective algorithms to compute and reduce the terms of these series.Comment: 18 pages, submitted to Journal of Physics A: Mathematical and Genera