Caspian Journal of Mathematical Sciences
Volume:2 Issue: 1, Winter Spring 2013

Let M be a right R-module. We call M Rad-H-supplemented if for each Y ≤ M there exists a direct summand D of M such that (Y +D)/D ⊆ (Rad(M)+D)/D and (Y +D)/Y ⊆ (Rad(M)+Y )/Y . It is shown that: (1) Let M = M1 ⊕ M2, where M1 is a fully invariant submodule of M. If M is Rad-H-supplemented, then M1 and M2 are Rad-Hsupplemented. (2) Let M = M1 ⊕M2 be a duo module and Rad-⊕- supplemented. If M1 is radical M2-sejective (or M2 is radical M1- sejective), then M is Rad-H-supplemented. (3) Let M = ⊕ n i=1Mi be a finite direct sum of modules. If Mi is generalized radical Mj - projective for all j > i and each Mi is Rad-H-supplemented, then M is Rad-H-supplemented.

In this work, by employing the Leggett-Williams fixed point theorem, we study the existence of at least three positive solutions of boundary value problems for system of third-order ordinary differential equations with (p1, p2, . . . , pn)-Laplacian  (φpi (u 00 i (t)))0 + ai(t)fi(t, u1(t), u2(t), . . . , un(t)) = 0 0 ≤ t ≤ 1, αiui(0) − βiu 0 i(0) = µi1ui(ξi), γiui(1) + δiu 0 i(1) = µi2ui(ηi), u00 i (0) = 0, where φpi (s) = |s| pi−2 s,, are pi-Laplacian operators, pi > 1, 0 < ξi < 1, 0 < ηi < 1 and µi1, µi2 > 0 for i = 1, 2, . . . , n.

In this paper, we study inextensible flows of curves in three dimensional Lie groups with a bi-invariant metric. The necessary and sufficient conditions for inextensible curve flow are expressed as a partial differential equation involving the curvatures. Also, we give some results for special cases of Lie groups.

In this paper we give a characterization for all commutative rings with 1 whose zero-divisor graphs are C4-free.

The aim of this paper is to introduce and study setvalued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers.

In this paper, using a fixed point method, we prove the generalized Hyers-Ulam stability of random homomorphisms in random C ∗ -algebras and random Lie C ∗ -algebras and of derivations on Non-Archimedean random C∗ -algebras and Non-Archimedean random Lie C∗ -algebras for the following m-variable additive functional equation: Xm i=1 f(xi) = 1 2m   Xm i=1 f  mxi + Xm j=1 ,i6=j xj   + f Xm i=1 xi !  .

In this paper, sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation are provided. By applying Kranoselskii‘s fixed–point theorem in a cone, the existence of solutions of an auxiliary BVP formulated by truncating the response function is first proved. Then the Arzela–Ascoli theorem is used to take C 1 limits off sequences of such solutions

In this paper, an efficient algorithm for solving a system of linear equations based on the homotopy analysis method is presented. The proposed method is compared with the classical Jacobi iterative method, and the convergence analysis is discussed. Finally, two numerical examples are presented to show the effectiveness of the proposed method.