Abstract: We obtain some results concerning the investigation of the solutions of three-point Cauchy-Nicoletti type boundary value problems for a certain class of linear functional differ- ential equations. We show that it is useful to reduce the given problem to the parametrized two-point boundary value problem for a suitably perturbed system containing some artificially introduced parameters both in the constructed inhomogeneous two-point boundary conditions and in the modified functional differential equations. To study the transformed parametrized two-point problem, we use a method which is based upon special type of successive approximations constructed in an analytic form. We prove the uniform convergence of these approximations to the parametrized limit function. Our technique leads to a certain system of algebraic equations with respect to the introduced parameters whose solutions provide those numerical values of the parameters that correspond to the solutions of the given three-point boundary value problem.

Abstract: We discuss successive approximation techniques for the investigation of solutions of some linear two-point boundary value problems for differential equations with special types of argument deviation. 2000 Mathematics Subject Classification: 34B15

Abstract: For an algebra A, the lattice QuordA of all quasiorders of A, i. e., of all reflexive and transitive relations compatible with all fundamental operations of A, is dealt with. In the present paper we prove that if A is a monounary algebra, then QuordA is distributive if and only if it is modular and we find necessary and sufficient conditions for A under which QuordA is distributive. 2000 Mathematics Subject Classification: 08A60, 08A02, 08B99

Abstract: Classifications of subdirectly irreducible involution rings via some properties of trace elements are given. As an application, von Neumann regular involution rings with central idempotent norm elements are described. The structure of certain involution rings in which the norms are multiplicatively generated by nilpotents is also determined. 2000 Mathematics Subject Classification: 16N60, 16W10

Abstract: In this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrodinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (gfq-positivity) for non cooperative systems.

Abstract: . We study the solutions of a special matrix equation, particularly, their eigenvalues. These matrix solutions have an interesting relationship to unitary matrices.

Abstract: In this paper, we study the existence of nontrivial symmetric solution for the secondorder three-point boundary value problem for a function f W Œ0;1 R! R which is continuous and f .t; / is symmetric on Œ0;1. We shall formulate conditions on f which guarantee the existence of nontrivial symmetric solution. As an application, we also give some examples to demonstrate our results. 2000 Mathematics Subject Classification: 34B10, 34B15

Abstract: Using a recent extension of Fréchet differentiability (approach of Taylor mappings, see [1]), the notion of Clarke subdifferential in binormed spaces, and the notion of closed pair of multifunctions, we present a convenient test for the weak metric regularity of a non-strictly Fréchet differentiable functions in terms of the surjectivity of its Taylor strict derivative. As an application, we give an example of a non-strictly Fréchet differentiable function for which the given test works. 2000 Mathematics Subject Classification: 49J52, 49L25, 49J40, 49J50

Abstract: Bachet elliptic curves are the curves y 2 = x 3 +a 3 and in this work thegroup structure E(F p ) of these curves over finite fields F p is considered. Itis shown that there are two possible structures E(F p ) ∼= C p+1 or E(F p ) ∼=C n ×C nm , for m,n∈ N,according to p≡ 5 (mod6) and p≡ 1 (mod6),respectively. A result of Washington is restated in a more specific waysaying that if E(F p ) ∼= Z n ×Z n ,then p≡ 7 (mod12) and p= n 2 ∓n+1. 1 Introduction 12 Let p be a prime. We shall consider the elliptic curvesE : y 2 ≡ x 3 +a 3 (modp) (1)where a is an element of F ∗p = F − {0}. Let us denote the group of the pointson E by E (F p ).If Fis a field, then an elliptic curve over Fhas, after a change of variables,a formy 2 = x 3 +Ax +Bwhere A and B ∈ Fwith 4A 3 +27B 2 6= 0 in F. Here D = −164A 3 +27B 2 iscalled the discriminant of the curve. Elliptic curves are studied over finite andinfinite fields. Here we take Fto be a finite prime field F p with characteristicp > 3. Then A,B ∈ F p and the set of points (x,y) ∈ F