Δελτίο της Ελληνικής Μαθηματικής Εταιρίας: Τεύχος 47
In this paper we use a method of O.Kolberg to prove the following congruences for moduli 5 and 7 for the convolution of divisor sum function
In this paper we will extend in infinite dimensions some results of Ekeland ? Temam, Ioff? and Olech concerning the study of lower semicontinuity of an integral functional I_f associated to a normal integral f. We give also a lower closure theorem for epigraphs and we establish the equivalence between a growth condition of Olech and the lower compactness property given by Ioff?.
Stokes flow characterizes the steady and non ? axisymmetric flow of an incompressible, viscous fluid at low Reynolds number and is described by a pair of partial differential equations connecting the velocity with the pressure field. Spherical geometry provides the most widely used framework for representing small particles embedded within a fluid that flows according to Stokes law and thus, the flow is assumed to be axisymmetric. The two different complete representations of the flow fields are considered here. The first one, named Stokes representation, is obtained, expressing the equation of motion in spherical coordinates, according to which stream function is given in full series expansion in terms of separable eigenmodes. The second ine, also valid in non ? axisymmetric geometries, is the Papkovich ? Neuber differential representation, where the flow fields are provided in terms of harmonic spherical eigefunctions. In the interest of producing ready-to-use basic functions for axisymmetric Stokes flow in spherical coordinates by showing the different approach of solving such problems, we calculate the Stokes (2-D) and Papkovich ? Neuber (3-D) eigensolutions, demonstrating the full series expansion. In the present work, connection formulae are obtained which relate the spherical harmonic eigenfunctions of the Papkovich ? Neuber representation, considering rotational symmetry, with the separable spherical stream eigenfunctions, excluding singularities. In that way, we transform any solution of the Stokes symmetric system from one representation to the other taking advantages of each one, as the case may be.
It is well known and not difficult to prove that the vector spaces Fμν, Mμxν(F), L(Fμ,Fν), L(V,W), Mνxμ(F), Fνμ are all F ? isomorphic, where L(V,W) is the space of all linear maps of the F ? space V into the F ? space W with finite dimV=μ, dimW=ν and F any-field. Here we establish the isomorphisms (F(Λ))K?F(Λ)K?MK?(Λ)(F) ?L(V,W) ?L(F(K),F(Λ)) ? M(K)?Λ(F) ? F(K)Λ? (F(Κ))Λ so that VΛ?WK. Where dimV=|K|, dimW=|Λ|, and K, Λ?? arbitrary sets of indices.
A nonlinear singularly perturbed boundary - value problem is considered in the critical case of conditional stability. An asymptotic solution is constructed under certain assumptions and utilizing boundary functions and pseudoinverse of matrices and projectors.
This work provides an analytic approximation of the electric potential and the magnetic field generated by a dipole source which is located within a spherical volume conductor, in the case where the time ? dependent ? variations of both fields are considered to be negligible. The first terms of their multipole expansion are provided in Cartesian coordinates via formulae between the spheroidal and the Cartesian coordinate systems. This work is an attempt to brake he complete isotropy of the spherical system by inserting 2-D anisotropy through the spheroidal geometry. This will generalize existing results in an attempt to reveal the physical and geometrical structures as well as to facilitate computational techniques. Both the potential field and the magnetic field, in the exterior of a bounded volume conductor, are experimentally measurable and provide useful data towards an understanding and interpreting of electroencephalographic and magnetoencephalographic data.
In this work we treat an exterior boundary value problem in two ? dimensional linear elasticity. First, we consider the case of a single elastic inclusion and take the integral through the layer-theoretic approach. In the sequence we examine the case of two disjoint cavities and via the layer - theoretic approach we reformulate the problem in integral form. In order to face the non-uniqueness arising at the irregular frequencies we adopt the modified Green?s function technique. So, we introduce two terms in the modification of the free ? space Green?s function and we establish the conditions that the coefficients of the modifications must satisfy in order to overcome the failure of uniqueness. The case of the single inclusion can be recovered as degenerate case of the two inclusions.
In this paper we introduce a new class of mapping called fuzzy strongly α ? continuous functions. We obtain several characterizations and some of their properties. Also, we investigate relationships with other type of functions.
It is generally accepted that probability generating functions are a very strong analytic tool for establishing properties of discrete probability distributions. Moreover, transformations of probability generating functions are operations which provide valuable information concerning the structure of these functions. This paper investigates a transformation for probability generating functions of discrete infinitely divisible distributions with nonnegative support and finite mean. Finally, the paper makes use of this transformation in order to establish a characterization of the Poisson distribution.