Nous savons que dans le champ gravitationnel de la relativité (i.e. défini par les équations Rμv = 0) les ondes dites gravitationnelles se propagent avec la vitesse de la lumière. Nous allons maintenant voir, dans le présent travail que si, dans le même continuum, on impose aux potentiels gμv, une oscillation de fréquence assez élevée, il en résulte une onde du type maxwellien.

The problem of the field equations and the equations of motion in general relativity theory is now sufficiently clarified. The equations of motion can be deduced from pure field equations by treating matter as singularities, [2; 3], or from field equations with the energy momentum tensor [4]. Recently two papers appeared in which the problem of the coordinate system was considered [5; 8]. The two papers are in general agreement as far as the role of the coordinate system is concerned. Yet there are some differences which require clarification.

The efforts of most theoretical physicists of this century have been directed towards that branch of the physical science which is commonly called “Quantum Theory.” Physically, Quantum Theory was postulated because of a vast amount of physical evidence which led to the postulates of states, observables, superposition, and commutation relations. From these four postulates, all quantum mechanics follows.

In this note the problem of determining the propagation of a plane shock moving through a polytropic gas into an undisturbed body of the gas, leaving a non-isentropic disturbance behind it, is reduced to the solution of the problem of Cauchy for a Monge-Ampére partial differential equation of special type. The application of this result to specific examples is being studied with a view to later publication.

The five Platonic solids can be drawn in elliptic or hyperbolic space just as well as in Euclidean space. Their numerical properties are, of course, the same in all three. So are the various angles subtended at the centre. But the face-angles and dihedral angles are greater in elliptic space, smaller in hyperbolic. It is a special feature of the non-Euclidean spaces that we cannot change the size of a solid without changing its shape.

In this paper I establish the following bounding formula for the integral of a function of n variables:

(1.1)

We shall present in this paper a certain theorem concerning complex manifolds provided with an Hermitian metric satisfying the Kaehler restriction. The variables z1, z2, …, zn denote local complex coordinates in the manifold and their conjugates. The subscripts a, b, c, … run from 1 to n and by .

The subject of this paper is the study of boundary value theorems for harmonic p-tensors on a Riemannian space with an indefinite metric of the normal hyperbolic signature.

The purpose of this paper is to characterize all ways in which an initial interval of natural numbers can be partitioned into a unique arithmetic sum of certain of its subsets.

Let

be a sequence of real terms with which we associate the generating power series

We consider the following definition due to Schoenberg [7, p. 362]:

Let S be a completely regular topological space. Let C(S) denote the set of bounded, real-valued, continuous functions on 5. It is well known that C(S) forms a distributive lattice under the ordinary pointwise joins and meets. For any distributive lattice L and any ideal I⊆L, a quasi-ordering of L can be defined as follows : f⊇g if, for all h ∈ L, f ∩ h ∈ I implies g ∩ h ∈ I. If equivalent elements under this quasi-ordering are identified, a homomorphic image of L is obtained.

In this note the authors find all continuous real functions defined on the real axis and such that for an integer n > 2, and for each x,

Krall and Frink [4] aroused interest in what they term Bessel polynomials. They studied in some detail what may, in hypergeometric form, be written as

Let the function of two real variablesf(x, y) be given over the square

Following Wiener's fundamental work on the Operational Calculus [9, pp. 557-584], Widder suggested [5, p. 219] that the inversion operator for the convolution transform

The distribution of heat in an infinite rod is closely bound up with the theory of the Weierstrass transform. This connection is exhibited most clearly in the theory of Widder [3]. Consider the heat equation

Soit K un espace compact, C(K) l'espace des fonctions complexes continues sur K, muni de la norme uniforme, son dual (espace des mesures de Radon sur K). Cet article est consacré essentiellement à l'étude des applications linéaires faiblement compactes de C(K) dans des espaces localement convexes F quelconques i.e. les applications linéaires qui transforment la boule unité de C(K) en une partie faiblement relativement compacte de F.

This note concerns itself primarily with the representation of continuous multiplicative functionals on L2 types of rings or Banach algebras to the real or complex fields where convolution is taken as the ring multiplication. In a recent publication [1] such functionals were studied for the continuous function ring C(S) over a compact space S.

If f(z) is an integral function of non-integral order with only real negative zeros, there is a close connection between the rates of growth of the function and of n (r), the number of zeros of absolute value not exceeding r. The best known theorem is that of Valiron [12], which may be stated as follows.

In recent years Boolean Algebra has come to play a prominent role in the analysis and synthesis of switching circuits [1; 4]. One general synthesis problem in which this algebra has proved useful is the following. Let there be given n input leads each of which can assume one of two possible states. It is desired to construct a network with these n input leads and a single output lead also capable of assuming either of two states. Furthermore, the state of the output lead for each of the 2n states of the input leads is prescribed.