Abstract: A direct proof is given of the completeness of ultraproduct spaces when the factor spaces are Banach spaces The method of proof also shows the completeness of the ultraproduct even when the factor spaces are not complete for many (possibly all) ultrafilters It is also shown that ultraproduct spaces are separable only when they are finite dimensional

Abstract: The aim of this paper is to define some mathematical concepts which are useful to measure the speed of convergence of a sequence and to compare two converging sequences. In that way we define the order, the relative order and the α-equivalence of sequences. The asymptotic expansion of a series is studied and an application to Aitken acceleration process is given. A theorem similar to l'Hospital's rule is also proved for sequences.

Abstract: A positive integern is called a pseudoprime ifn|2 n −2 andn is composite. W. Sierpinski put forward the following problem: Do there infinitely many arithmetical progressions formed of four pseudoprimes? In this paper it is proved that answer to this problem is in the affirmative.

Abstract: In discussing Lagrange problems of optimal control for simple as well as for multiple integrals Cesari has introduced an upper semicontinuity property of variable sets called property (Q) which plays a role analogous to that of Tonelli's and McShane's concept, of seminormality for free problems of the calculus of variations. This paper deals with analytical criteria for property (Q) which is the unifying idea in the study of lower semicontinuity and lower closure with unbounded controls. In section 1 we state the concepts of seminormality, normality, and property (Q). In section 2 we establish new criteria for property (Q) in the particular situation whenf 0(t,x,u) is continuous and seminormal (or normal) andf(t,x,u) is linear in the variableu. In section 3 we consider the role of property (Q) for restricted sets. In section 4 we discuss the intermediate properties (Q p).

Abstract: Some types of extensions of skew fields are now known: Galois quadratic extensions ([7]), cyclic extensions ([1]), general quadratic extensions ([4]), binomial extensions ([5]). All these extensions belong to the class of pseudolinear extensions ([8]).

Abstract: This paper is devoted to the construction of direct limits in the categories of non finitary heterogeneous algebras. In Sec. 1, we give the definition of a category,H m whose objects are non finitary heterogeneous algebras, with respect to the sets of indicesI and Ω.

Abstract: We investigate transmission problems in a polygon, for general elliptic operators within Sobolev weight spaces. Existence theorems and stability theorems for nullity, deficiency, index have been proved.

Abstract: We prove that some caracterizations of differentiable real valued functions ([1], [2], [4]) are valid also if these functions take values in a reflexive real Banach space.

Abstract: In this paper we give some existence and uniqueness theorems for weak solutions of boundary value problems for a particular class of parabolic systems of linear partial differential equations of the second order with real coefficients. In particular some uniqueness theorems for equations with complex coefficients are deduced from the previous results.

Abstract: Ritz method is used to obtain an approximate solution of the stationary neutron transport Boltzmann equation in its integral form in plane and spherical symmetry. Such a method is based on the maximum property of the quadratic form corresponding to a symmetric transformation in a finite dimensional subspace spanned by the firstn functions of a complete orthonormal set.

Abstract: With Schauder's fixpoint principle we establish an existence theorem for solutions of two simultaneous nonlinear operator equations of the formL iu=Miu, i=1,2, Li linear,M i continous. By applying this result to boundary value problems with ordinary differential equations we generalize results of Conti and Ehrmann in various directions.

Abstract: We prove in this paper the existence of maximal spatial submanifolds with prescribed boundary conditions in a lorentzian manifoldV=R×U whereU is a complete riemannian manifold.

Abstract: Dans un article [11], M. K. Singal et A. R. Singal ont introduit le concept d'application presque fermee. Le but de ce travail est d'etudier quelques proprietes de cette application.

Abstract: In our preceding paper [2], we have studied the fundamental properties of the heterogeneous algebras, and constructed the projective limits in the category of these algebras and in the category of abstract automata. The present article is devoted to the study ofdirect limits in the same categories.

Abstract: Let Open image in new window be a De Possel differentiation basis in a complete measure space Open image in new window , with μ≥0, μ(X)<+∞; letB be a Banach space and Open image in new window .

Abstract: We discuss the relations between the convergence fields of the functional Norlund methods (N, p, q, π) and (N, πr+ρp+p*r,q, πρ) in the ordinary and absolute case,p, q, r being suitable Lebesgue integrable functions and π, ρ∈ϱ.

Abstract: We give some solution existence and uniqueness theorems for the Volterra type equations systems (1) and (6)

Abstract: The present paper points out that some recent results about differentiable manifolds follow by comparison between tensor fields depending on linear connections.

Abstract: Letx:M 2→E n be the immersion of a surfaceM 2 in ann-dimensional Euclidean space. Letj and μ be the canonical isomorphism defined by the metricg ofM 2 and by the canonical volume element ofM 2, respectively. IfM 2 carries a concircular tangent vector fieldX. then the following properties are proved: (i) The gaussian curvatureK ofM 2 is identically zero. (ii) X defines an infinitesimal homothety onM2. (iii) The vector field (j −1 o μ) (X) is a Killing vector field.

Abstract: LetG be a finitep-group in which every minimal subgroup is quasinormal inG. Then, ifp≥5, such property holds in .

Abstract: In this paper we establish some characterizations of functions which are derivable or approximately derivable almost everywhere with respect to another one supposed increasing.

Abstract: The problem stated in the paper is to find solutions of equation (1) in the strip 0≤y≤a, and satisfying conditions (2), (3), α1, α1, α2,z, δ andf being functions which satisfy suitable conditions. This problem is equivalent with that to find solutions of (4), (5). If δ=0, the problem is one of generalized periodicity. Theorem 1–3 give sufficient conditions for the existence of required solutions.

Abstract: The aim of the present article is to show that the minimax principle plays a fundamental part in defining a solution of a random program. By this principle, a random program is reduced to a convex program (linear or non-linear), under suitable conditions, and the solved by available techniques (if any).

Abstract: We determine the subgroups of the group of general similarity transformations of the planeR 2. This result then allows us to classify the measurable families (following the definition of M. I. Stoka [3]) of non degenerate equilater hyperbolas ofR 2. At the same time we give an example of a family of varieties not admitting any measure.

Abstract: At first Cauchy-problem for the equation:\(L[u(X,t)] \equiv \sum\limits_{i = 1}^n {\frac{{\partial ^2 u}}{{\partial x_1^2 }} + \frac{{2v}}{{\left| X \right|^2 }}} \sum\limits_{i = 1}^n {x_i \frac{{\partial u}}{{\partial x_i }} - \frac{{\partial u}}{{\partial t}} = 0} \) wheren≥1,v—an arbitrary constant,t>0,X=(x1, …, xn)∈En/{0}, |X|= =(x12+…+xn2)1/2, with 0 being a centre of coordinate system, is studied. Basing on the above, the solution of Cauchy-Nicolescu problem is given which consist in finding a solution of the equationLp [u (X, t)]=0, withp∈N subject the initial conditions\(\mathop {\lim }\limits_{t \to \infty } L^k [u(X,t)] = \varphi _k (X)\),k=0, 1,…,p−1 and ϕk(X) are given functions.

Abstract: In this paper some necessary and sufficient conditions are given for convergence of a series with non-negative terms. As a particular case, one finds again the well-known ratio-test for convergence of series with positive terms; in such a connection, some observations are made of didactical interest. Finally, some relations are emphasiged concerning theorems of convergence for real series (here obtained) and fixed point theorems already known.

Abstract: In this note we determine the sub-sets of the set of parabolas that have measures in respect of affine group in the projective plane.

Abstract: We introduce in a U. F. D.,A, and in its quotient fieldK two metricsd and $$\bar d$$ connected to the (p)-adic topology onA and its extension toK; we prove that: $$\bar d\left( {\frac{x}{y},\frac{{x'}}{{y'}}} \right) = \inf \left( {\frac{{d(xy',yx')}}{{2d(yy',0)}},1} \right)$$ .