Une classe d'algèbres de Fréchet à caractères continus

We prove in a simpler and direct manner using the spectral theory that every Fréchet algebra which is rationnally generated by a real or orthogonal subset is functionally continuous. These results include as a special case the results of R. Arens, H. Goldmann, E. A. Michael and W. Zelazko.

     

A non-commutative version of the first alexandroff decomposition theorem in ordered topological groups

In this paper we establish a decomposition theorem for a positive regular measure on an orthoalgebra with values in an ordered topological group not necessarily commutative. We deduce from it the A. D. Alexandroff’s classical first decomposition theorem and we discuss its uniqueness in the setting of metric spaces. This research is partially supported by the project Analisi Reale of Ministero dell’Università e della Ricerca Scientifica e Tecnologica (Italy) and by Gruppo Nazionale per l’Analisi Funzionale e Applicazioni (Italy).     

Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities

In this paper we obtain an extension of discrete Hilbert’s inequality, by using some numerical methods. We shall obtain, in a similar way as Yang did in [10], that the parameter from the kernel can be taken from the interval [3/2, 3). We also compare our findings with existing results, known from the literature.     

Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation

Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation are given. Applications for the trapezoid and mid-point inequalities are also provided. Received: 19 May 2008     

A generalization of an inequality by N. V. Krylov

In Krylov (Journal of the Juliusz Schauder Center 4 (1994), 355–364), a parabolic Littlewood–Paley inequality and its application to an L ^p -estimate of the gradient of the heat kernel are proved. These estimates are crucial tools in the development of a theory of parabolic stochastic partial differential equations (Krylov, Mathematical Surveys and Monographs vol. 64 (1999), 185–242). We generalize these inequalities so that they can be applied to stochastic integrodifferential equations.      

On some general Hilbert’s inequalities with non-conjugate parameters

A generalized discrete Hilbert’s and Hardy-Hilbert’s inequality with non-conjugate parameters can be established by means of Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our results with some previously known from the literature. We also obtain the improvements on some earlier results.     

On translation planes of orderq 3 that admit a collineation group of orderq 3, II

Let II be a translation plane of orderq ³ with kernel GF(q) that admits a collineation groupG of orderq ³ in the linear translation complement such thatG fixes a point at infinity and acts transitively on the remaining points at infinity.In this paper, we show that any such translation plane II is one of the following types of planes:     

On the reducibility of the postulation Hilbert scheme

We give a condition in terms of the possible graded Betti numbers compatible with a given Hilbert functionH of 0-dimensional subschemes of ℙ ⁿ which implies the reducibility of the postulation Hilbert scheme and of its subscheme which parametrizes reduced subschemes with Hilbert functionH.     

Limit theorems for random walks with dynamical random transitions

Let be an ergodic and conservative non-singular transformation of (, ,m) (thedynamic environment), let _w be a random probability on a locally compact second countable groupG, and define

On Lipschitz property of solutions of functional equations

In this work it is proved that under certain conditions the continuous vector-valued solutionsf of the functional equation

Automorphisms fixing elements of prime order in finite groups

Let σ be an automorphism of a finite group G and suppose that σ fixes every element of G that has prime order or order 4. The main result of this paper shows that the structure of the subgroup H=[G, σ] is severely limited in terms of the order n of σ. In particular, H has exponent dividing n and it is nilpotent of class bounded in terms of n.     

On the derivability of Lipschitz functions

We show that given any Borel measure onR, every Lipschitz function is μ-a.e. differentiable with respect to μ.     

The Gibbs phenomenon for bestL 1-trigonometric polynomial approximation

The classical Gibbs phenomenon for the Fourier sections (bestL ₂-trigonometric polynomial approximants) of a jump function asserts that, near the jump, these sections overshoot the function by an asymptotically constant factorg (theL ₂-Gibbs constant). In this paper we show that, for a class of one-jump discontinuous functions, a similar phenomenon holds for the trigonometric polynomials of bestL ₁-approximation. We determine theL ₁-Gibbs constant , which is substantially smaller thang. Furthermore, we prove that uniform convergence of bestL ₁-approximants takes place on intervals that avoid the jump. In the analysis we obtain some strong uniqueness theorems for bestL ₁-approximants.Communicated by Vladimir N. Temlyakov.     

A description of the segment [1,T], where T is the meeting number of a set-lattice

To 80^th birthday of Paul Erds     

Existence theorems for nonlinear functional differential equations of neutral type

Conditions are found upon satisfaction of which the differential equation

On two-point boundary value problems for systems of higher-order ordinary differential equations with singularities

The sufficient conditions of solvability and unique solvability of the two-point boundary value problems of Vallèe-Poussin and Cauchy-Niccoletti have been found for a system of ordinary differential equations of the form

An oscillation criterion for functional differential equations with deviating arguments

An oscillation criterion is given for the differential equation

Density theorems for bipartite graphs and related Ramsey-type results

In this paper, we present several density-type theorems which show how to find a copy of a sparse bipartite graph in a graph of positive density. Our results imply several new bounds for classical problems in graph Ramsey theory and improve and generalize earlier results of various researchers. The proofs combine probabilistic arguments with some combinatorial ideas. In addition, these techniques can be used to study properties of graphs with a forbidden induced subgraph, edge intersection patterns in topological graphs, and to obtain several other Ramsey-type statements. Research supported by an NSF Graduate Research Fellowship and a Princeton Centennial Fellowship. Research supported in part by NSF CAREER award DMS-0812005 and by USA-Israeli BSF grant.     

Structures and uniqueness conditions of MK-weighted pseudoinverses

For given matricesM, A andK of appropriate sizes, we study the following two kinds of MK-weighted pseudoinverses ofA. The first kind of weighted pseudoinverseX is characterized by the following four Moore-Penrose like conditions:

An extension of the Erdős-Stone theorem

LetK _p(u₁, ..., u_p) be the completep-partite graph whoseith vertex class hasu _i vertices (lip). We show that the theorem of Erds and Stone can be extended as follows. There is an absolute constant >0 such that, for allr1, 0<1 and=">1/r, every graphG=G ⁿ of sufficiently large order |G|=n with at least