In this paper we consider nonlinear hemivariational inequalities involving the p-Laplacian at resonance. We prove the existence of a nontrivial solution. Our approach is variational based on the critical point theory for nonsmooth, locally Lipschitz functionals due to Chang.

We construct and describe two classes of examples of twisted bicrossed product Hopf algebras corresponding to matched pairs of finite groups.

This paper is concerned with finding periodic solutions of differential delay systems

and

where ri (i = 1, 2,…, n − 1) are positive constants. By using the theory of Hamiltonian systems, we obtain some sufficient conditions under which these systems have many periodic solutions with known periods.

To each pseudovariety of Abelian groups residually containing the integers, there is naturally associated a profinite topology on any finite rank free Abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can effectively compute membership in the closure of a subgroup and, more generally, in the closure of a rational subset of such a free Abelian group. Several applications to monoid kernels and finite monoid theory are discussed.

Consider the error term in the asymptotic formula

In this note we obtain δ(k) ≍ 1/(k6 log2k) which, for large values of k, presents a substantial improvement over the previously known result .

Let p be a prime number, K be a finite non-ramified extension of ℚp and E be an elliptic curve defined over K. Let K(Ep) be the field of the p-division points of E. In this paper we determine the valuation of the different of the extension K(Ep)/K.

The objectives of this study of slice convergence are two-fold. The first is to derive results regarding the passage of certain semi–convergences through Young–Fenchel conjugation. These semi–convergences arise from the splitting of the usual slice topology in the primal and dual spaces into (non-Hausdorff) topologies: the upper slice topology ; a topology generating a convergence closely resembling the bounded–weak* upper Kuratowski convergence; along with the respective primal and dual lower Kuratowski topologies. This gives rise to topological convergences not reliant on sequentially–based definitions found in many such studies, and associated topological continuity results for conjugation (in normed spaces), in contrast to the usual sequential continuity exhibited by analogues of Mosco convergence. The second objective is to study the passage of slice convergence through addition. Such sum theorems have been derived in other works and we establish previous theorems from a unified framework as well as obtaining a new result.

We give explicit constructions of semigroups and operators with particular properties. First we build a bounded C0-semigroup which is invertible and which is not similar to a semigroup of contractions. Afterwards we exhibit operators which admit bounded imaginary powers of angle ω > 0 on a Hilbert space but which do not admit a bounded functional calculus on the sector of angle ω. (This gives the limit of McIntosh's fundamental result.) Finally we build, in the 2-dimensional Hilbert space, an operator which is not the negative generator of a semigroup of contractions, although its imaginary powers are bounded by eπ|s|/2.

There is an approach due to Bergman describing ordinary polynomial identities for Mn (K) by means of commutative algebra. In the paper we apply this approach to the matrix algebra of even order M2n (K, *) with symplectic involution *.

We prove the following result: Let f(x, y) be a polynomial of degree d in two variables whose coefficents are integers in an unramified extension of Qp. Assume that the reduction of f modulo p is irreducible of degree d and not a binomial. Assume also that p > d2 + 2. Then the number of solutions of the inequality |f(ζ1, ζ2)| < p−1, with ζ1, ζ2 roots of unity in Q̄p or zero, is at most pd2.

Let Cp(X) be the space of all continuous real-valued functions on a Tychonoff space X with the pointwise topology. In this note, we show that if X is a space, then Cp(X) is isocompact. This gives an answer to a recent question of Arkhangel'skii in the class of spaces.

A Banach space X is called a twisted sum of the Banach spaces Y and Z if it has a subspace isomorphic to Y in such a way that the corresponding quotient is isomorphic to Z. In this paper we study twisted sums of Banach spaces with either have the Dunford-Pettis property, are c0-saturated or l1-saturated. Amongst other things, we show that every Banach space is a complemented subspace of a twisted sum of two Banach spaces with the Dunford-Pettis property.

A generalisation of the Ostrowski integral inequality for mappings of bounded variation and applications for general quadrature formulae are given.

We study the ring of invariant Laurent polynomials associated to the action of a finite diagonal group G on the symmetric algebra of a vector space over a field F. Here the characteristic p of the field F necessarily does not divide the order q = |G| of the group, so G is said to be non-modular. For certain representations of such groups, we can characterise generators of the ring of invariant polynomials in the original symmetric algebra, extending results of Campbell, Hughes, Pappalardi and Selick. In particular we obtain a recursive formula for the number of minimal generators for these rings of invariants.

Let M be an n-dimensional compact Riemannian manifold. We study the fundamental group of M when the universal covering space of M, M is close to some Euclidean space ℝs asymptotically.