This is the first of three papers in which we generalise the classical McAlister structure theory for E-unitary inverse semigroups to those 0-E-unitary inverse semigroups which admit a 0-restricted, idempotent pure prehomomorphism to a primitive inverse semigroup. In this paper, we concentrate on finding necessary and sufficient conditions for the existence of such prehomomorphisms in the case of 0-E-unitary inverse monoids. A class of inverse monoids which satisfy our conditions automatically are those which are unambiguous except at zero, such as the polycyclic monoids.

Tate cohomology of finite groups [5] is very good at emphasising periodic cohomological behaviour and hence at the study of free actions on spheres [8]. Tate cohomology of spaces was introduced by Swan [10] for finite dimensional spaces to systematically ignore free actions, and hence to simplify various arguments in fixed point theory.

Let G be a torsion free group, F the free group generated by t. The equation r(t) = 1 is said to have a solution over G if there is a solution in some group that contains G. In this paper we generalize a result due to Klyachko who established the solution when the exponent sum of t is one.

The object of this note is to derive a form of Poisson's equation from general relativistic mechanics, without assuming the field to be either static or “weak”. The problem is essentially a “local” problem, all observations being made by one observer; this observer determines the apparent gravitational field in his vicinity by observing the motions of free (isolated) particles. Defining gravitational mass by means of Poisson's equation, we find the relation between the densities of gravitational and inertial mass relative to any observer. We also find what may be called the non-rotating frame of reference belonging to any observer.

Fundamental statements for (associative) rings are that (a) the endomorphisms of each commutative group (U, +) form a ring and (b) eachring may be embedded in such a ring of endomorphisms. In order to generalise these theorems to groups and rings whose addition may not be commutative, one has to deal with partial endomorphisms. But thesering-theoretical Theorems 4a and 4b turn out to be specialisations of similarones for semi-near-rings, near-rings and semirings, developed here inSection 2 after some preliminaries on semi-near-rings in Section 1. A glance at Definition 1 and the ring-theoretical theorems and remarks at the end of Section 2 may give more orientation.

The boundary value problem

is studied with a view to obtaining the existence of positive solutions in C1([0, 1])∩C2((0, 1)). The function f is assumed to be singular in the second variable, with the singularity modeled after the special case f(x, y) = a(x)y−p, p>0.

This boundary value problem arises in the search of positive radially symmetric solutions to

where Ω is the open unit ball in ℝN, centered at the origin, Γ is its boundary and |x| is the Euclidean norm of x.

This paper is a continuation of (4). The main aim of this paper is the introduction of the concept of sex-linked duplication. In addition, we shall give several equivalent definitions for the concept of a genetic algebra and make several remarks on overlapping of generations.

In this article, using an Halpern extragradient method, we study a new iterative scheme for finding a common element of the set of solutions of multiple set split equality equilibrium problems consisting of pseudomonotone bifunctions and the set of fixed points for two finite families of Bregman quasi-nonexpansive mappings in the framework of p-uniformly convex Banach spaces, which are also uniformly smooth. For this purpose, we design an algorithm so that it does not depend on prior estimates of the Lipschitz-type constants for the pseudomonotone bifunctions. Furthermore, we present an application of our study for finding a common element of the set of solutions of multiple set split equality variational inequality problems and fixed point sets for two finite families of Bregman quasi-nonexpansive mappings. Finally, we conclude with two numerical experiments to support our proposed algorithm.

The notion of Arens regularity of a bilinear form on a Banach space E is extended to continuous m-linear forms, in such a way that the natural associated linear mappings, E→L (m−1E) and (m – l)-linear mappings E × … × E → E', are all weakly compact. Among other applications, polynomials whose first derivative is weakly compact are characterized.

Consider the Darboux problem

where φ,ψ:I→Rd (I=[0,1]) are given absolutely continuous functions with φ(0)=ψ(0), and the mapping f : Q × Rd→Rd (Q = I × I) satisfies the following hypotheses:

(A1) f(.,.,z) is measurable for every z ∈ Rd;

(A2) f(x, y,.) is continuous for a.a. (almost all) (x, y) ∈ Q;

(A3) there exists an integrable function α:Q →[0, + ∞) such that |f(x, y, z)|≦α(x, y) for every (x, y, z)∈ Q × Rd.

The classical Hamburger moment problem can be formulated as follows: Given a sequence {cn:n=0,1,2,…} of real numbers, find necessary and sufficient conditions for the existence of a distribution function ψ (i.e. a bounded, real-valued, non-decreasing function) on (– ∞,∞) with infinitely many points of increase, such that , n = 0,1,2, … This problem was posed and solved by Hamburger [5] in 1921. The corresponding problem for functions ψ on the interval [0,∞) had already been treated by Stieltjes [15] in 1894. The characterizations were in terms of positivity of Hankel determinants associated with the sequence {cn}, and the original proofs rested on the theory of continued fractions. Much work has since been done on questions connected with these problems, using orthogonal functions and extension of positive definite functionals associated with the sequence. Accounts of the classical moment problems with later developments can be found in [1,4,14]. Good modern accounts of the theory of orthogonal polynomials can be found in [2,3].

We study the differential geometry of hypersurfaces in hyperbolic space. As an application of the theory of Lagrangian singularities, we investigate the contact of hypersurfaces with families of hyperspheres or equidistant hyperplanes.

AMS 2000 Mathematics subject classification: Primary 53A35. Secondary 58C27

In this paper, we prove some reverse discrete inequalities with weights of Muckenhoupt and Gehring types and use them to prove some higher summability theorems on a higher weighted space $l_{w}^{p}({\open N})$ form summability on the weighted space $l_{w}^{q}({\open N})$ when p>q. The proofs are obtained by employing new discrete weighted Hardy's type inequalities and their converses for non-increasing sequences, which, for completeness, we prove in our special setting. To the best of the authors' knowledge, these higher summability results have not been considered before. Some numerical results will be given for illustration.

We show that Ribet sections are the only obstruction to the validity of the relative Manin–Mumford conjecture for one-dimensional families of semi-abelian surfaces. Applications include special cases of the Zilber–Pink conjecture for curves in a mixed Shimura variety of dimension 4, as well as the study of polynomial Pell equations with non-separable discriminants.

We consider symplectic difference systems, which contain as special cases linear Hamiltonian difference systems and Sturm–Liouville difference equations of any even order. An associated discrete quadratic functional is important in discrete variational analysis, and while its positive definiteness has been characterized and is well understood, a characterization of its positive semidefiniteness remained an open problem. In this paper we present the solution to this problem and offer necessary and sufficient conditions for such discrete quadratic functionals to be non-negative definite.

AMS 2000 Mathematics subject classification: Primary 39A12; 39A13. Secondary 34B24; 49K99

In this paper we generalize techniques used by Klyachko and the authors to prove some tessellation results about S2. These results are applied to prove the solvability of certain equations with torsion-free coefficients.

The separating subspace of any Lie derivation on a semisimple Banach algebra A is contained in the centre of A.

In this paper we examine periodic problems driven by the scalar $p$-Laplacian. Using non-smooth critical-point theory and a recent multiplicity result based on local linking (the original smooth version is due to Brezis and Nirenberg), we prove three multiplicity results, the third for semilinear problems with resonance at zero. We also study a quasilinear periodic eigenvalue problem with the parameter near resonance. We prove the existence of three distinct solutions, extending in this way a semilinear and smooth result of Mawhin and Schmitt.

AMS 2000 Mathematics subject classification: Primary 34C25

We study a nonlinear second-order periodic problem driven by the scalar $p$-Laplacian with a non-smooth potential. We consider the so-called doubly resonant situation allowing complete interaction (resonance) with both ends of the spectral interval. Using variational methods based on the non-smooth critical-point theory for locally Lipschitz functions and an abstract minimax principle concerning linking sets we establish the solvability of the problem.

AMS 2000 Mathematics subject classification: Primary 34B15; 34C25

Let C[0,1] be the Banach space of continuous functions defined on [0,1] and let C be the set of functions f∈C[0,1] mapping [0,1] into itself. If f∈C, fk will denote the kth iterate of f and we put Ck = {fk:f∈C;}. The set of increasing (≡ nondecreasing) and decreasing (≡ nonincreasing) functions in C will be denoted by ℐ and D, respectively. If a function f is defined on an interval I, we let C(f) denote the set of points at which f is locally constant, i.e.

We let N denote the set of positive integers and NN denote the Baire space of sequences of positive integers.