We use a variation on a construction due to Corner 1965 to construct (Abelian) groups A that are torsion as modules over the ring End (A) of group endomorphisms of A. Some applications include the failure of the Baer-Kaplansky Theorem for Z[X]. There is a countable reduced torsion-free group A such that IA = A for each maximal ideal I in the countable commutative Noetherian integral domain, End (A). Also, there is a countable integral domain R and a countable. R-module A such that (1) R = End(A), (2) T0 ⊗RA ≠ 0 for each nonzero finitely generated (respectively finitely presented) R-module T0, but (3) T ⊗RA = 0 for some nonzero (respectively nonzero finitely generated). R-module T.

In this paper the authors prove an abstract theorem for solutions of a variational inequality on a cone and use it to study the free boundary problem of elastohydrodynamic lubrication from mechanical engineering. The mathematical model is set in a one-dimensional geometry. The existence of a solution for every non-negative lubricant viscosity is proved, and some properties useful for the numerical analysis are obtained.

We study the class of groups having no nontrivial linear representations over certain fields. After showing the class to be closed under perfect extensions with locally soluble kernel, we expand considerably the number of acyclic groups known to be in the class, by application to both binate groups and the acyclic automorphism groups of de la Harpe and McDuff.

A short proof determining the structure of Q-rings with infinite identities is given. The structure of pQ-rings is determined and it is shown that essentially all wQ-rings with finite identities are pQ-rings.

Let f(z) be a meromorphic function, let P(z) and Q(z) be two polynomials. We shall investigate the asymptotic behaviour of the ratio T(r, f(P))/T(r, f(Q)), and discuss the growth of the meromorphic solutions of some functional equations.

Let R be a graded λ-ring. We extend a well-known formula in the universal ring of Witt vectors by replacing the power operations by the Adams operations. Our method provides us an easy way to compute the inverse image by the symmetric power operators of certain elements of R. As a corollary we get identities, found by Klyachko and Hanlon, in the rings 1 + ℤ[[t]]+ and 1 + Rˆ[[t]]+, where R is the representation ring of the symmetric groups.

In this paper we study optimality conditions for an efficient solution in various senses of a general multiobjective optimisation problem in abstract spaces. We utilise properties of the Clarke's generalised differential and properties of a conesubconvexlike function to derive a few necessary and/or sufficient conditions for a feasible solution to be a weak minimum (a minimum, a strong minimum or a proper minimum) of the vector optimisation problem. The results in this paper are extensions and refinements of some known results in vector optimisation.

A finitely presented group G is quasi-simply-filtrated (abbreviated qsf) if, given a finite complex with fundamental group G, the universal cover of the complex can be “approximated” by simply connected finite complexes. This notion is a generalisation of a concept of Casson's used in the study of three-manifolds.

In this paper we show that any extension of a finitely presented infinite group by a finitely presented infinite group is qsf.

In this paper the inverse problem for determining the source term of a linear, uniformly elliptic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by use of the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces, moreover, the continuous dependence of the solution to the inverse problem on measurement is also obtained.

We define a notion of representation induced from cocycles which encompasses the case of Kawakami's generalised induced representation. Our purpose is to formulate Kawakami's construction within the context of Rieffel's formalism of induced representations of C*-algebras.

In this paper we study the symmetric powers of quantum GLn. These are comodules and we give a complete description of the subcomodule structure.

In this paper we study almost sure convergence for arrays of independent and identically distributed random variables. We obtain a condition under which Marcinkiewicz's strong law holds and get a rate analogous to the law of the iterated logarithm under a condition weaker than Hu and Weber's.

We consider a quasilinear elliptic partial differential equation with nonlinear boundary condition under assumptions which do not allow the application of standard degree theory results or techniques such as the method of continuity. An approximation using mollifiers is introduced, allowing the application of Leray-Schauder degree theory, and homotopy arguments are then used to prove the existence of solutions to the approximating problems. A subsequent paper will discuss the question of the convergence of these approximate solutions to a classical solution of the original problem.

The paper provides irrationality measures for certain values of binomial functions and definite integrals of some rational functions. The results are obtained using Jacobi type polynomials and divisibility considerations of their coefficients.

We generalise the notion of proper Hughes subgroup in a group, asking that, for some prime p, the set-complement of the union of two proper subgroups consist solely of elements of order p. A structure theorem for non-p–groups of this type is proved.

We consider some subgroups of Brauer groups arising from twists of matrix algebras by some continuous characters. Explicit descriptions of these subgroups are given in terms of Gauss sums of Dirichlet characters.

Let R be a left linearly compact ring with left ideals I ⊆ J such that RJ is finitely generated and R(J/I) is Artinian. We prove that if J is nil over I then J is nilpotent over I.

This article is a sequel to a paper in which a quasilinear partial differential equation with nonlinear boundary condition was approximated using mollifiers, and the existence of solutions to the approximating problem shown under quite general conditions. In this paper we show that standard a priori Hölder estimates ensure the convergence of these solutions to a classical solution of the original problem. Some partial results giving such estimates for special cases are described.

In this paper, existence results for both integro-differential and functional differential equations are discussed using topological transversality arguments. As applications, third and fourth order boundary value problems are considered. For third order problems, an example has been cited to show that our results cover a wider class of problems than Theorem 2.3 of D.J. O'Regan, Topological transversality: Applications to third order boundary value problems, SIAM J. Math. Anal. 18 (1987) 630–641.

The main result is a necessary and sufficient condition for the class group of a real quadratic field to be determined by primality properties of the well-known Rabinowitsch polynomial.