In this paper we consider the error estimates for some boundary-flux calculation procedures applied to two-point semilinear and strongly nonlinear elliptic boundary value problems. The case of semilinear parabolic problems is also studied. We prove that the computed flux is superconvergent with second and third order of convergence for linear and quadratic elements respectively. Corresponding estimates for higher order elements may also be obtained by following the general line of argument.

This paper is a survey of the current state of knowledge on groups of exponent 8. It contains a report on a first stage of an attempt to answer the Burnside questions for these groups.

This paper study nearly extremal Cohen–Macaulay and Gorenstein algebras and characterise them in terms of their minimal free resolutions. Explicit bounds on their graded Betti numbers and their multiplicities are obtained.

Nearlattices, or lower semllattices in which any two elements have a supremum whenever they are bounded above, provide an interesting generalization of lattices. In this context, we study standard, neutral, and central elements, as well as standard ideals. A new perspective is obtained in the well established case of lattices.

We give derivative-free characterizations for bounded and compact generalized composition operators between (little) Zygmund type spaces. To obtain these results, we extend Pavlović’s corresponding result for bounded composition operators between analytic Lipschitz spaces.

In this paper, the unique fixed points of multi-valued and single-valued operators of monotone type are approximated by Ishikawa iteration processes or Mann and Ishikawa iteration processes with errors in uniformly smooth Banach spaces. The operators may not satisfy the Lipschitzian conditions and the domain or the range of the operators may not be bounded. The results presented improve and extend some recent results.

The aim of the present paper is to give some general surjectivity theorems for multifunctions using tangent cones and generalized differentiability assumptions.

The p-norm of the Hilbert transform is the same as the p-norm of its truncation to any Lebesgue measurable set with strictly positive measure. This fact follows from two symmetry properties, the joint presence of which is essentially unique to the Hilbert transform. Our result applies, in particular, to the finite Hilbert transform taken over (−1, 1), and to the one-sided Hilbert transform taken over (0, ∞). A related weaker property holds for integral operators with Hardy kernels.

During the 1920's and 30's, two distinct theories of “completions” for topological spaces were being developed: the French school of mathematics was describing the familiar notion of “complete relative to a uniformity”, and the Russian school the less well-known idea of “absolutely closed”. The two agree precisely for compact spaces.

The first part of this article describes these two notions of completeness; the remainder is a presentation of the interesting, but apparently unrecorded, fact that the two ideas coincide when put in the context of topological groups.

It is proved that in every neighbourhood of a system of linear differential equations with almost periodic skew-adjoint matrix with frequency module ℱ there exists a system with frequency module contained in the rational hull of ℱ possessing all almost periodic solutions.

We give a simple argument which shows that Gabor systems consisting of odd functions of $d$ variables and symplectic lattices of density $2^{d}$ cannot constitute a Gabor frame. In the one-dimensional, separable case, this follows from a more general result of Lyubarskii and Nes [‘Gabor frames with rational density’, Appl. Comput. Harmon. Anal.34(3) (2013), 488–494]. We use a different approach exploiting the algebraic relation between the ambiguity function and the Wigner distribution as well as their relation given by the (symplectic) Fourier transform. Also, we do not need the assumption that the lattice is separable and, hence, new restrictions are added to the full frame set of odd functions.

For a commutative domain R with 1, R-module M is called a semi-Baer module if for all divisible R-modules D. We show that finitely generated modules of projective dimension at most 1 are semi-Baer modules and if R is Prüfer or Matlis, then all modules of projective dimension at most 1 are semi-Baer modules.

The abstract triangle groups Δ(2, 4, r) can be defined for any positive integer r by Δ(2, 4, r) = 〈x, y | x2 = y4 = (xy)r = 1〉. In this paper we show that for every r ≥ 6, all but finitely many of the alternating groups An can be obtained as quotients of Δ(2, 4, r).

The recovery of flow curves for non-Newtonian fluids from Couette rheometry measurements involves the solution of a quite simple first kind Volterra integral equation with a discontinuous kernel for which the solution, as a summation of an infinite series, has been known since 1953. Various methods, including an Euler-Maclaurin sum formula, have been proposed for the estimation of the value of the summation. They all involve the numerical differentiation of the observational data. In this paper, the properties of Bernoulli polynomials, in conjunctions with the special structure of the integral equation, are exploited to derive a parametric family of representations for its solution. They yield formulas similar to, but more general than, the previously published Euler-Maclaurin sum formula representations. The parameterisation is then utilised to derive two new classes of approximations. The first yields a family of finite difference approximations, which avoids the direct numerical differentiation of the observational data, while the second generates a framework for the construction of improved power law approximations.

Standard homological methods and a theorem of Harrison on cotorsion groups are used to prove the result mentioned.

In this note Z denotes an infinite cyclic group, Q the additive group of rational numbers, Zp ∞ a p–quasicyclie group, and Ip the group of p–adic integers.

Pascual Llorente proves in [3] that Ext(Q,z) is an uncountable group, and gives explicitly a countably infinite subset. Very little extra effort produces the result embodied in the title, as follows.

The dynamic response of a prestressed incompressible Mooney material is studied by investigating plane wave propagation and the response of the material to impulsive lines of force. The choice of an initial deformation which is axially symmetric gives a particularly simple form for the secular equation for the plane wavefront velocities. The speeds of propagation and the amplitudes of the two permissible transverse waves are found and necessary and sufficient conditions for there to exist two real wave speeds in all directions are established. The simple form of the secular equation enables the response of the material to concentrated disturbances to be readily solved using Fourier transforms. The motions caused by a line of impulsive forces is examined in some detail.

Let K be a bounded closed convex set in the plane containing no points of the integral lattice in its interior and having width w, area A, perimeter p and circumradius R. The following best possible inequalities are established:

Some existence theorem for solutions of two kinds of differential inclusions with monotone type mappings in Hilbert spaces are given.

We advance a new conjecture in the spirit of the dynamical Manin–Mumford conjecture. We show that our conjecture holds for all polarisable endomorphisms of abelian varieties and for all polarisable endomorphisms of $(\mathbb{P}^{1})^{N}$. Furthermore, we show various examples which highlight the restrictions one would need to consider in formulating any general conclusion in the dynamical Manin–Mumford conjecture.