In the paper we prove a result on the existence of positive solutions for a class of nonvariational elliptic system with nonlocal source by Galerkin methods and a fixed point theorem in finite dimensions. We establish another existence result by the super and subsolution method and a monotone iteration.

Laue et al have described basic algorithms for computing in a finite soluble group G given by an AG-presentation, among them a general algorithm for the computation of the orbits of such a group acting on some set Ω. Among other applications, this algorithm yields straightforwardly a method for the computation of the conjugacy classes of elements in such a group, which has been implemented in 1986 in FORTRAN within SOGOS by the first author and in 1987 in C within CAYLEY. However, for this particular problem one can do better, as discussed in this note.

Some properties of projective planes having a certain type of collineation group are proved, and a class of these planes which properly contains the class of all Hall planes of odd order is explicitly constructed.

We recall the definition and properties of an algebra cone C of a complex unital Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A, and A is then called an ordered Banach algebra. The Banach algebra ℒ(E) of all bounded linear operators on a complex Banach lattice E is an example of an ordered Banach algebra, and an interesting aspect of research in ordered Banach algebras is that of investigating in an ordered Banach algebra-context certain problems that originated in ℒ(E). In this paper we investigate the problems of providing conditions under which (1) a positive element a with spectrum consisting of 1 only will necessarily be greater than or equal to 1, and (2) f (a) will be positive if a is positive, where f (a) is the element defined by the holomorphic functional calculus.

In this paper, we give a simple criterion for the Arens regularity of a bilinear mapping on normed spaces, which applies in particular to Banach module actions, and then investigate those conditions under which the second adjoint of a derivation into a dual Banach module is again a derivation. As a consequence of the main result, a simple and direct proof for several older results is also included.

The purpose of this paper is to obtain some common fixed point theorems for a family of mappings in a complete metric space. The results herein improve some of the recent theorems of Kiyoshi Iséki (Bull. Austral. Math. Soc. 10 (1974), 365–370).

It is shown that in a variety of (not necessarily associative) algebras which satisfies a variant of Andrunakievich's Lemma, a class C containing no solvable algebras is the semi-simple class corresponding to some supernilpotent radical class if and only ifCis hereditary and is closed under extensions and sub-direct products. Semi-simple classes in general are not characterized by these properties. If the variety satisfies the further condition that some proper power of every ideal is an ideal, then analogous results hold for the semi-simple classes corresponding to radical classes containing no solvable algebras. In particular, for algebras over a field in the latter situation, all semi-simple classes are characterized by the three closure properties mentioned.

The aim of this note is to prove a theorem on the pointwise degree of approximation of continuously differentiable functions by positive linear operators. As can be seen from the applications to Bernstein and Hermite-Fejér operators, our inequality yields better constants and sometimes even a higher degree of approximation than the known general results.

In an earlier article we obtain a sharp inequality for an arbitrary isometric immersion from a Riemannian manifold admitting a Riemannian submersion with totally geodesic fibres into a unit sphere. In this article we investigate the immersions which satisfy the equality case of the inequality. As a by-product, we discover a new characterisation of Cartan hypersurface in S4.

We give a short proof the local boundedness of a monotone operator as an easy consequence of the continuity of an associated convex function.

In this paper some results concerning the Cauchy functional equation, that is the functional equation f(x+y) = f(x) + f(y) in complex hermitian Banach *-algebras with an identity element are presented. As an application a generalization of Kurepa's extension of the Jordan-Neumann characterization of pre-Hilbert space is obtained.

We carry out an in-depth study of some domination and smoothing properties of linear operators and of their role within the theory of eventually positive operator semigroups. On the one hand, we prove that, on many important function spaces, they imply compactness properties. On the other hand, we show that these conditions can be omitted in a number of Perron–Frobenius type spectral theorems. We furthermore prove a Kreĭn–Rutman type theorem on the existence of positive eigenvectors and eigenfunctionals under certain eventual positivity conditions.

We prove that a Küchle fourfold $X$ of type d3 has a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of $X$.

We characterise all the perfect k-error correcting codes that can be defined on the graph associated with the Towers of Hanoi puzzle. In particular, a short proof for the existence of 1-error correcting code on such a graph is given.

Let ℚp denote the p-adic numbers. We consider curves in defined by p-adic polynomials of one p-adic variable. We show that maximal averages along these curves are bounded, where 1 < q < ∞.

We introduce a definition of generalised solutions of the Hessian equation Sm(D2u) = f in a convex set ω ⊂ ℝn, where Sm(D2u) denotes the m-th symmetric function of the eigenvalues of D2u, f ∈ Lp(ω), p ≥ 1, and m ∈ {1, …, n}. Such a definition is given in the class of semi-convex functions, and it extends the definition of convex generalised solutions for the Monge-Ampère equation. We prove that semiconvex weak solutions are solutions in the sense of the present paper.

We calculate the dimensions of using Erokhin's work on Niemeier lattices and geometric methods involving the hyperelliptic locus.

Real ideals of the ring ℜL of real-valued continuous functions on a completely regular frame L are characterized in terms of cozero elements, in the manner of the classical case of the rings C(X). As an application, we show that L is realcompact if and only if every free maximal ideal of ℜL is hyper-real—which is the precise translation of how Hewitt defined realcompact spaces, albeit under a different appellation. We also obtain a frame version of Mrówka’s theorem that characterizes realcompact spaces.

Let a(z) and b(w) be two rational functions in z or W with algebraic coefficients, where a(0) = 0 and let

Assume that 0 < |z| < 1, that z is not a pole of for n ≥ 0, that w is neither a pole nor a zero of b(w, n) for n ≥ 1, and that the series

for fixed w is a transcendental function of z. Then, if z and W are algebraic numbers, f(z, w) is a transcendental number.