We prove that the classical sequence James space has the fixed point property. This gives an example of Banach space with a non-unconditional basis where the Maurey-Lin's method applies.

It is shown that a condition of Kurzwell concerning fixed-points of certain operators on a finite group G is sufficient to ensure that G is soluble. The result generalizes those of Martineau on elementary abelian fixed-point-free operator groups.

The rôle of the conjugacy relation is certainly important in the structure theory of groups. Here we study this relation in a considerably more general setting, namely in the theory of loops. We first recall some basic facts about quasigroups, their multiplication groups, their inner mapping groups and the conjugacy relation. After this we estimate the size and the number of the conjugacy classes and we study the structure of loops having only two conjugacy classes. Finally, the values of the centraliser function are discussed.

A consequence of the main proposition includes results of Tacon, and John and Zizler and says: If a Banach space X possesses a continuous Gâteaux differentiable function with bounded nonempty support and with norm-weak continuous derivative, then its dual X* admits a projectional resolution of the identity and a continuous linear one-to-one mapping into c0 (Γ). The proof is easy and selfcontained and does not use any complicated geometrical lemma. If the space X is in addition weakly countably determined, then X* has an equivalent dual locally uniformly rotund norm. It is also shown that l∞ admits no continuous Gâteaux differentiable function with bounded nonempty support.

Several papers have, as their raison d’être, the exploration of the generalised Lau product associated to a homomorphism $T:B\rightarrow A$ of Banach algebras. In this short note, we demonstrate that the generalised Lau product is isomorphic as a Banach algebra to the usual direct product $A\oplus B$. We also correct some misleading claims made about the relationship between this generalised Lau product and an older construction of Monfared [‘On certain products of Banach algebras with applications to harmonic analysis’, Studia Math. 178(3) (2007), 277–294].

In this paper Lp stability and convergence properties of discrete orthogonal projections on the finite element space Sh of continuous polynomial splines of order r are proved. The discrete inner products are defined by composite quadrature rules with positive weights on a sequence of nonuniform grids. It is assumed that the basic quadrature rule Q has at least r quadrature points in order to resolve Sh, but no accuracy is required. The main results are derived under minimal further assumptions, for example the rule Q is allowed to be non-symmetric, and no quasi-uniformity of the mesh is required. The corresponding stability of the orthogonal L2-projections has been studied by de Boor [1] and by Crouzeix and Thomee [2]. Stability of the first derivative of the projection is also proved, under an assumption (unless p = 1) of local quasi-uniformity of the mesh.

We extend some results known for FC-groups to the class FC* of generalized FC-groups introduced in de Giovanni et al. [‘Groups with restricted conjugacy classes’, Serdica Math. J.28(3) (2002), 241–254]. The main theorems pertain to the join of pronormal subgroups. The relevant role that the Wielandt subgroup plays in an FC*-group is pointed out.

Let G be a connected reductive algebraic group defined over a finite field k. The finite group G(k) of k-rational points of G acts on the spherical building B(G), a polyhedron which is functorially associated with G. We identify the subspace of points of B(G) fixed by a regular semisimple element s of G(k) topologically as a subspace of a sphere (apartment) in B(G) which depends on an element of the Weyl group which is determined by s. Applications include the derivation of the values of certain characters of G(k) at s by means of Lefschetz theory. The characters considered arise from the action of G(k) on the cohomology of equivariant sheaves over B(G).

If an optimal solution exists for a nonlinear fractional programming problem, then this solution is shown to be obtainable by solving two associated programming problems whose objective functions are no longer fractional. A certain restriction is assumed on the constraint sets of the latter problems. This result includes various known theorems as special cases.

Let $\Gamma $ be a $G$-vertex-transitive graph and let $(u,v)$ be an arc of $\Gamma $. It is known that if the local action $G_v^{\Gamma (v)}$ (the permutation group induced by $G_v$ on $\Gamma (v)$) is permutation isomorphic to the dihedral group of degree four, then either $|G_{uv}|$ is ‘small’ with respect to the order of $\Gamma $ or $\Gamma $is one of a family of well-understood graphs. In this paper, we generalise this result to a wider class of local actions.

This paper produces new types of designs, called product designs, which prove extremely useful for constructing orthogonal designs. An orthogonal design of order 2t and type

is constructed. This design often meets the Radon bound for the number of variables.

We also show that all orthogonal designs of order 2t and type (a, b, c, d, 2t-a-b-c-d), with 0 < a + b + c + d < 2t, exist for t = 5, 6, and 7.

Let R be a commutative ring. It is shown that if an R-module M is a sum of δ-local submodules and a semisimple projective submodule, then every finitely generated submodule of M is δ-supplemented. From this result, we conclude that finitely generated δ-supplemented modules over commutative rings are amply δ-supplemented.

We characterise the relatively congruence distributive subquasivarieties of a modular variety using the modular commutator. Our characterisation allows us to extend the results of Dziobiak concerning relatively congruence distributive quasivarieties of nonassociative R-algebras.

Several theorems concerning the norming constants {aṇ} and {bn} making a normed Markov chain {an (Xn+bn): n ≥ 0} convergent in distribution (or in probability) are given. It is shown that if Rényi's mixing conditions holds, and , whereas in the general case with α ≠ 0 and exists and are finite. Examples regarding maxima of independent and identically distributed random variables, random walk, and branching processes are considered.

This is a report on a family of varieties of algebraic systems that are groups with an additional unary operation satisfying certain laws. The study was inspired by the theory of Fibonacci groups, and the free one-generator algebras of our varieties turn out to have, in fact, the abelianized Fibonnaci groups as their underlying groups.

Let Ω be a bounded convex domain in R2 with a smooth boundary. Let 0 < γ < 1. Let be a solution, positive in Ω, of

Then the function uα is concave for α = (l–γ)/2.

Criteria for a holomorphic function f defined in |z| < 1 to be Bloch, namely, , are obtained in terms of the area and the length of the images of non-Euclidean disks and non-Euclidean circles, respectively.

We prove a joint universality theorem in the Voronin sense for the periodic Hurwitz zeta-functions.

The ranges of the Y-integral transform in some spaces of functions are described.

In this paper, we prove that for an algebroid function w (z) with finite lower order, satisfying , there exists a T direction dealing with multiple values.