Let E be a normed space, a Fréchet space or a complete (DF)-space satisfying the dual density condition. Let Ω be a Radon measure space. We prove that a function f: Ω → Eis Bochner p-integrable if (and only if) fis p-integrable with respect to the topology of uniform convergence on the norm-null sequences from E′.

We study two variants of weak Hadamard differentiability of continuous convex functions on a Banach space, uniform weak Hadamard differentiability and weak Hadamard directional differentiability, and determine their special properties on Banach spaces which do not contain a subspace topologically isomorphic to l1.

Several interesting criteria for constructing triangulations associated with a given set of points in a plane have been introduced. In order to obtain optimal triangula-tion with respect to the min-max-angle criterion, it is essential to study the nature of neutral cases with respect to the criterion. Our aim in this paper is to establish precise equations for neutral set curves with respect to the min-max-angle criterion and to develop an algorithm to obtain a locally optimal triangulation with respect to the criterion.

Milnor's classic result that the fundamental group of a compact Riemannian manifold of negative sectional curvature has exponential growth is generalised to the case of negative Ricci curvature and non-positive sectional curvature.

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

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

We consider category theory enriched in a locally finitely presentable symmetric monoidal closed category ν. We define the ν-filtered colimits as those colimits weighted by a ν-flat presheaf and consider the corresponding notion of ν-accessible category. We prove that ν-accessible categories coincide with the categories of ν-flat presheaves and also with the categories of ν-points of the categories of ν-presheaves. Moreover, the ν-locally finitely presentable categories are exactly the ν-cocomplete finitely accessible ones. To prove this last result, we show that the Cauchy completion of a small ν-category Cis equivalent to the category of ν-finitely presentable ν-flat presheaves on C.

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

We show that the ring of locally bounded Nash meromorphic functions on a connected d-dimensional Nash submanifold of ℝn is a Prüfer domain and every finitely generated ideal in this ring can be generated by d + 1 elements.

Moreover, every finitely generated ideal can be generated by d elements if and only if the Nash manifold is noncompact.

Higher-order necessary and sufficient optimality conditions for a nonsmooth minimax problem with infinitely many constraints of inequality type are established under suitable basic assumptions and regularity conditions.

We give a bound for the number of generators for groups of exponent p depending on the rank of the centre when centre and commutator subgroup coincide, provided that the group is isomorphic to the quotient group modulo the centre of some group.

Let g denote a finite dimensional nilpotent Lie algebra over ℂ containing an Abelian ideal a of codimension 1, with z ∈ g/a. We give a combinatorial description of the Betti numbers of g in terms of the Jordan decomposition induced by ad(z)|a. As an application we prove that the filiform-nilpotent Lie algebras arising in the case t = 1 have unimodal Betti numbers.