Let G = (N, E) be a supply graph, with the node set N and edge set E, and (T, S) be a demand graph, with T ⊆ N , S ∩ E = ∅. Observe paths whose end-vertices form pairs in S (called S-paths). The following path packing problem for graphs is fundamental: what is the maximal number of S-paths in G? In this paper this problem is studied under two assumptions: (a) the node degrees in N \ T are even,...

Z. Li characterized spaces with a weak-development consisting of point-countable sfp-covers by pseudo-sequence-covering, quotient, and π-s-image of metric spaces. In this paper, we omit ”pseudo-sequence-covering” in the above result, and prove that a space has a weak-development consisting of point-countable sfp-covers iff it is a quotient, and π-s-image of a metric space.

Let K = Func(C) be the function field of a smooth curve C. For every Del Pezzo surface S/K which is an appropriately generic, weak approximation for S holds at every place of K, i.e., for every closed point c of C. This combines earlier work in (arXiv:0810.2597) with an analysis of weak approximation near boundary points of the parameter spaces for Del Pezzo surfaces of degrees 1 and 2.

In the title compound, C(24)H(21)NO(4)S, the indole ring system makes dihedral angles of 77.8 (1) and 85.4 (1)°, respectively, with the S- and C-bound phenyl rings. The mol-ecular structure is stabilized by a weak intra-molecular C-H⋯O hydrogen bond. In the crystal, a weak inter-molecular C-H⋯O hydrogen bond and a C-H⋯π inter-action are also observed.

The main object of this paper is to introduce a new concept of weak statistically Cauchy sequence in a normed space. It is shown that in a reflexive space, weak statistically Cauchy sequences are the same as weakly statistically convergent sequences. Finally, weak statistical convergence has been discussed in l p spaces. under the Creative Commons Attribution License, which permits unrestricted...

The slice condition and the more general weak slice conditions are geometric conditions on Euclidean space domains which have evolved over the last several years as a tool in various areas of analysis. This paper explores some of the finer distinctive properties of the various weak slice conditions.

A hierarchy of weak variants of Martin’s Axiom is extended and shown to be strict.