sn-networks were first introduced by Lin [12], which are the concept between weak bases and cs-networks. sn-metrizable spaces [6] (i.e., spaces with σ-locally finite sn-networks) are one class of generalized metric spaces, and they play an important role in metrization theory, see [6, 13]. In this paper, we give a mapping theorem on sn-metrizable spaces, discuss relationships among spaces with ...

Let Fq[t] denote the polynomial ring over the finite field Fq, and let SN denote the subset of Fq[t] containing all polynomials of degree strictly less than N . For non-zero elements r1, ⋅ ⋅ ⋅ , rs of Fq satisfying r1 + ⋅ ⋅ ⋅ + rs = 0, let Dr(SN ) denote the maximal cardinality of a set A ⊆ SN which contains no non-trivial solution of r1x1 + ⋅ ⋅ ⋅+ rsxs = 0 with xi ∈ A (1 ≤ i ≤ s). We prove tha...

The title compound, [Sn(4)(C(8)H(17))(8)O(2)(C(6)H(5)N(2)O(2))(4)], is a tetra-nuclear Sn(IV) complex, built up by inversion symmetry around the central Sn(2)O(2) ring. The Sn(IV) coordination geometries are distorted SnO(3)C(2) trigonal-bipyramidal and distorted SnO(4)C(2) octa-hedral. The three-coordinate μ(3)-oxido bridging O atom in the Sn(2)O(2) ring is attached to three Sn atoms. All non-...

We present single-epoch spectropolarimetry of the Type II supernovae (SNe II) 1997ds, 1998A, and 1999gi. SN 1997ds and SN 1998A were both observed during the early photospheric phase, less than 50 days after explosion, while spectropolarimetry of SN 1999gi was obtained near the start of the transition to the nebular phase, about 110 days after explosion. Uncorrected for interstellar polarizatio...

In this paper we highlight some enumerative results concerning matroids of low rank and prove the tail-ends of various sequences involving the number of matroids on a finite set to be log-convex. We give a recursion for a new, slightly improved, lower bound on the number of rank-r matroids on n elements when n = 2 − 1. We also prove an adjacent result showing the point-lines-planes conjecture t...

The Cu-Sn metallurgical soldering reaction in two-segmented Cu-Sn nanowires is studied by in situ transmission electron microscopy. By varying the relative lengths of Cu and Sn segments, we show that the metallurgical reaction results in a Cu-Sn solid solution for small Sn/Cu length ratio while Cu-Sn intermetallic compounds (IMCs) for larger Sn/Cu length ratios. Upon heating the nanowires to ∼5...

The title distannoxane, [Sn(4)(CH(3))(8)(C(3)H(4)N(3)S)(2)(CH(3)O)(2)O(2)], lies about a center of inversion; the tetra-nuclear mol-ecule features a three-rung-staircase Sn(4)O(4) core in which the two crystallographically independent Sn(IV) atoms are bridged by the triazolide group. The negatively charged N atom of the triazolide group binds to the terminal Sn atom at a shorter distance [Sn-N ...

An Sn,k refers to a generalized version of an n-star graph (Sn), where Sn,n−1 and Sn are isomorphic and Sn,1 is obviously a complete graph of n vertices (Kn). This study constructs a set of many-to-one vertex-disjoint paths in an (n, k)-star graph (Sn,k), and computes the upper bound of Rabin number of an Sn,k, where 2≤k≤n−1. The upper bound of the Rabin number of an Sn,k is calculated by const...