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...

The tetra-nuclear title compound, [Sn4(CH3)8(C2H5O)2O2(C3H4N3S)2], lies about a center of inversion; the mol-ecule features a three-rung-staircase Sn4O4 core in which two Sn(IV) atoms are bridged by the 4-methyl-5-sulfanyl-idene-4,5-dihydro-1H-1,2,4-triazol-1-ide group. The negatively charged N atom of the group binds to the terminal Sn(IV) atom at a shorter distance [Sn-N = 2.240 (3) Å] compar...

We set sensitive upper limits to the X-ray emission of four Type Ia supernovae (SNe Ia) using the Chandra X-ray Observatory. SN 2002bo, a normal, although reddened, nearby SN Ia, was observed 9.3 days after explosion. For an absorbed, high temperature bremsstrahlung model the flux limits are 3.2 × 10 ergs cm s (0.5–2 keV band) and 4.1 × 10 ergs cm s (2–10 keV band). Using conservative model ass...

BACKGROUND The potential morbidity of an axillary lymph node dissection in patients with breast cancer can be avoided in patients with a negative sentinel node (SN). HYPOTHESIS It may be possible to identify a subset of patients with a positive SN and without metastases in the remaining axillary lymph nodes. DESIGN Case-control study. SETTING Both primary and referral hospital care. PAT...

We have employed ab initio molecular dynamics to investigate the equilibrium geometries, energetics, and the nature of bonding in mixed Li-Sn clusters. Our studies reveal that a small percentage of Sn in Li-rich clusters introduces significant changes in the equilibrium geometries. It is also seen that the geometries of Sn-rich clusters are influenced by the Sn10 motif. Analysis of the nature o...

In this paper, we consider the fault Hamiltonicity, and the fault Hamiltonian connectivity of the (n, k)-star graph Sn,k. Assume that F V(Sn,k) E(Sn,k). For n k ≥ 2, we prove that Sn,k F is Hamiltonian if F ≤ n 3 and Sn,k F is Hamiltonian connected if F ≤ n 4. For n k 1, Sn,n 1 is isomorphic to the n-star graph Sn which is known to be Hamiltonian if and only if n > 2 and Hamiltonian connected i...

The formyl-meth-oxy-nitro-phenoxide ions in the polymeric title compound, [Sn(C(7)H(7))(3)(C(8)H(6)NO(5))](n), link adjacent triorganotin(IV) cations into linear chains lying close to (101) [Sn-O = 2.1227 (12) Å and Sn← O = 2.4936 (13) Å]. The Sn(IV) atom is displaced out of the C(3)Sn girdle of the trans-C(3)SnO(2) trigonal-bipyramidal polyhedron in the direction of the covalently-bonded O ato...

In this paper we will address the question of how many nonvanishing, linearly independent tangent vector fields can exist on a sphere Sn−1 ⊆ R. By this we mean the following, a tangent vector field on Sn−1 = {x ∈ R : ‖x‖ = 1} is a map v : Sn−1 → R such that v(x) ⊥ x for all x ∈ Sn−1. However, by assumption v is nonvanishing, so we can normalize such that ‖v(x)‖ = 1 and we obtain a map v : Sn−1 ...

A patterned coreeshell tin (Sn) nanorod anode is fabricated by pulse electrodeposition of Sn onto a selfassembled Tobacco Mosaic Virus (TMV) structured nickel current collector. Pulse electrodeposition onto the virus assembled 3D electrode surfaces produces homogenous Sn coatings with significant void space to accommodate the large volume change associated with Sn lithiation. The TMV enabled 3D...

Howell et al. have reported the discovery of SN Ia SN 2003fg (SNLS-03D3bb) and conclude that SN 2003fg is very likely a super-Chandrasekhar-mass SN Ia perhaps with a mass∼ 2M⊙. Their work is the first strong evidence that has been presented for a super-Chandrasekhar SN Ia. We have performed an analysis of the SN 2003fg data using the Yoon & Langer binding energy formula for a rotating super-Cha...