The multiple originator broadcasting problem in graphs

AbstractGiven a graph G and a vertex subset S of V(G), the broadcasting time with respect to S, denoted by b(G,S), is the minimum broadcasting time when using S as the broadcasting set. And the k-broadcasting number, denoted by bk(G), is defined by bk(G)=min{b(G,S)|S⊆V(G),|S|=k}.Given a graph G and two vertex subsets S, S′ of V(G), define d(v,S)=minu∈Sd(v,u), d(S,S′)=min{d(u,v)|u∈S, v∈S′}, and d(G,S)=maxv∈V(G)d(v,S) for all v∈V(G). For all k, 1⩽k⩽|V(G)|, the k-radius of G, denoted by rk(G), is defined as rk(G)=min{d(G,S)|S⊆V(G), |S|=k}.In this paper, we study the relation between the k-radius and the k-broadcasting numbers of graphs. We also give the 2-radius and the 2-broadcasting numbers of the grid graphs, and the k-broadcasting numbers of the complete n-partite graphs and the hypercubes

Applying Neural Network based on Fuzzy Cluster Pre-processing to Thermal Error Modeling for Coordinate Boring Machine

AbstractTo investigate the effect of the thermal characteristics of a motorized spindle system on the precision of a machine tool, a thermal error model for spindle axial expansion and radial thermal declination is proposed. With precision CNC coordinate boring machine as an object, using the five-point method to calibrate spindle system thermal errors by the eddy current sensors for axial thermal elongation and radial thermal tilted values, and temperatures of measurement points are obtained by the PT100. The relationships between the rotational speed and temperature field, thermal errors are analyzed. Then fuzzy clustering analysis method is used to group and optimize the temperature variables, selecting the variables for thermal error-sensitive. Finally the MIMO artificial neural network approach is established for the spindle axial thermal elongation and radial thermal drifts. The results indicated that the model prediction accuracy could reach 86% with perfect generalization ability under different cutting conditions, providing a theoretical model and thermal characteristic parameters for both thermal error compensation and thermal equilibrium design

Tris[tris­(1,10-phenanthroline-κ2 N,N′)iron(II)] dodeca­tungstoferrate dihydrate

The title compound, [Fe(C12H8N2)3]3[FeW12O40]·2H2O, was prepared under hydro­thermal conditions. The discrete Keggin-type [FeW12O40]6− heteropolyoxoanion has threefold symmetry, with the FeII atom located on the threefold rotation axis. The central FeO4 tetra­hedron in the anion shares its O atoms with four W3O13 trinuclear units, each of which is made up of three edge-shared WO6 octa­hedral units. The FeII atom in the complex cation, viz [Fe(phen)3]2+ (phen is 1,10-phen­anthroline), shows a slightly distorted octa­hedral geometry defined by six N atoms from three phen ligands. The polyoxoanions pack together with the cations, with the disordered water mol­ecules located in voids; the site occupancy factor for each water O atom is 0.33

2,2′-[(4,6-Dinitro-1,3-phenyl­ene)dioxy]diacetic acid hemihydrate

The skeletons of both independent mol­ecules of the carboxylic acid hemihydrate, C10H8N2O10·0.5H2O, are approximately planar [maximum deviations 0.642 (3) and 0.468 (1) Å]. The deviations arise from the twisting of the nitro groups with respect to the aromatic rings [dihedral angles = 3.24 (2) and 27.01 (1), and 7.87 (1) and 16.37 (2)° in the two molecules]. The crystal structure features inter­molecular O—H⋯O hydrogen bonds, which the link the dicarboxylic acid and water mol­ecules into a supra­molecular layer network

3-Benzyl-6-isopropyl-5-phen­oxy-3H-1,2,3-triazolo[4,5-d]pyrimidin-7(6H)-one

In the title compound, C20H19N5O2, all atoms of the 1,2,3-triazolo[4,5-d]pyrimidine ring system are essentially coplanar [maximum deviation = 0.015 (2) Å], indicating the existence of a conjugate system in which each carbon and nitrogen atom is sp 2 hybridized and ten π electrons (three from carbon atoms and seven from nitrogen atoms) constitute an aromatic heterocycle. The ring system forms dihedral angles of 68.37 (10) and 71.57 (9)° with the phenyl rings. The crystal packing is stabilized by van der Waals inter­actions and intermolecular C—H⋯π interactions

Spin Fluctuation Induced Linear Magnetoresistance in Ultrathin Superconducting FeSe Films

The discovery of high-temperature superconductivity in FeSe/STO has trigged great research interest to reveal a range of exotic physical phenomena in this novel material. Here we present a temperature dependent magnetotransport measurement for ultrathin FeSe/STO films with different thickness and protection layers. Remarkably, a surprising linear magnetoresistance (LMR) is observed around the superconducting transition temperatures but absent otherwise. The experimental LMR can be reproduced by magnetotransport calculations based on a model of magnetic field dependent disorder induced by spin fluctuation. Thus, the observed LMR in coexistence with superconductivity provides the first magnetotransport signature for spin fluctuation around the superconducting transition region in ultrathin FeSe/STO films

(E)-2-Chloro-N′-(2-hydr­oxy-1-naphthyl­methyl­ene)benzohydrazide

In the structue of the title compound, C18H13ClN2O2, a new Schiff base, the dihedral angle between the benzene and naphthyl ring system mean planes is 22.5 (2)°. The mol­ecule has an E configuration about the C=N bond, and an intra­molecular hydrogen bond involving the hydoxyl substituent on the naphthyl ring and the N′ atom of the hydrazide. The crystal structure is stabilized by inter­molecular N—H⋯O hydrogen bonds, forming one-dimensional chains running parallel to the a axis