Degree Bounded Spanning Trees

In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set ${S \subseteq V(G)}In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set S í V(G){S \subseteq V(G)} of cardinality n(k−1) + c + 2, there exists a vertex set X í S{X \subseteq S} of cardinality k such that the degree sum of vertices in X is at least |V(G)| − c −1. Then G has a spanning tree T with maximum degree at most k+éc/nù{k+\lceil c/n\rceil} and ?_{v ? V(T)}max{d_T(v)-k,0} ￡ c{\sum_{v\in V(T)}\max\{d_T(v)-k,0\}\leq c} .     

The Synthesis of Fluorine Containing Phenyl Benzoates and Their Properties as Liquid Crystals

A new series of fluorine containing phenyl benzoates has been synthesized and the transition temperatures of these compounds have been determined. A series of 4-trifluoromethylphe 4nyl 4-n-alkybenzoates showed no liquid crystalline behaviour, but the 4-trifluoromethylphenyl 4-n-alkoxybenzoates series, with six carbons or more in alkoxy chain, was mesomorphic. The 4-cyanophenyl 4-perfluoroalkylbenzoates showed smectic liquid crystalline properties.     

Dependence of the Electrically Controlled Birefringence on Applied Frequency in a Nematic Liquid Crystal

Detailed studies on the dependence of the ECB effect on the applied frequency have been made in a nematic liquid crystal MBBA. It is found experimentally that, when the applied voltage is just above the threshold voltage, there are strong dependences of both the delay time and the mean deformation angle of the molecular director subjected to a constant voltage setup on the applied frequency. Those applied frequency dependences of the ECB effect can be interpreted in terms of the dielectric alignment in an electrically conducting nematic liquid crystal. We have measured the capacitance of the deformed liquid crystal cell varying the applied frequency. The experimental results are compared with the Gruler and Cheung theoretical prediction, and good agreements are obtained between them when the applied voltage is just above the threshold voltage.     

Topological Effects on Conductance of Nanotubes

Abstract

Electronic states in junctions of nanotubes with different circumferences are studied in an effective-mass approximation. The junction is characterized by boundary conditions which mix wave functions associated with K and K′ points. At ε=0, they decay linearly with the distance from the thicker nanotube, showing that the conductance decays with the junction length in proportion to its third power.     

Long-term depression and other synaptic plasticity in the cerebellum

Cerebellar long-term depression (LTD) is a type of synaptic plasticity and has been considered as a critical cellular mechanism for motor learning. LTD occurs at excitatory synapses between parallel fibers and a Purkinje cell in the cerebellar cortex, and is expressed as reduced responsiveness to transmitter glutamate. Molecular induction mechanism of LTD has been intensively studied using culture and slice preparations, which has revealed critical roles of Ca²⁺, protein kinase C and endocytosis of AMPA-type glutamate receptors. Involvement of a large number of additional molecules has also been demonstrated, and their interactions relevant to LTD mechanisms have been studied. In vivo experiments including those on mutant mice, have reported good correlation of LTD and motor learning. However, motor learning could occur with impaired LTD. A possibility that cerebellar synaptic plasticity other than LTD compensates for the defective LTD has been proposed.     

A kinetics study of ligand substitution reaction on dinuclear platinum complexes: Stochastic versus deterministic approach

The kinetics on a basic ligand substitution reaction on dinuclear platinum complexes [Pt(PEt₃)₂PhPt(PEt₃)₂]²⁺ and [Pt(PEt₃)₂PhCOPhPt(PEt₃)₂]²⁺ , with the ligands pyridine and 3-chloropyridine, is studied. This is a fundamental step in a self-assembly, and the time evolution has been observed with a new experimental technique, QASAP (quantitative analysis of self-assembly process), which is recently developed by Hiraoka's group. As a result of numerical calculations based on master equation, we succeed in specifying the reaction rate constants with a simple reaction model. In addition, the time evolutions of all the intermediate components produced and consumed in chemical reaction are revealed, including those unobserved in the experiments. The convergence behavior of the existence ratios of specific chemical species calculated with the stochastic algorithm method is compared with those obtained from deterministic formalism based on rate equations, revealing a clear dependence on the number of constituent molecules. © 2018 Wiley Periodicals, Inc.     

Asymptotic behavior toward nonlinear waves for radially symmetric solutions of the multi-dimensional Burgers equation

The present paper is concerned with the asymptotic behaviors of radially symmetric solutions for the multi-dimensional Burgers equation on the exterior domain in ${\mathbb{R}}^n,n\ge 3$, where the boundary and far field conditions are prescribed. We show that in some case where the corresponding 1-D Riemann problem for the non-viscous part admits a shock wave, the solution tends toward a linear superposition of stationary and rarefaction waves as time goes to infinity, and also show the decay rate estimates. Furthermore, we improve the results on the asymptotic stability of the stationary waves which are treated in the previous papers [2], [3]. Finally, for the case of $n=3$, we give the complete classification of the asymptotic behaviors, which includes even a linear superposition of stationary and viscous shock waves.