Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Regularity of Harmonic Functions in Cheeger-Type Sobolev Spaces

We give a geometric approach to the study of the regularity of harmonic functions in Cheeger-type Sobolev spaces, and prove the Hölder continuity of such functions. In the proof, we give a definition of an upper curvature bound of the unit sphere of a Banach space, which seems to be of independent interest.     

Products, cones, and suspensions of spaces with the measure contraction property

This article concerns several geometric properties of metricmeasure spaces satisfying the measure contraction property (MCP),which can be considered as a generalized notion of lower Riccicurvature bounds. We prove that the MCP of spaces descends totheir products and Euclidean cones. We also show that a positivelycurved space in terms of the MCP with a maximal diameter canbe represented as the spherical suspension of some topologicalmeasure space.     

Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations

We study here instability problems of standing waves for the nonlinear Klein–Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave's frequency or the wave's speed of propagation and on the nonlinearity.     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

Formation of non-racemic E- and Z-olefins based on discrimination of enantiotopic carbonyl groups in α-diketones by a chiral phosphonate reagent

A chiral HWE reagent reacted with an alternative carbonyl group of meso-α-diketones of bicyclo[2.2.1] system to give non-racemic (Z)- and (E)-olefins, respectively.     

Electrothermal atomic-absorption spectrometry of arsenic and its application to environmental samples

Electrothermal atomization of arsenic with a metal micro-tube atomizer has been studied. Thiourea and thionalide were found to give effective atomization of arsenic. A method involving extraction of the thionalide complex for determining traces of arsenic in water and soil is described.     

Bioactive constituents of chinese natural medicines. VI. Moutan cortex. (2): structures and radical scavenging effects of suffruticosides A, B, C, D, and E and galloyl-oxypaeoniflorin

Five paeonol glycosides, suffruticosides A, B, C, D, and E, and a monoterpene glucoside, galloyl-oxypaeoniflorin, were isolated from the glycosidic fraction of Chinese Moutan Cortex, the root cortex of Paeonia suffruticosa Andrews, together with paeonolide, apiopaeonoside, galloyl-paeoniflorin, oxypaeoniflorin, and paeoniflorin. The structures of five suffruticosides and galloyl-oxypaeoniflorin were elucidated on the basis of chemical and physicochemical evidence. Suffruticosides A, B, C, and D, galloyl-oxypaeoniflorin, and galloyl-paeoniflorin exhibited more potent radical scavenging effects than alpha-tocopherol.