Oscillation of certain partial difference equations

In this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients, which may change sign. We obtain oscillation criteria for these equations. There are no results for the oscillation of these equations up to now.     

A new alternating‐direction finite element method for hyperbolic equation

A modified backward difference time discretization is presented for Galerkin approximations for nonlinear hyperbolic equation in two space variables. This procedure uses a local approximation of the coefficients based on patches of finite elements with these procedures, a multidimensional problem can be solved as a series of one‐dimensional problems. Optimal order H₀¹ and L² error estimates are derived. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A new generalized algebra method and its application in the (2 + 1) dimensional Boiti–Leon–Pempinelli equation

In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics.     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

Superferromagnetic state of α-Fe in Fe implanted Co6Ag94 studied by Mössbauer spectroscopy

After having introduced by ion implantation ⁵⁷Fe to a local concentration of 7 at% into Co₆Ag₉₄, we observed it by conversion electron Mössbauer spectroscopy in the as-prepared state and after isochronal annealing. A superferromagnetic state is inferred, which is correlated with the ordering of the magnetic moments on the Fe clusters through chain-like or dendritic Co/Fe linear structures. The magnetic moment disordering temperature lies above 473 K.     

The spectrum of BSA(v, 3, λ; α) with α = 2,3

In this article, a kind of auxiliary design BSA^* for constructing BSAs is introduced and studied. Two powerful recursive constructions on BSAs from 3‐IGDDs and BSA^*s are exploited. Finally, the necessary and sufficient conditions for the existence of a BSA(v, 3, λ; α) with α = 2, 3 are established. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 61–76, 2007     

A simple model for high fluence ultra-short pulsed laser metal ablation

The ultra-short laser metal ablation is a very complex process, the complete simulation of which requires applications of complicated hydrodynamics or molecular dynamics models, which, however, are often time-consuming and difficult to apply. For many practical applications, where the laser ablation depth is the main concern, a simplified model that is easy to apply but at the same time can also provide reasonably accurate predictions of ablation depth is very desirable. Such a model has been developed and presented in this paper, which has been found to be applicable for laser pulse duration up to 10 ps based on comparisons of model predictions with experimental measurements.     

The Monitoring System Using FOBG Sensor for The Health of the Rocket

A novel heath monitoring system of the rocket based on fiber optic Bragg gratings is brought forward, its component units and working principle are also described.     

Adaptive regulation for deterministic systems

For the linear deterministic system with unknown orders and coefficients adaptive controls are given so that the closed-loop system is stabilized and the unknown parameters are consistently estimated. Moreover, if the parameter estimation is ignored, then the system input and output can be reduced to zero with an exponential rate.This project is supported by the National Natural Science Foundation of China.In Commemoration of the 15th Anniversary of the Acta Mathematicae Applicatae Sinica.