The existence of nonoscillatory solutions of higher order nonlinear neutral equations

In this work, we consider the existence of nonoscillatory solutions of variable coefficient higher order nonlinear neutral differential equations. Our results include as special cases some well-known results for linear and nonlinear equations of first, second and higher order. We use the Banach contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.     

A novel class of graded cylinders neutral to host shafts of arbitrary cross-sections under torsion

A novel class of graded cylinders is proposed as neutral inclusions inside host shafts of arbitrary cross-section under Saint-Venant's torsion. The graded cylinder is made of cylindrically orthotropic materials with position varying quantities. The profiles of the two distinct shear moduli in the radial and tangential directions follow specific forms based on an arbitrarily selected function along the radial distance. We show that this type of graded cylinders can serve as universal neutral inclusions within host shafts of arbitrary cross-sections. In addition, we find that the associated warping fields can be exactly determined in terms of simple exponents of the selected function. This suggests that, by tuning the gradation parameter, one can manipulate the warping field of the inserted cylinder without disturbing the fields inside the host shaft. This finding is an original contribution to the existing solvable configurations of composite shafts under torsion.     

Electromagnetic processes in a χEFT framework

Recently,we have derived a two–nucleon potential and consistent nuclear electromagnetic currents in chiral effective field theory with pions and nucleons as explicit degrees of freedom.The calculation of the currents has been carried out to include N 3 LO corrections,consisting of two–pion exchange and contact contributions.The latter involve unknown low-energy constants (LECs),some of which have been fixed by fitting the np Sand P-wave phase shifts up to 100 MeV lab energies.The remaining LECs entering the current operator are determined so as to reproduce the experimental deuteron and trinucleon magnetic moments,as well as the np cross section.This electromagnetic current operator is utilized to study the nd and n 3 He radiative captures at thermal neutron energies.Here we discuss our results stressing on the important role played by the LECs in reproducing the experimental data.     

具多偏差变元的一阶泛函微分方程的振动性

本文首先考虑多时滞泛函微分方程的振动性,给出了方程振动的几个新的充分条件.然后,把这些结果推广到微分不等式,并应用于多时滞中立型方程的振动性.     

Delay-Dependent Criterion for Guaranteed Cost Control of Neutral Delay Systems

In this article, the guaranteed cost control problem for a class of neutral delay systems is investigated. A linear--quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be solved easily by various efficient optimization algorithms.     

一类退化中立型微分系统的周期解

该文考虑一类退化中立型微分系统，利用不动点定理，得到了这类系统周期解存在的充分条件．     

On the pth moment exponential stability criteria of neutral stochastic functional differential equations

The paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the Ito type. This investigation can be very complicated, even in many special cases, by using usual methods based on Lyapunov functionals. In this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations.     

中立型抛物方程解的强迫振动性

本文讨论中立型抛物方程解的强迫振动，其中Ω是Rn中具有光滑边界Ω的有界区域，     

Nonlinear Sigma Models in (1+2) Dimensions and an Infinite Number of Conserved Currents

In this Letter, we treat nonlinear sigma models such as the C P¹-model, Q P¹-model, etc. in 1+2 dimensions. For submodels of such models, we definitely construct an infinite number of nontrivial conserved currents. Our result is a generalization of Alvarez, Ferreira and Guillen.     

The Patterson–Sullivan Embedding and Minimal Volume Entropy for Outer Space

Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map from the Culler–Vogtmann outer space CV (F _k ) into the space of projectivized geodesic currents on a free group. We prove that this map is a continuous embedding and thus obtain a new compactification of the outer space. We also prove that for every k ≥ 2 the minimum of the volume entropy of the universal covers of finite connected volume-one metric graphs with fundamental group of rank k and without degree-one vertices is equal to (3k − 3) log 2 and that this minimum is realized by trivalent graphs with all edges of equal lengths, and only by such graphs. Received: December 2005, Accepted: March 2006