三角代数上 Jordan 积为幂等元处的高阶ξ-Lie 可导映射

设U=Tri（A，M，B）是三角代数，{φ_n}_n∈N：U→U是一列线性映射.本文利用代数分解的方法，证明了如果对任意U，V∈U且U?V=P为标准幂等元，有φ_n（[U，V]_ξ=Σ_i+j=n（φ_i（U）φ_j（V）-ξφ_i（V）φ_j（U））（ξ≠1），则{φ_n}_n∈N是一个高阶导子，其中φ₀=id为恒等映射，U?V=UV+VU为Jordan积，[U，V]_ξ=UV-ξVU为ξ-Lie积.     

Higher order asymptotic solution of mode I crack growth in elastic-perfectly plastic media

A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-I quasi-static steady crack growth in the incompressible (v=1/2) elastic perfectly-plastic media. The results show that the near-tip stress and strain are fully continuous, and the strain possesses In (A/r) singularity at the crack tip. The expressions of the stress, strain and velocity in each region are also given. The project supported by National Natural Science Foundation of China     

关于工业产品生产许可证管理的探讨

对工业产品生产许可证管理方面存在的一些问题进行了探讨。经分析认为,在做好实地核查及证后监管的前提下,生产许可证制度的关键在于宣贯和相关细节的明确上。     

Obtaining certificates for complete synchronisation of coupled oscillators

In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson’s Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators.     

A generating function for the cubic interactions of higher spin fields

We present an off-shell generating function for all cubic interactions of higher spin gauge fields constructed in Manvelyan et al. (2010) [1]. It is a generalization of the on-shell generating function proposed by Sagnotti and Taronna [2], is written in a very compact way, and turns out to have a remarkable structure.     

Dynamics of the infinitely-thin kink

We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes - implicit collective coordinates - is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.     

Convolution powers of complex functions on

Repeated convolution of a probability measure on leads to the central limit theorem and other limit theorems. This paper investigates what kinds of results remain without positivity. It reviews theorems due to Schoenberg, Greville, and Thomée which are motivated by applications to data smoothing (Schoenberg and Greville) and finite difference schemes (Thomée). Using Fourier transform arguments, we prove detailed decay bounds for convolution powers of finitely supported complex functions on . If M is an hermitian contraction, an estimate for the off‐diagonal entries of the powers of is obtained. This generalizes the Carne–Varopoulos Markov chain estimate.     

Uniqueness of complete spacelike hypersurfaces via their higher order mean curvatures in a conformally stationary spacetime

We study complete noncompact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds endowed with a timelike conformal vector field V. In this setting, by using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds, we establish new characterizations of totally umbilical hypersurfaces in terms of their higher order mean curvatures. For instance, supposing an appropriated restriction on the norm of the tangential component of the vector field V, we are able to show that such hypersurfaces must be totally umbilical provided that either some of their higher order mean curvatures are linearly related or one of them is constant. Applications to the so‐called generalized Robertson‐Walker spacetimes are given. In particular, we extend to the Lorentzian context a classical result due to Jellett  29 .     

一类具非线性边界条件的高阶方程的双参数奇摄动问题

研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性.