一类间接控制系统的绝对稳定性问题

利用厄米特二次型和若当标准形理论研究了一般间接控制系统的绝对稳定性问题,给出了绝对稳定性的代数形式的判别准则。所得到的结果是新的和有用的。     

正规Cayley图

综述了自１９９０年以来１２－传递图研究的一些新成果,正规Ｃａｙｌｅｙ图的相关结论。     

Density-Functional Theory Calculations of Normal Modes and Raman Intensities for Tetraazaporphin

The structure, harmonic frequencies, and nonresonance Raman intensities for porphin, tetraazaporphin (TAP), and three of its isotopomers are calculated by the density-functional theory of B3LYP/6-31G(d). Scaling of force constants for porphin in nonredundant natural coordinates is performed. The scaling factors obtained were used to predict the force field and normal modes of TAP and three of its isotopomers. Two alternative methods are used to carry out reliable assignment of the TAP frequencies: wavenumber-linear scaling method and frequency-shift method. There is good agreement between the frequencies predicted within the framework of the three methods used. The conservativeness of the out-of-plane B _2g - and B _3g -modes for porphin and TAP is examined. The Raman spectrum for TAP is simulated. A refinement of the assignment of the experimental frequencies for TAP of even symmetry types on the basis of the calculations performed is made.     

X射线天文望远镜的进展

综述了近年来X射线天文望远镜(如准直型望远镜、编码孔径望远镜、正入射周期多层膜望远镜、掠入射单层膜望远镜和掠入射非周期多层膜望远镜以及新型的“龙虾眼”型望远镜)的发展；阐述了各种X射线天文望远镜工作的原理和成像特点，指出各种X射线天文望远镜之间的性能是相互补充的；简要说明了国内近年来在X射线天文望远镜研究方面取得的进展，并展望了下一步工作．     

Asymptotically optimal neighbour sum distinguishing colourings of graphs

Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1,2,…,k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by . The definition of this parameter, which makes sense for graphs containing no isolated edges, immediately implies that , where Δ is the maximum degree of G. On the other hand, it was conjectured by Flandrin et al. that for all those graphs, except for C₅. We prove this bound to be asymptotically correct by showing that . The main idea of our argument relays on a random assignment of the colours, where the choice for every edge is biased by so called attractors, randomly assigned to the vertices. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 776–791, 2015     

Bifurcations and spatiotemporal patterns in a ratio‐dependent diffusive Holling‐Tanner system with time delay

In this paper, we concentrate on the spatiotemporal patterns of a delayed reaction‐diffusion Holling‐Tanner model with Neumann boundary conditions. In particular, the time delay that is incorporated in the negative feedback of the predator density is considered as one of the principal factors to affect the dynamic behavior. Firstly, a global Turing bifurcation theorem for τ = 0 and a local Turing bifurcation theorem for τ > 0 are given. Then, further considering the degenerated situation, we derive the existence of Bogdanov‐Takens bifurcation and Turing‐Hopf bifurcation. The normal form method is used to study the explicit dynamics near the Turing‐Hopf singularity. It is shown that a pair of stable nonconstant steady states (stripe patterns) and a pair of stable spatially inhomogeneous periodic solutions (spot patterns) could be bifurcated from a positive equilibrium. Moreover, the Turing‐Turing‐Hopf–type spatiotemporal patterns, that is, a subharmonic phenomenon with two spatial wave numbers and one temporal frequency, are also found and explained theoretically. Our results imply that the interaction of Turing and Hopf instabilities can be considered as the simplest mechanism for the appearance of complex spatiotemporal dynamics.     

Remark on the well-posedness of the problem of minimization of integral functionals

In this note, we study the well-posedness of the problem of constrained minimization of an integral functional and show that global well-posedness is equivalent to pointwise well-posedness almost everywhere. Our result extends an earlier one by Zolezzi.This research was supported by NSF Grant No. DMS 88-02688.     

Continuity properties of the normal cone to the level sets of a quasiconvex function

Two main properties of the subgradient mapping of convex functions are transposed for quasiconvex ones. The continuity of the functionxf(x)^–1f(x) on the domain where it is defined is deduced from some continuity properties of the normal coneN to the level sets of the quasiconvex functionf. We also prove that, under a pseudoconvexity-type condition, the normal coneN(x) to the set {x:f(x)f(x)} can be expressed as the convex hull of the limits of type {N(x _n)}, where {x _n} is a sequence converging tox and contained in a dense subsetD. In particular, whenf is pseudoconvex,D can be taken equal to the set of points wheref is differentiable.This research was completed while the second author was on a sabbatical leave at the University of Montreal and was supported by a NSERC grant. It has its origin in the doctoral thesis of the first author (Ref. 1), prepared under the direction of the second author.The authors are grateful to an anonymous referee and C. Zalinescu for their helpful remarks on a previous version of this paper.     

TH型区间值模糊正规子群

本文在区间值模糊集空间上，引入了幂等区间范数ＴＨ，在此基础上，定义了ＴＨ型区间值模糊正规子群，并研究了它的一些性质和结构特征，从而拓广了区间值模糊集的理论。     

超薄靶激光质子加速实验研究

在超短超强飞秒SILEX-Ⅰ激光装置上,开展了薄膜靶激光质子加速的实验研究。实验发现激光预脉冲、靶厚度对质子加速有很大的影响。在激光强度3×1018~3×1019W/cm2条件下,采用前表面厚度为3μm铜、后表面镀4μm厚CH靶,质子的最大能量达到3.15 MeV。而对190 nm厚CH膜靶,质子的最大能量为0.54 MeV。初步研究了激光偏振对质子加速的影响,相同激光功率条件下,圆偏振激光加速产生的质子最大能量略低于P偏振打靶。这些结果与靶后鞘层加速机制相一致。