Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.     

Are there more than five linearly-independent collision invariants for the Boltzmann equation?

The problem of finding the summational collision invariants for the Boltzmann equation is tackled with the aim of proving that the most general solution of the problem is not different from the standard one even when the equation defining a collision invariant is only satisfied almost everywhere inR ³×R ³×S ². The collision invariant is assumed to be in the Hilbert spaceH of the functions which are square integrable with respect to a Maxwellian weight.     

Structure and protonation of some indolizine derivatives studied by ab initio MO calculations

Some gauge invariant atomic orbitals-coupled-perturbed Hartree-Fock (GIAO-CPHF) calculations were performed for seven indolizine derivatives and their monoprotonated forms. Chemical shift, molecular geometry, and charge distribution data are reported for each molecule. The calculations support the results of nuclear magnetic resonance (NMR) spectroscopy measurements showing that protonation occurs preferentially at N1. The good agreement between the calculated and observed ¹³C and ¹⁵N chemical shifts show that such calculations can be used for chemical shift assignment purposes. Cation structures and probable sites for electrophilic reaction or second protonation are also discussed.     

排序集抽样下Inverse Rayleigh分布的Fisher信息量及其在参数估计中的应用

文章分别在简单随机抽样和排序集抽样下研究了Inverse Rayleigh分布中对应样本所含刻度参数θ的Fisher信息量.数值结果表示,同等样本容量的排序集样本比简单随机样本提供更多关于θ的信息.接着分别基于简单随机样本和排序集样本构造了θ的一些优良估计,并对估计结果进行了数值比较.     

旋转输液管动力稳定性理论分析北大核心CSCD

基于Lagrange原理和假设模态法建立了旋转输液管的动力学模型.通过降阶升维的方法求解系统的特征值问题,并分析了旋转输液管自由振动特性.得到了不同端部集中质量和转速下,系统特征值随流速升高的演变轨迹.揭示了临界流速随系统参数的变化规律.研究发现,内部流体的流动对旋转输液管动力学特性存在显著影响.在某些参数组合下,系统低阶模态能够形成不同形式的内共振关系.预示了旋转输液管模型蕴含丰富的动力学现象.     

General constructions of biquandles and their symmetries

Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set theoretic solutions of the well-known Yang-Baxter equation. The first half of this paper proposes some natural constructions of biquandles from groups and from their simpler counterparts, namely, quandles. We completely determine all words in the free group on two generators that give rise to (bi)quandle structures on all groups. We give some novel constructions of biquandles on unions and products of quandles, including what we refer as the holomorph biquandle of a quandle. These constructions give a wealth of solutions of the Yang-Baxter equation. We also show that for nice quandle coverings a biquandle structure on the base can be lifted to a biquandle structure on the covering. In the second half of the paper, we determine automorphism groups of these biquandles in terms of associated quandles showing elegant relationships between the symmetries of the underlying structures.     

Homology and cohomology intersection numbers of GKZ systems

We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twisted period relation, we obtain a formula of cohomology intersection numbers in terms of a Laurent series. We show that the cohomology intersection number depends rationally on the parameters. We also prove a conjecture of F. Beukers and C. Verschoor on the signature of the monodromy invariant hermitian form.     

Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.     

Complex homogeneous spaces of real groups with top homology in codimension two

SupposeX=G/H is a connected homogeneous complex manifold, whereG is a Lie group andH is a closed subgroup. Assume (X) and letG/H G/I be the holomorphic reduction ofX. If the top nonvanishing homology group ofX with coefficients in ₂ is in codimension two, then either a complex Lie group acts tansitively onG/I (see [3]) orG/I is biholomorphic to the unit disk.Partially supported by NSERC Grant A3494 and by the Deutsche Forschungsgemeinschaft     

Multiple separatrix crossing in multi-degree-of-freedom Hamiltonian flows

Summary We study separatrix crossing in near-integrablek-degree-of-freedom Hamiltonian flows, 2 <k < , whose unperturbed phase portraits contain separatrices inn degrees of freedom, 1 <n <k. Each of the unperturbed separatrices can be recast as a codimension-one separatrix in the 2k-dimensional phase space, and the collection of these separatrices takes on a variety of geometrical possibilities in the reduced representation of a Poincaré section on the energy surface. In general 0 l n of the separatrices will be available to the Poincaré section, and each separatrix may be completely isolated from all other separatrices or intersect transversely with one or more of the other available separatrices. For completely isolated separatrices, transitions across broken separatrices are described for each separatrix by the single-separatrix crossing theory of Wiggins, as modified by Beigie. For intersecting separatrices, a possible violation of a normal hyperbolicity condition complicates the analysis by preventing the use of a persistence and smoothness theory for compact normally hyperbolic invariant manifolds and their local stable and unstable manifolds. For certain classes of multi-degree-of-freedom flows, however, a local persistence and smoothness result is straightforward, and we study the global implications of such a local result. In particular, we find codimension-one partial barriers and turnstile boundaries associated with each partially destroyed separatrix. From the collection of partial barriers and turnstiles follows a rich phase space partitioning and transport formalism to describe the dynamics amongst the various degrees of freedom. A generalization of Wiggins' higher-dimensional Melnikov theory to codimension-one surfaces in the multi-separatrix case allows one to uncover invariant manifold geometry. In the context of this perturbative analysis and detailed numerical computations, we study invariant manifold geometry, phase space partitioning, and phase space transport, with particular attention payed to the role of a vanishing frequency in the limit approaching the intersection of the partially destroyed separatrices. The class of flows under consideration includes flows of basic physical relevance, such as those describing scattering phenomena. The analysis is illustrated in the context of a detailed study of a 3-degree-of-freedom scattering problem.