项链李代数的性质

研究项链李代数的性质,给出了其中心元的表示形式,证明了项链李代数非半单、非可解,通过构造项链李代数的可解非幂零子代数,证明了当箭图中有长度大于1的循环时,项链李代数非幂零.还给出了没有圈的箭图上项链李代数的分解.     

Towards the generalized purely wild inertia conjecture for product of alternating and symmetric groups

We obtain new evidence for the Purely Wild Inertia Conjecture posed by Abhyankar and for its generalization. We show that this generalized conjecture is true for any product of simple Alternating groups in odd characteristics, and for any product of certain Symmetric or Alternating groups in characteristic two. We also obtain important results towards the realization of the inertia groups which can be applied to more general set up. We further show that the Purely Wild Inertia Conjecture is true for any product of perfect quasi p-groups (groups generated by their Sylow p-subgroups) if the conjecture is established for individual groups.     

Binary Quasi-Cyclic Goppa Codes

We obtain here a necessary and sufficient condition for a certain class of binary Goppa code to be quasi-cyclic. We also give another sufficient condition which is easier to check. We define a class of quasi-cyclic Goppa codes. We find the true dimension for a part of those quasi-cyclic codes. and also a class of extended quasi-cyclic codes the minimum distance of which is equal to the designed distance.     

Approximation by matrices with restricted spectra

We investigate the properties of the approximation of a matrix by matrices whose spectra are in a closed convex set of the complex plane. We explain why the Khalil and Maher characterization of an approximant, which spectrum is in a strip, is not quite correct. We prove that their characterization is valid but for another kind of approximation. We formulate a conjecture which leads to some algorithm for computing approximants. The conjecture is motivated by numerical experiments and some theoretical considerations. Separately we consider the approximation of normal matrices.     

Existence,uniqueness and ergodicity of Markov branching processes with immigration and instantaneous resurrection

We consider a modified Markov branching process incorporating with both state-independent immigration and instantaneous resurrection.The existence criterion of the process is firstly considered.We prove that if the sum of the resurrection rates is finite,then there does not exist any process.An existence criterion is then established when the sum of the resurrection rates is infinite.Some equivalent criteria,possessing the advantage of being easily checked,are obtained for the latter case.The uniqueness criterion for such process is also investigated.We prove that although there exist infinitely many of them,there always exists a unique honest process for a given q-matrix.This unique honest process is then constructed.The ergodicity property of this honest process is analysed in detail.We prove that this honest process is always ergodic and the explicit expression for the equilibrium distribution is established.     

On the Guignard constraint qualification for mathematical programs with equilibrium constraints

We recapitulate the well-known fact that most of the standard constraint qualifications are violated for mathematical programs with equilibrium constraints (MPECs). We go on to show that the Abadie constraint qualification is only satisfied in fairly restrictive circumstances. In order to avoid this problem, we fall back on the Guignard constraint qualification (GCQ). We examine its general properties and clarify the position it occupies in the context of MPECs. We show that strong stationarity is a necessary optimality condition under GCQ. Also, we present several sufficient conditions for GCQ, showing that it is usually satisfied for MPECs.     

Covering partially directed graphs with directed paths

We consider graphs which contain both directed and undirected edges (partially directed graphs). We show that the problem of covering the edges of such graphs with a minimum number of edge-disjoint directed paths respecting the orientations of the directed edges is polynomially solvable. We exhibit a good characterization for this problem in the form of a min-max theorem. We introduce a more general problem including weights on possible orientations of the undirected edges. We show that this more general weighted formulation is equivalent to the weighted bipartite b-factor problem. This implies the existence of a strongly polynomial algorithm for this weighted generalization of Euler's problem to partially directed graphs (compare this with the negative results for the mixed Chinese postman problem). We also provide a compact linear programming formulation for the weighted generalization that we propose.     

Characterization and Enumeration of Certain Classes of Tenable Pólya Urns Grown by Drawing Multisets of Balls

We study necessary and sufficient conditions for the strong tenability of Pólya urn schemes under the sampling of multisets of balls. We also investigate sufficient conditions for the tenability (not necessarily in the strong sense) of Pólya urn schemes under the sampling of multisets of balls. We enumerate certain balanced classes and give algorithmic constructions for the replacement matrices for members in the class. We probabilistically analyze the zero-balanced tenable class, and find the asymptotic average proportion of each color, when the starting number of balls is large. We also give an algorithm to determine tenability and construct the Markov chain underlying the scheme, when it is tenable.     

Spherical basis functions and uniform distribution of points on spheres

The main purpose of the present paper is to employ spherical basis functions (SBFs) to study uniform distribution of points on spheres. We extend Weyl's criterion for uniform distribution of points on spheres to include a characterization in terms of an SBF. We show that every set of minimal energy points associated with an SBF is uniformly distributed on the spheres. We give an error estimate for numerical integration based on the minimal energy points. We also estimate the separation of the minimal energy points.     

Wick–Itô formula for regular processes and applications to the Black and Scholes formula

We derive a Wick–Itô formula, that is, an Itô-type formula based on Wick integration. We derive it in the context of regular Gaussian processes which include Brownian motion and fractional Brownian motion with Hurst parameter greater than 1/2. We then consider applications to the Black and Scholes formula for the pricing of a European call option. It has been shown that using Wick integration in this context is problematic for economic reasons. We show that it is also problematic for mathematical reasons because the resulting Black and Scholes formula depends only on the variance of the process and not on its dependence structure.     

Paradoxical Decomposition of Semigroups

We introduce the concept of paradoxical decomposition for semigroups. We show that a semigroup S admits a left paradoxical decomposition if and only if S is not left amenable. Also Rosenbelatt and Willis introduced the configuration concept for groups and showed that amenability of groups is equivalent with existence of normalised solution for any system of configuration equations. We generalise it for semigroups.     

Sparre Andersen模型中破产概率的边界

研究在Andersen Spaxre模型中,当破产概率的初始边界已知的时候,根据更新方程和更新方程中函数的单调性来改进破产概率的边界,并进一步改进了严重损失函数G（x,y）的边界．     

An Algebraic Approach to Knowledge Base Models Informational Equivalence

In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first order knowledge which is based on first order logic. We define categories of knowledge and knowledge base models. These notions are defined for the fixed subject of knowledge. The key notion of informational equivalence of two knowledge base models is introduced. We use the idea of equivalence of categories in this definition. We prove that for finite models there is a clear way to determine whether the knowledge base models are informationally equivalent.     

Rings of invariants for modular representations of elementary abelian <Emphasis Type="Italic">p</Emphasis>-groups

We initiate a study of the rings of invariants of modular representations of elementary abelian p-groups. With a few notable exceptions, the modular representation theory of an elementary abelian p-group is wild. However, for a given dimension, it is possible to parameterise the representations. We describe parameterisations for modular representations of dimension two and of dimension three. We compute the ring of invariants for all two-dimensional representations; these rings are generated by two algebraically independent elements. We compute the ring of invariants of the symmetric square of a two-dimensional representation; these rings are hypersurfaces. We compute the ring of invariants for all three-dimensional representations of rank at most three; these rings are complete intersections with embedding dimension at most five. We conjecture that the ring of invariants for any three-dimensional representation of an elementary abelian p-group is a complete intersection.     

Regularity of harmonic maps into a static Lorentzian manifold

We study the regularity of harmonic maps from Riemannian manifold into a static Lorentzian manifold. We show that when the domain manifold is two-dimensional, any weakly harmonic map is smooth. We also show that when dimension n of the domain manifold is greater than two, there exists a weakly harmonic map for the Dirichlet problem which is smooth except for a closed set whose (n − 2)-dimensional Hausdorff measure is zero.     

Invariants of Characteristics of Some Systems of Partial Differential Equations

We introduce the notion of an invariant of characteristics for a system of first-order partial differential equations. We prove that the existence of invariants is connected with passiveness of some systems. We describe a few methods for construction of new invariants from those already known. We give a scheme for application of the invariants to reduction and integration of systems of partial differential equations. As an application we consider the equation of gas dynamics.     

Partitions of Graphs into Cographs

Cographs from the minimal family of graphs containing K₁ which are closed with respect to complements and unions. We discuss vertex partitions of graphs into the smallest number of cographs, where the partition is as small as possible. We shall call the order of such a partition the c-chromatic number of the graph. We begin by axiomatizing several well-known graphical parameters as motivation for this function. We present several bounds on c-chromatic number in terms of well-known expressions. We show that if a graph is triangle-free, then its chromatic number is bounded between the c-chromatic number and twice this number. We show both bounds are sharp, for graphs with arbitrarily high girth. This provides an alternative proof to a result in [3]; there exist triangle-free graphs with arbitrarily large c-chromatic numbers. We show that any planar graph with girth at least 11 has a c-chromatic number of at most two. We close with several remarks on computational complexity. In particular, we show that computing the c-chromatic number is NP-complete for planar graphs.     

Pluricanonical maps of varieties of maximal Albanese dimension

Let X be a smooth complex projective algebraic variety of maximal Albanese dimension. We give a characterization of in terms of the set . An immediate consequence of this is that the Kodaira dimension is invariant under smooth deformations. We then study the pluricanonical maps . We prove that if X is of general type, is generically finite for and birational for . More generally, we show that for the image of is of dimension equal to and for , is the stable canonical map. Received July 7, 2000 / Published online April 12, 2001     

Existence, uniqueness and ergodicity of Markov branching processes with immigration and instantaneous resurrection

We consider a modified Markov branching process incorporating with both state-independent immigration and instantaneous resurrection. The existence criterion of the process is firstly considered. We prove that if the sum of the resurrection rates is finite, then there does not exist any process. An existence criterion is then established when the sum of the resurrection rates is infinite. Some equivalent criteria, possessing the advantage of being easily checked, are obtained for the latter case. The uniqueness criterion for such process is also investigated. We prove that although there exist infinitely many of them, there always exists a unique honest process for a given q-matrix. This unique honest process is then constructed. The ergodicity property of this honest process is analysed in detail. We prove that this honest process is always ergodic and the explicit expression for the equilibrium distribution is established.     

The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process,which is a stochastic fluid model itself

We introduce the Stochastic Fluid–Fluid Model, which offers powerful modeling ability for a wide range of real-life systems of significance. We first derive the infinitesimal generator, with respect to time, of the driving stochastic fluid model. We then use this to derive the infinitesimal generator of a particular Laplace–Stieltjes transform of the model, which is the foundation of our analysis. We develop expressions for the Laplace–Stieltjes transforms of various performance measures for the transient and limiting analysis of the model. This work is the first direct analysis of a stochastic fluid model that is Markovian on a continuous state space.