Resolvable Representation of Polyhedra

The paper proposes a new method for the boundary representation of three-dimensional (not necessarily convex) polyhedra, called a resolvable representation , in which small numerical errors do not violate the symbolic part of the representation. In this representation, numerical data are represented partly by the coordinates of vertices and partly by the coefficients of face equations in such a way that the polyhedron can be reconstructed from the representation in a step-by-step manner. It is proved that any polyhedron homeomorphic to a sphere has a resolvable representation, and an algorithm for finding such a representation is constructed. Received January 21, 1997, and in revised form April 29, 1998.     

Representation of Hilbert algebras and implicative semilattices

In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.     

On Generic Extensions of Representations of a Dynkin Quiver of Type D

The notion of generic extensions of representations of a Dynkin quiver plays a big role in the study of the structure of the corresponding quantum group. In this paper, we describe the generic extensions of a simple representation by any representation and that of any representation by a simple representation of a Dynkin quiver Q of type D.     

Continuity and measurability of multiplier and projective representations

It is shown that various kinds of measurability of a multiplier representation of a locally compact group are equivalent, and are equivalent to the continuity of an ordinary representation of a related group. A unitary representation with measurable coefficients is the sum of a strongly continuous representation and a representation all of whose coefficients are locally null functions. Similar results are obtained for projective unitary representations. This work is carried out without any separability assumptions.     

Comparison of Gelfand-Tsetlin Bases for Alternating and Symmetric Groups

Young’s orthogonal basis is a classical basis for an irreducible representation of a symmetric group. This basis happens to be a Gelfand-Tsetlin basis for the chain of symmetric groups. It is well-known that the chain of alternating groups, just like the chain of symmetric groups, has multiplicity-free restrictions for irreducible representations. Therefore each irreducible representation of an alternating group also admits Gelfand-Tsetlin bases. Moreover, each such representation is either the restriction of, or a subrepresentation of, the restriction of an irreducible representation of a symmetric group. In this article, we describe a recursive algorithm to write down the expansion of each Gelfand-Tsetlin basis vector for an irreducible representation of an alternating group in terms of Young’s orthogonal basis of the ambient representation of the symmetric group. This algorithm is implemented with the Sage Mathematical Software.     

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

Regularization and integral representations of Hermite processes

It is known that Hermite processes have a finite-time interval representation. For fractional Brownian motion, the representation has been well known and plays a fundamental role in developing stochastic calculus for the process. For the Rosenblatt process, the finite-time interval representation was originally established by using cumulants. The representation was extended to general Hermite processes through the convergence of suitable partial sum processes. We provide here an alternative and different proof for the finite-time interval representation of Hermite processes. The approach is based on regularization of Hermite processes and the fractional Gaussian noises underlying them, and does not use cumulants nor convergence of partial sums.     

Caractérisations de la représentation de Burau

This paper is devoted to characterizations of the (reduced) Burau representation of the Artin braid group, in terms of rigid local systems. We prove that the Burau representation is the only representation of the Hecke algebra for which some local system associated to every linear representation of the braid group is irreducible and rigid in the sense of Katz. We also use previous results to give a characterization of the corresponding Knizhnik-Zamolodchikov system.     

On the representability of neatly embeddable CA’s by cylindric relativized algebras

Neat embedding theorems yield an abstract algebraic characterization for the representability of a given class of algebras by set algebras. Resek and Thompson’s theorem called attention to a new kind of representation in the theory of cylindric algebras, to the representation by cylindric relativised set algebras. In this paper, we present the algebraic characterization of this kind of representation; we formulate neat embedding theorems for this representation.     

Binary Representations of Finite Fields and Their Application to Complexity Theory

Binary representations of finite fields are defined as an injective mapping from a finite field tol-tuples with components in {0, 1} where 0 and 1 are elements of the field itself. This permits one to study the algebraic complexity of a particular binary representation, i.e., the minimum number of additions and multiplications in the field needed to compute the binary representation. The two-way complexity of a binary representation is defined as the sum of the algebraic complexities of the binary representation and of its inverse mapping. Two particular binary representations are studied: the standard representation and the logarithmic representation. A method of surrogate computation is developed and used to deduce relationships between the algebraic complexities of certain functions. The standard representation of a finite field is shown to be among the two-way easiest representations of this field. In particular, the standard representation of a finite field with characteristicpis two-way easy wheneverp− 1 has only small prime factors. For any finite field having a two-way easy binary representation, the algebraic complexity in this field is shown to be essentially equivalent to Boolean circuit complexity. For any finite field, the Boolean circuit complexity of Zech's (or Jacobi's) logarithm is shown to be closely related to the Boolean circuit complexity of the discrete logarithm problem that is used in public-key cryptography.     

Analysis on the minimal representation of O(p,q) I. Realization via conformal geometry

This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent coadjoint orbit in the philosophy of Kirillov–Kostant. We begin by applying methods from conformal geometry of pseudo-Riemannian manifolds to a general construction of an infinite-dimensional representation of the conformal group on the solution space of the Yamabe equation. By functoriality of the constructions, we obtain different models of the unitary representation, as well as giving new proofs of unitarity and irreducibility. The results in this paper play a basic role in the subsequent papers, where we give explicit branching formulae, and prove unitarization in the various models.     

Hardy空间上复合算子的伴随表示

Hardy空间上的复合算子的伴随算子具有很好的性质,但对一般情形而言,一直没有关于它的明确表达式．Cowen于1988年给出了(?)为D上的线性分式自映射情形时C*(?)的表达式,并且于2000年给出了n个变量情形的推广．他指出,正是由于没有一般情形的C*(?)的表达式,在很大程度上,阻碍了复合算子理论的发展．该文给出了Hardy空间上的复合算子伴随的准确表达式．     

Polynomials with and without determinantal representations

The problem of writing real zero polynomials as determinants of linear matrix polynomials has recently attracted a lot of attention. Helton and Vinnikov [9] have proved that any real zero polynomial in two variables has a determinantal representation. Brändén [2] has shown that the result does not extend to arbitrary numbers of variables, disproving the generalized Lax conjecture. We prove that in fact almost no real zero polynomial admits a determinantal representation; there are dimensional differences between the two sets. The result follows from a general upper bound on the size of linear matrix polynomials. We then provide a large class of surprisingly simple explicit real zero polynomials that do not have a determinantal representation. We finally characterize polynomials of which some power has a determinantal representation, in terms of an algebra with involution having a finite dimensional representation. We use the characterization to prove that any quadratic real zero polynomial has a determinantal representation, after taking a high enough power. Taking powers is thereby really necessary in general. The representations emerge explicitly, and we characterize them up to unitary equivalence.     

The Moments of the M/M/s Queue Length Process

A representation for the moments of the number of customers in a M/M/s queueing system is deduced from the Karlin and McGregor representation for the transition probabilities. This representation allows us to study the limit behavior of the moments as time tends to infinity. We study some consequences of the representation for the mean.     

Galois representations attached to representations of GU(3)

For a fixed prime we compute the -adic Lie algebra of the image of the -adic Galois representation attached to a stable cuspidal automorphic representation of the unitary similitude group GU(3). This result depends on whether admits extra twists in the sense defined below. Two cases emerge: orthogonal image and non-orthogonal image. We show that in the orthogonal case there exists a character such that is the Galois representation attached to the unitary adjoint lift of a cuspidal representation of GL(2). Received: 22 November 1999 / Accepted: 25 July 2000 / Published online: 23 July 2001     

信息不完备条件下地震应急案例结构化方法研究

地震突发事件具有紧迫性、破坏性和信息不完备性,给人民群众生命财产安全造成了重大危害。案例推理是处置突发事件的有效方法。其中,案例表示是案例推理的基础,但是目前的案例表示方法并没有考虑突发事件的信息不完备性。这削弱了突发事件应急案例表示效果,并影响案例检索的准确性和案例适配的效果。本文在研究案例表示方法的基础上,结合案例推理的结构化和定量化需求,将证据理论的基本信任分配函数引入框架表示法中,提出了信息不完备条件下地震应急案例的框架表示法。接下来,本文提出了信息不完备条件下地震应急案例检索方法。最后,文章对提出的信息不完备条件下地震应急案例的结构化方法进行了应用验证。     

Hilbert Module Realization of the Square of White Noise and Finite Difference Algebras

We develop an approach to the representations theory of the algebra of the square of white noise based on the construction of Hilbert modules. We find the unique Fock representation and show that the representation space is the usual symmetric Fock space. Although we started with one degree of freedom we end up with countably many degrees of freedom. Surprisingly, our representation turns out to have a close relation to Feinsilver's finite difference algebra. In fact, there exists a holomorphic image of the finite difference algebra in the algebra of square of white noise. Our representation restricted to this image is the Boukas representation on the finite difference Fock space. Thus we extend the Boukas representation to a bigger algebra, which is generated by creators, annihilators, and number operators.     

基于正交规范化的小波的有限差分表示

本文研究了在时域内小波的一种表达形式.利用正交规范化,获得了小波的有限差分表示.不仅该形式构造了任意次B样条正交小波.而且在时域中用来直接获得小波滤波器是有效的.     

NEW SYMPLECTIC MAPS： INTEGRABILITY AND LAX REPRESENTATION

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