Proximity between life distributions and exponential distributions (II)

This paper is a continuation of the foregoing one [1]. In this paper, we study the proximity between exponential distributions and life distributions in variousW-type classes, whereW-type classes indicate DFR, DFRA, NWU, NWUE, IMRL and HNWUE.This research was partially supported by the National Natural Science Foundation of China.     

A non-increasing Lindley-type equation

In this paper we study the Lindley-type equation W=max {0,B−A−W}. Its main characteristic is that it is a non-increasing monotone function in its main argument W. Our main goal is to derive a closed-form expression of the steady-state distribution of W. In general this is not possible, so we shall state a sufficient condition that allows us to do so. We also examine stability issues, derive the tail behaviour of W, and briefly discuss how one can iteratively solve this equation by using a contraction mapping. This research has been carried out when the author was affiliated with EURANDOM, The Netherlands.     

On the spanning trees of weighted graphs

Given a weighted graph, letW ₁,W ₂,W ₃,... denote the increasing sequence of all possible distinct spanning tree weights. Settling a conjecture due to Kano, we prove that every spanning tree of weightW ₁ is at mostk–1 edge swaps away from some spanning tree of weightW _k . Three other conjectures posed by Kano are proven for two special classes of graphs. Finally, we consider the algorithmic complexity of generating a spanning tree of weightW _k .This work was supported in part by a grant from the AT&T foundation and NSF grant DCR-8351757.Primarily supported by a 1967 Science and Engineering Scholarship from the Natural Sciences and Engineering Research Council of Canada.     

Reciprocity of growth functions of Coxeter groups

The growth series W(t) of a Coxeter system (W, S) is always a rational function. We prove that for a very general class of infinite Coxeter groups, this function satisfies W(t ^–1)=±W(t).Partially supported by NSF grant DMS-8905378.     

The entropies of renewal systems

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX _W ⊂A ^Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems. The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716.     

Configurations of weighted circles in finite inversive planes

A weighted configurationW of circles in I(n), a finite inversive plane of ordern, is an incidence structure in I(n) whose blocks are circles, to each of which is assigned a positive integer called itsweight. W must satisfy the condition that the sum of the weights of the circles meeting at any point must ben + 1. Some properties ofW, particularly whenI(n) is the Miquelian plane M(q), are developed. It is shown that any spreadS in PG(3,q) induces weighted configurations {W(S)} in M(q), calledspecial. Thus properties ofS may be derived from properties ofThis research was supported by NSERC Grant No. A4827 (Canada). The paper was written while the author held a visiting apointment at Clemson University, Clemson, South Carolina.     

The paradox of trees in type theory

We show how to represent a paradox similar to Russell's paradox in Type Theory withW-types and a type of all types, and how to use this in order to represent a fixed-point operator in such a theory. It is still open whether such a construction is possible without theW-type.This research was partly supported by ESPIRIT Basic Research Action Logical Frameworks.     

The Neumann problem for the Laplace equation on general domains

The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set G in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on ∂G. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on G a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed. The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503.     

Worst-case analysis of greedy algorithms for the subset-sum problem

Given a set ofn positive integers and another positive integerW, the Subset-Sum Problem is to find that subset whose sum is closest to, without exceeding,W. We present a polynomial approximation scheme for this problem and prove that its worst-case performance dominates that of Johnson's well-known scheme. Research supported by Ministero Pubblica Istruzion, Italy.     

Algebraically constructible functions and signs of polynomials

LetW be a real algebraic set. We show that the following families of integer-valued functions onW coincide: (i) the functions of the formω →λ(X _ω ), where X _ω are the fibres of a regular morphismf :X →W of real algebraic sets, (ii) the functions of the formω →χ(X _ω ), where X _ω are the fibres of a proper regular morphismf :X →W of real algebraic sets, (iii) the finite sums of signs of polynomials onW. Such functions are called algebraically constructible onW. Using their characterization in terms of signs of polynomials we present new proofs of their basic functorial properties with respect to the link operator and specialization. Research partially supported by an Australian Research Council Small Grant. Second author also partially supported by KBN 610/P3/94.     

Anticipative Stochastic Differential Equations with Non-smooth Diffusion Coefficient

In this paper we prove the existence and uniqueness of the solutions to the one-dimensional linear stochastic differential equation with Skorohod integral Xt（ω）=η（w）＋∫^t 0 asXs（ω）dWs＋∫^t 0 bsXs（ω）ds, t∈[0,1] where （Ws） is the canonical Wiener process defined on the standard Wiener space （W,H,u）, a is non-smooth and adapted, but η and b may be anticipating to the filtration generated by （Ws）. The intention of the paper is to eliminate the regularity of the diffusion coefficient a in the Malliavin sense, in the existing literature. The idea is to approach the non-smooth diffusion coefficient a by smooth ones.     

Seidel-equivalence inLB 3(6) graphs

It is proved that the Seidel-equivalent of aLB ₃(6) graphG with respect to a partition (W ₁,W ₂) of its vertex set is a pseudo-LB ₃(6) graph if and only ifW ₁ consists of six vertices lying on a line ofG. Research supported by NSF Grant GP-20537. At present at Department of Mathematics, University of Bombay, India.     

Regularity results for a class of obstacle problems

We prove some optimal regularity results for minimizers of the integral functional ∫ f(x, u, Du) dx belonging to the class K ≔ {u ∈ W ^1,p (Ω): u ⩾ ψ, where ψ is a fixed function, under standard growth conditions of p-type, i.e.

Nets in Weyl spaces and their metrically equipped subspaces

Let the surfaceW _m⊂W_n be metrically equipped by a normal planeR _n−m. A correspondence between the nets belonging toW _m andW _n is established. Relations between the coefficients of the derivation equations for the fields of directions of the corresponding nets are found. The apparatus for studying the connection between the properties of the corresponding nets is constructed. The influence of the choice that the net belonging toW _m be Chebyshev of the first kind or geodesic or c-net on the corresponding net belonging toW _n is investigated and the results are formulated in theorems 2.6, 2.9, 2.10, 2.11, 2.12 being a generalization of the results received in [2].

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Sunto Supponiamo che la superficieW _m⊂W_n sia dotata di un piano normaleR _n−m. Si stabilisce una corrispondenza tra le reti diW _m e quelle diW _n e si propone un metodo per studiare la relazione tra le proprietà delle reti corrispettive.

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The present investigation is partially supported by the National Science Fund of the Ministry of Science and Education, Republic of Bulgaria under grant MM 528.     

Interpolation and sampling hypersurfaces for the Bargmann-Fock space in higher dimensions

We study those smooth complex hypersurfaces W in having the property that all holomorphic functions of finite weighted L^p norm on W extend to entire functions with finite weighted L^p norm. Such hypersurfaces are called interpolation hypersurfaces. We also examine the dual problem of finding all sampling hypersurfaces, i.e., smooth hypersurfaces W in such that any entire function with finite weighted L^p norm is stably determined by its restriction to W. We provide sufficient geometric conditions on the hypersurface to be an interpolation or sampling hypersurface. The geometric conditions that imply the extension property and the restriction property are given in terms of some directional densities. The first author is supported by projects MTM 2005-08984-Co2-O2 and 2001SGR00611 The third author is partially supported by NSF grant DMS0400909     

The local time of iterated Brownian motion

We define and study the local time process {L ^*(x,t);x¹,t0} of the iterated Brownian motion (IBM) {H(t):=W ₁(|W ₂ (t)|); t0}, whereW ₁(·) andW ₂(·) are independent Wiener processes.Research supported by Hungarian National Foundation for Scientific Research, Grant No. T 016384.Research supported by an NSERC Canada Grant at Carleton University, Ottawa.Research supported by a PSC CUNY Grant, No. 6-66364.     

Non-broken circuits of reflection groups and factorization inD n

The set of non-broken circuits of a reflection group W, denoted NBC(W), appears as a basis of the Orlik-Solomon algebra ofW. The factorization of their enumerating polynomial with respect to their cardinality involves the exponentsd _i-1 ofW. A simple explanation of this factorization is known only for the symmetric groupsS _n (Whitney [13]) and for the hyperoctahedral groupsB _n (Lehrer [7]). In this paper, we present an elementary proof of the fact that the set NBC(W) of any refection groupW is in bijection with the group elements ofW. We give a simple characterization of the non-broken circuits of the Weyl groups of typeD _n and we use this characterization to prove the factorization of their enumerating polynomial. Work partially supported by FGIA from ASU. Work partially supported by NSERC (Canada).     

An obstruction to the positivity of relative Yamabe invariants

For a supergroup , we describe an obstruction to the existence of positive scalar curvature metrics with minimal boundary condition on a compact n-dimensional -manifold W with nonempty boundary M, , in terms of the bordism class [M] in the Stolz obstruction group associated to [St2]. In par ticular, when W is a 5-dimensional spin manifold and the -invariant of a connected component of M is nonzero, we prove that W does not admit a positive scalar curvature metric with minimal boundary condition. Received: 4 July 2001; in final form: 5 February 2002 / Published online: 8 November 2002 RID="*" ID="*" Partially supported by the Grants-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No. 11640070.     

Removable sets for Sobolev spaces

We study removable sets for the Sobolev spaceW ^1,p. We show that removability for sets lying in a hyperplane is essentially determined by their thickness measured in terms of a concept ofp-porosity. The author was partially supported by the NSF and the Academy of Finland, SA-34082.     

Riesz transforms and elliptic PDEs with VMO coefficients

The present paper is concerned withL ^p-theory of the uniformly elliptic differential operator