The coefficients of a p-adic measure and its Γ-transform

In this paper we show how the coefficients of the power series associated to a p-adic valued measure on _p are related to the coefficients of the measure on 1+p_p associated to the -transform of . In particular, we prove congruences modulo p amongst these coefficients. Finally, we show how these congruences can be used to relate the coefficients of to the -invariant of the Iwasawa series of the -transform of .     

A dissipative transformation with a trivial tail-algebra

Summary In [1], an example was given of a measure-preserving dissipative transformation T in a -finite measure space (X, , ), such that T is conservative in the measure space (X, , ) where . Here we shall show that for this transformation we actually have R ={ØX}[].     

On Subfields of the Hermitian Function Field

The Hermitian function field H= K(x,y) is defined by the equationy ^q+ y=x ^q+1(q being a powerof the characteristic of K). OverK= q ² it is a maximalfunction field; i.e. the numberN(H)of q²-rationalplaces attains the Hasse--Weil upper boundN(H)=q ²+1+2g(H)·q.All subfields K EHare also maximal.In this paper we construct a large number of nonrational subfields EH, by considering the fixed fieldsH under certaingroups type="Italic">g0 that occur as the genus of some maximal function field over q ².     

Estimates for the Distributions of the Sums of Subexponential Random Variables

Let be a random walk with independent identically distributed increments . We study the ratios of the probabilities P(S _n >x) / P(₁ > x) for all n and x. For some subclasses of subexponential distributions we find upper estimates uniform in x for the ratios which improve the available estimates for the whole class of subexponential distributions. We give some conditions sufficient for the asymptotic equivalence P(S > x) E P(₁ > x) as x . Here is a positive integer-valued random variable independent of . The estimates obtained are also used to find the asymptotics of the tail distribution of the maximum of a random walk modulated by a regenerative process.     

Vector-valued stochastic processes. I. Vector measures and vector-valued stochastic processes with finite variation

In this paper we study the relationship _V (M)=E(1 _M dV _S ) between operatorvalued processesV with finite variation V and operator-valued stochastic measures _V with finite variation | _V |. The variations satisfy the inequality | _V | _|V|, which, under certain conditions, is an equality (for example, ifV is measurable).     

A Characterisation of the Generalized Quadrangle Q (5, q) Using Cohomology

If a GQ S of order (s, s) is contained in a GQ S of order (s, s ²) as a subquadrangle, then for each point X of S\S the set of points of S collinear with X form an ovoid of S. Thas and Payne proved that if S= (4,q),q even, and is an elliptic quadric for each XS\S,thenS (5,q). In this paper we provide a single proof for the q odd and q even cases by establishing a link between the geometry involved and the first cohomology group of a related simplicial complex.     

Multiple wiener integrals and nonlinear functionals of a nuclear space valued Wiener process

In this work we develop techniques for the study of nonlinear functionals of a -valued Wiener processW _t, where is the dual of a countably Hilbert nuclear space. We construct stochastic integrals and multiple Wiener integrals of operator-valued processes with respect toW _t. The Wiener decomposition of the space of -valued nonlinear functionals ofW _t is established. We also obtain multiple stochastic integral expansions and representations of -valued nonlinear functionals ofW _t as operator-valued stochastic integrals of Itô type.This research was partially supported by CONACYT grants 22537 and PCEXCNA-040651, and Air Force Office of Scientific Research No. F49620 85 C 0144.Presently at CIMAT, A.P. 402 Guanajuato 36000, GTO, México.     

Staircase kernels for orthogonald-polytopes

LetS be a finite union of boxes inR ^d . Forx inS, defineA _x ={yx is clearly visible fromy via staircase paths inS}, and let KerS denote the staircase kernel ofS. Then KerS={A _x x is a point of local nonconvexity ofS}. A similar result holds with clearly visible replaced by visible and points of local nonconvexity ofS replaced by boundary points ofS.Supported in part by NSF grant DMS-9207019.     

Calculs de facteurs epsilon de paires sur un corps local, II

Let F a locally compact non-Archimedean field, of residue characteristic p, and a nontrivial additive character of F. Let , be irreducible representations of the absolute Weil group of F, each of degree a power of p and not induced from a nontrivial unramified extension of F. We give a formula for the value at , modulo roots of unity in of order a power of p. Via the Langlands correspondence, we get an analogous formula for supercuspidal representations of GL_n(F).     

On Paley-Wiener and Hardy theorems for <Emphasis Type="Italic">NA</Emphasis> groups

Let N be a H-type group and let S=NA be an one dimensional solvable extension of N. For the Helgason Fourier transform on S we prove the following analogue of Hardys theorem. Let (,Y,Z) stand for the Helgason Fourier transform of f and let h denote the heat kernel associated to the Laplace-Beltrami operator. Suppose a function f on S satisfies the conditions |f(x)| ch (x) and for all xS, where being the dimension of the centre of N. Then f=0 or f=ch depending on whether < or =. We also establish a stronger version of Hardys theorem and a Paley-Wiener theorem. These are generalisations of the corresponding results for rank one symmetric spaces of noncompact type.     

The permutational power of a priority queue

A priority queue transforms an input permutation of some set of sizen into an output permutation. It is shown that the number of such pairs (, ) is (n + 1) ^n–1. Some related enumerative and algorithmic questions are also considered.Supported by the National Science and Engineering Research Council of Canada under Grant A4219.     

Weak invariance principles for weightedU-statistics

We prove that the distribution of a properly normalized weightedU-statisticU _n in i.i.d. random variables is close to the distribution of a certain functionV _n in i.i.d. standardized Gaussian random variables in the sense that their Lévy-Prokhorov distance tends to zero asn. This property is then used to determine the limit laws ofU _n under special assumptions on the kernel function. This generalizes a method due to Rotar' who proved similar results for random multilinear forms.     

Transportation cost for Gaussian and other product measures

Consider the canonical Gaussian measure _N on , a probability measure on ^N , absolutely continuous with respect to _N . We prove that the transportation cost of to _N , when the cost of transporting a unit of mass fromx toy is measured by x–y², is at most d. As a consequence we obtain a completely elementary proof of a very sharp form of the concentration of measure phenomenon in Gauss space. We then prove a result of the same nature when _N is replaced by the measure of density 2^–N exp (– _iN |x _i |). This yields a sharp form of concentration of measure in that space.Work partially supported by an NSF Grant.     

Designs and partial geometries over finite fields

Let be a finite field, and let (, B) be a nontrivial 2-(n, k, 1)-design over . Then each point induces a (k–1)-spread S on /. (, B) is said to be a geometric design if S is a geometric spread on / for each . In this paper, we prove that there are no geometric designs over any finite field .Research partially supported by NSF grant DMS-8703229.     

Krasnosel'skii numbers for bounded finitely starlike sets inR d

For eachk andd, 1kd, definef(d, d)=d+1 andf(d, k)=2d if 1kd–1. The following results are established:Let be a uniformly bounded collection of compact, convex sets inR ^d . For a fixedk, 1kd, dim {MM in }k if and only if for some > 0, everyf(d, k) members of contain a commonk-dimensional set of measure (volume) at least.LetS be a bounded subset ofR ^d . Assume that for some fixedk, 1kd, there exists a countable family of (k–l)-flats {H _i :i1} inR ^d such that clS S {H_i i 1 } and for eachi1, (clS S) H _i has (k–1) dimensional measure zero. Every finite subset ofS sees viaS a set of positivek-dimensional measure if and only if for some>0, everyf(d,k) points ofS see viaS a set ofk-dimensional measure at least .The numbers off(d,d) andf(d, 1) above are best possible.Supported in part by NSF grant DMS-8705336.     

The Busy Period of the M/GI/∞ Queue

An equation for the distribution Z() of the duration T of the busy period in a stationary M/GI/ service system is constructed from first principles. Two scenarios are examined, being distinguished by the half-plane Re()>₀ for some ₀0 in which the generic service time random variable S, always assumed to have a finite mean E(S), has an analytic Laplace–Stieltjes transform E(e^–S ). If ₀<0 then E(e^–T ) is analytic in a half-plane (₁,), where ₀₁<0 and ₁ is determined by the distribution of S; then for any 0<s<|₁|.When ₀=0, E(e^–T ) is analytic in (0,), and now more is known about T. Inequalities on the tail () are used to show that for any 1, E(T ) is finite if and only if E(S ) is finite. It follows that the point process consisting of the starting epochs of busy periods is long range dependent if and only if E(S ²)=, in which case it has Hurst index equal to [frac12](3–), where is the moment index of S.If also the tail (x)=Pr{Sx} of the service time distribution satisfies the subexponential density condition ₀ ^x (x–u) (u)du/ (x)2E(S) as x, then (x)/ (x)e^E(S), where is the arrival rate.     

Deformation of a submanifold in an Euclidean space with fixed Gauss image

In a previous paper [4] the present author studied a C mapping where M is an m-dimensional C manifold, I is some interval and for each tI the mapping is an immersion satisfying the following conditions, (i) The Gauss map associated with the immersion is regular. (ii) The Gauss image of the immersed submanifold is fixed against t for each point p of M. Such a mapping was called an admissible deformation. The purpose of the present paper is to give results obtained since then.     

Non removable edges in 3-connected cubic graphs

LetG be a cyclicallyk-edge-connected cubic graph withk 3. Lete be an edge ofG. LetG be the cubic graph obtained fromG by deletinge and its end vertices. The edgee is said to bek-removable ifG is also cyclicallyk-edge-connected. Let us denote by S _k (G) the graph induced by thek-removable edges and by N _k (G) the graph induced by the non 3-removable edges ofG. In a previous paper [7], we have proved that N ₃(G) is empty if and only ifG is cyclically 4-edge connected and that if N ₃(G) is not empty then it is a forest containing at least three trees. Andersen, Fleischner and Jackson [1] and, independently, McCuaig [11] studied N ₄(G). Here, we study the structure of N _k (G) fork 5 and we give some constructions of graphs such thatN _k (G) = E(G). We note that the main result of this paper (Theorem 5) has been announced independently by McCuaig [11].

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Résumé SoitG un graphe cubique cyliquementk-arête-connexe, aveck 3. Soite une arête deG et soitG le graphe cubique obtenu à partir deG en supprimante et ses extrémités. L'arêtee est ditek-suppressible siG est aussi cycliquementk-arête-connexe. Désignons par S _k (G) le graphe induit par les arêtesk-suppressibles et par N _k (G) celui induit par les arêtes nonk-suppressibles. Dans un précédent article [7], nous avons montré que N ₃(G) est vide si et seulement siG est cycliquement 4-arête-connexe et que si N ₃(G) n'est pas vide alors c'est une forêt possédant au moins trois arbres. Andersen, Fleischner and Jackson [1] et, indépendemment, McCuaig [11] ont étudié N ₄(G). Ici, nous étudions la structure de N _k (G) pourk 5 et nous donnons des constructions de graphes pour lesquelsN _k (G) = E(G). Nous signalons que le résultat principal de cet article (Théorème 5) a été annoncé indépendamment par McCuaig [11].

     

Characterization of Certain Holomorphic Geodesic Cycles on Quotients of Bounded Symmetric Domains in terms of Tangent Subspaces

Let be an irreducible bounded symmetric domain and Aut() be a torsion-free discrete group of automorphisms, X /. We study the problem of algebro-geometric and differential-geometric characterizations of certain compact holomorphic geodesic cycles S X. We treat special cases of the problem, pertaining to a situation in which S is a compact holomorphic curve, and to the case where is a classical domain dual to the hyperquadric. In both cases we consider algebro-geometric characterizations in terms of tangent subspaces. As a consequence we derive effective pinching theorems where certain complex submanifolds S X are proven to be totally geodesic whenever their scalar curvatures are pinched between certain computed universal constants, independent of the volume of the submanifold S, giving new examples of the gap phenomenon for the characterization of compact holomorphic geodesic cycles.Research funded by a CERG grant from Research Grants Council of Hong Kong.     

From Ginzburg-Landau to Gross-Pitaevskii

In this note we consider the Gross-Pitaevskii equation i _t ++(1–²)=0, where is a complex-valued function defined on ^N×, and study the following 2-parameters family of solitary waves: (x, t)=e ^it v(x ₁–ct, x), where and x denotes the vector of the last N–1 variables in ^N . We prove that every distribution solution , of the considered form, satisfies the following universal (and sharp) L -bound: