A Single Server Poisson Input Queue with a Second Optional Channel

Consider an M/G/1 queue such that over and above the first essential service having a general service time distribution, a unit may need a second optional service with another independent general service time. A unit may depart from the system either after the first essential service with probability (1–r) or at the end of the first service may immediately go for a second service with probability r (0r1). This is a generalization of a recent paper considered by Madan [5].     

Exceptional Families, Topological Degree and Complementarity Problems

By using the topological degree we introduce the concept of exceptionalfamily of elements specifically for continuous functions. This has importantconsequences pertaining to the solvability of the explicit, the implicit andthe general order complementarity problems. In this way a new direction forresearch in the complementarity theory is now opened.     

On a problem of H. N. Gupta

It is shown that the axiom For any points x, y, z such that y is between x and z, there is a right triangle having x and z as endpoints of the hypotenuse and y as foot of the altitude to the hypotenuse, when added to three-dimensional Euclidean geometry over arbitrary ordered fields, is weaker than the axiom Every line which passes through the interior of a sphere intersects that sphere.     

Algebraic K-Theory and Twisted Reciprocity Laws

We extend the classical reciprocity laws of algebraic number theory to higher odd K-groups of algebraic integers. Moreover, we show that a suitable renormalisation of the corresponding twisted Legendre symbols is independent in the average from the chosen prime when the number field considered is Galois over Q. This seems new even in the classical case.     

Five Kinds of Maximal Monotonicity

We discuss Gossez's type (D) maximal monotone multifunctions and the newer type (ED) subfamily (for which an analog of the Brøndsted-Rockafellar property holds). We then discuss the locally maximal monotone (= type (FP)) and maximal monotone locally (= type (FPV)) multifunctions of Fitzpatrick-Phelps and Fitzpatrick-Phelps-Verona-Verona. Finally, we discuss the strongly maximal monotone multifunctions. We prove that every maximal monotone multifunction of type (D) is locally maximal monotone, and every maximal monotone multifunction of type (ED) is both maximal monotone locally and strongly maximal monotone.     

Some Geometric Aspects of Integrability of Differential Equations in Two Independent Variables

The relation between scalar evolution equations which are the integrability condition of sl(2,R)-valued linear problems with parameter (kinematic integrability) and those which possess recursion operators (formal integrability) is studied: using that kinematically integrable equations describe one-parameter families of pseudo-spherical surfaces and vice versa, it is shown that every second order formally integrable evolution equation is kinematically integrable, and that this result cannot be extended as proven to the third-order case.Conservation laws of kinematically integrable equations obtained from their underlying pseudo-spherical structure are compared with the ones one finds from the Riccati equation version of their associated linear problems. Symmetries (generalized/nonlocal) for these equations are also studied, by considering infinitesimal deformations of the associated pseudo-spherical surfaces.Finally, conservation laws for equations describing pseudo-spherical surfaces immersed in a flat three-space are found, and the class of equations describing Calapso–Guichard surfaces is introduced.     

Experiments with an interactive paired comparison simplex method for molp problems

In this paper, an interactive paired comparison simplex based method formultipleobjectivelinearprogramming (MOLP) problems is developed and compared to other interactive MOLP methods. Thedecisionmaker (DM)'s utility function is assumed to be unknown, but is an additive function of his known linearized objective functions. A test for utilityefficiency for MOLP problems is developed to reduce the number of efficient extreme points generated and the number of questions posed to the DM. The notion of strength ofpreference is developed for the assessment of the DM's unknown utility function where he can express his preference for a pair of extreme points as strong, weak, or almost indifferent. The problem of inconsistency of the DM is formalized and its resolution is discussed. An example of the method and detailed computational results comparing it with other interactive MOLP methods are presented. Several performance measures for comparative evaluations of interactive multiple objective programming methods are also discussed.All rights reserved. This study, or parts thereof, may not be reproduced in any form without written permission of the authors.     

Compressible flow induced by the transient motion of a wavemaker

The effect of fluid compressibility on the evolution of the pressure distribution and free surface elevation, following the initiation of a horizontal motion of a vertical wavemaker, is analysed. This effect is significant even in a liquid (like water) when the time scale of the motion is very short (e.g. impulsive motions).In the leading order the present problem is analogous to that of supersonic flow about a thin wing, thus the solution is represented by means of an appropriate supersonic source distribution. Closed-form results are obtained for the case of impulsive motion (i.e. a step function velocity). The pressure field corresponds to systems of double rarefaction and double compression waves traversing the fluid domain intermittently. Following the passage of a rarefaction (compression) wave, the free surface becomes locally concave (convex). The resulting free surface profile consists of an elongating wavetrain in front of a jet riding up the vertical wall.On the compressible time-scale the pressure and velocity fields approach a steady long-time limit. This limit corresponds to the short-time incompressible flow prevailing after the attenuation of the pressure waves. The spatial nonuniformity of the asymptotic expansion in the neighbourhood of the waterline is briefly discussed.     

Gauss sums for symplectic groups over a finite field

For a nontrivial additive character and a multiplicative character of the finite field withq elements, the Gauss sums (trg) overgSp(2n,q) and (detg)(trg) overgGSp(2n, q) are considered. We show that it can be expressed as a polynomial inq with coefficients involving powers of Kloosterman sums for the first one and as that with coefficients involving sums of twisted powers of Kloosterman sums for the second one. As a result, we can determine certain generalized Kloosterman sums over nonsingular matrices and generalized Kloosterman sums over nonsingular alternating matrices, which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.Supported in part by Basic Science Research Institute program, Ministry of Education of Korea, BSRI 95-1414 and KOSEF Research Grant 95-K3-0101 (RCAA)Dedicated to my father, Chang Hong Kim     

‘Outside’ as a primitive notion in constructive projective geometry

In intuitionistic (or constructive) geometry there are positive counterparts, apart and outside, of the relations = and incident. In this paper it is shown that the relation outside suffices to define incident, apart and equality. The equivalence of the new system with Heyting's system is shown and as a simple corollary one obtains duality for intuitionistic projective geometry.     

d≤1 ∪d≥25 and constrained KP hierarchy from BRST invariance in thec≠3 topological algebra

The BRST invariance condition in a highest-weight representation of the topological ( twisted N=2) algebra captures the invariant content of two-dimensional gravity coupled to matter. The topological algebra allows reductions to either the DDK-dressed matter or the Kontsevich-Miwa-dressed matter related to Virasoro-constrained KP hierarchy. The standard DDK formulation is recovered by splitting the topological generators into c=–26 reparametrization ghosts + matter + Liouville, while a similar splitting involving c=–2 ghosts gives rise to the matter dressed in exactly the way required in order that the theory be equivalent to Virasoro constraints on the KP hierarchy. The two dressings of matter with the Liouville differ also by their ghost numbers, which is similar to the existence of representatives of BRST cohomologies with different ghost numbers. The topological central charge c3 provides a two-fold covering of the allowed regiond1 d25 of the matter central charge d via d=(c+1)(c+6)/(c–3). The Liouville field is identified as the ghost-free part of the topological U(1) current. The construction thus allows one to establish a direct relation (presumably an equivalence) between the Virasoro-constrained KP hierarchies, minimal models, and the BRST invariance condition for highest-weight states of the topological algebra.Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 239–250, May, 1993.     

A nonlinear equation for linear programming

We present a characterization of the normal optimal solution of the linear program given in canonical form max{c ^tx: Ax = b, x 0}. (P) We show thatx ^* is the optimal solution of (P), of minimal norm, if and only if there exists anR > 0 such that, for eachr R, we havex ^* = (rc – A^t_r)₊. Thus, we can findx ^* by solving the following equation for _r A(rc – A^t_r)₊ = b. Moreover,(1/r) _r then converges to a solution of the dual program.On leave from The University of Alberta, Edmonton, Canada. Research partially supported by the National Science and Engineering Research Council of Canada.     

Geometric modules and algebraicK-homology theory

Letp: XZ be a continuous map into a (proper) metric space. Using a variation on the geometric modules of Quinn, we associate top (and any reasonable ringR) an additive category (p, R). Mapsp, as above, are the objects of a category on which (-,R) becomes functorial. By composing with an open cone construction, we get a functor which associates to any topological space over a compact Lipschitz space an additive category. Finally, by using the algebraicK-theory spectrum for an additive category, we arrive at a functor which is our main object of study. We show that it is a homology theory in a suitable sense and we derive an Atiyah-Hirzebruch type spectral sequence for its calculation in many cases, including all triangulated objects. On our way, we show that the boundedK-theory of Pedersen and Weibel is essentially a special case of the boundedly controlledK-theory defined earlier by the authors and we establish a close connection, at least philosophically, between the latter theory and the K-theory with -control developed by Chapman, Ferry and Quinn.Partially supported by the NSF under grants numbered DMS-8504320 and DMS-8803149.Partially supported by the SNF (Denmark) under grants numbered 11-7062 and 11-7792.     

Linearity properties of Shimura varieties, II

Let A=A_{g, 1, n} denote the moduli scheme over Z[1/N] of p.p. g-dimensional abelian varieties with a level n structure; its generic fibre can be described as a Shimura variety. We study its Shimura subvarieties. If x A is an ordinary moduli point in characteristic p, then we formulate a local linearity property in terms of the Serre–Tate group structure on the formal deformation space (= formal completion of A at x). We prove that an irreducible algebraic subvariety of A is a Shimura subvariety if, locally at an ordinary point x, it is formally linear. We show that there is a close connection to a differential-geometrical linearity property in characteristic 0.We apply our results to the study of Oort's conjecture on subvarieties Z A with a dense collection of CM-points. We give a reformulation of this conjecture, and we prove it in a special case.     

The Brownian loop soup

We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.Cornell University; Research supported in part by the National Science FoundationUniversité Paris-Sud and IUFMathematics Subject Classification (2000):60J65, 81T40     

Generalized logic and the representation of rings

Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation.     

An approximate load-deflection relation for a long half-cylindrical tube compressed between parallel plates

Based on a new exact solution for finite elastic deformations of an incompressible Mooney material an approximate load-deflection relation is formulated for the problem of a long rubber halfcylindrical tube which is compressed uniformly along its length between parallel rigid metal plates. This solution includes a transition from a one-point contact to a two-point contact problem and the load-deflection relation obtained is approximate in the sense that boundary conditions of stress are satisfied in an average or mean sense only.

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Zusammenfassung Auf der Basis einer exakten Lösung für endliche elastische Deformationen eines inkompressiblen Mooney-Materials wird eine angenäherte Beziehung zwischen Last und Deformation formuliert für den Fall einer langen halbzylindrischen Gummiröhre, die gleichförmig über ihre gesamte Länge zwischen parallelen steifen Platten komprimiert wird. Diese Lösung schliesst den Übergang von Einpunkt- zu Zweipunktkontakt ein. Die Beziehung zwischen Last und Deformation ist angenähert in dem Sinne, dass die Randbedingungen der Spannungsverteilung nur im Mittel befriedigt sind.

     

La conjecture de Novikov pour les feuilletages hyperboliques

Nous définissons la notion de bolicité pour les feuilletages, qui est une notion plus faible que l'hyperbolicité de Gromov, et nous démontrons la conjecture de Novikov pour les feuilletages boliques à base compacte dont le groupoï de d'holonomie est séparé en établissant l'injectivité de l'application de Baum–Connes. Ce résultat généralise celui de Kasparov et Skandalis obtenu dans le cas des groupes boliques.We define the notion of bolicity for foliations, which is a weaker notion than Gromov's hyperbolicity, and we prove the Novikov conjecture for foliations with compact base and whose holonomy groupoid is Hausdorff, by showing that the Baum–Connes map is injective. This result generalizes that of Kasparov and Skandalis in the case of bolic groups.     

Differences of Convex Compact Sets in the Space of Directed Sets. Part I: The Space of Directed Sets

A normed and partially ordered vector space of so-called directed sets is constructed, in which the convex cone of all nonempty convex compact sets in R ⁿ is embedded by a positively linear, order preserving and isometric embedding (with respect to a new metric stronger than the Hausdorff metric and equivalent to the Demyanov one). This space is a Banach and a Riesz space for all dimensions and a Banach lattice for n=1. The directed sets in R ⁿ are parametrized by normal directions and defined recursively with respect to the dimension n by the help of a support function and directed supporting faces of lower dimension prescribing the boundary. The operations (addition, subtraction, scalar multiplication) are defined by acting separately on the support function and recursively on the directed supporting faces. Generalized intervals introduced by Kaucher form the basis of this recursive approach. Visualizations of directed sets will be presented in the second part of the paper.