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.     

Some New Transversality Properties

The theorems of Ceva and Menelaus are concerned with cyclic products of ratios of lengths of collinear segments of triangles or more general polygons. These segments have one endpoint at a vertex of the polygon and one at the intersection point of a side with a suitable line. To these classical results we have recently added a selftransversality theorem in which the suitable line is determined by two other vertices. Here we present additional transversality properties in which the suitable line is determined either by a vertex and the intersection point of two diagonals, or by the intersection points of two pairs of such diagonals. Unexpectedly it turns out that besides several infinite families of systematic cases there are also a few sporadic cases.     

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.     

On a family of pseudorandom binary sequences

Recently, numerous constructions have been given for finite pseudorandom binary sequences. However, in many applications, e.g., in cryptography one needs large families of good pseudorandom sequences. Very Recently L.~Goubin, C.~Mauduit, A.~Sárkzy succeeded in constructing large families of pseudorandom binary sequences based on the Legendre symbol. In this paper we will generate another type of large family of pseudorandom sequences by using the notion of index (discrete logarithm).     

Conformal spaces

A conformal space is a non-singular metric vector space to which has been adjoined a null-cone of points at infinity. We define a conformal space in terms of a higher dimensional coordinate space, and then state and prove a fundamental theorem of conformal geometry.     

Transient solution for a finite capacity M/G a,b /1 queueing system with vacations to the server

In this paper we consider a single server queueing system with Poisson input, general service and a waiting room that allows only a maximum of b customers to wait at any time. A minimum of a customers are required to start a service and the server goes for a vacation whenever he finds less than a customers in the waiting room after a service. If the server returns from a vacation to find less than a customers waiting, he begins another vacation immediately. Using the theory of regenerative processes we derive expressions for the time dependent system size probabilities at arbitrary epochs.     

Moduli of smoothness and best approximation in the spacesL p , 0<p<1

L ^p , 0<<1, .     

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.     

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.

     

Chains and Trees: ‘Strong’–‘Weak’ Order in Job Scheduling

We present a summary of recent NP-hardness and polynomial time solvability results for the distinction between strong and weak precedence for chains and trees in scheduling. We distinguish between chains and proper trees which are not chains, and demonstrate that the strong-weak precedence distinction for chains is not inclusive with regards to NP-hardness, and conjecture that the same holds for strong-weak tree precedence. The objective is to show that different interpretations for chain and tree order relations in scheduling might have far reaching computational implications.     

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.     

Division Algebras that Ramify only on a Plane Quartic Curve with Simply Connected Components

A central division algebra over the field of rational functions in two variables with coefficients over an algebraically closed field ramifies along a divisor on P ². If the ramification divisor of is a quartic curve which is the union of simply connected curves, we show that is a symbol algebra and satisfies the index equals exponent equation.     

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].     

Аппроксимация субга рмонических функций

The following statement is proved. Letu be a subharmonic function in the region and _u the associated measure. Then there exists a functionf holomorphic in and such that if _f is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for= _u and for= _f . In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.

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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.     

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.     

Minimaxtheoreme und das Integraldarstellungsproblem

In the present paper conditions for the strict determinateness of two-person zero-sum games are considered. In order to get such minimax theorems we first study games with concave-convex pay-off function. If a game does not have this convexity property one usually passes to a mixed extension where both players are allowed to use probability measures (-additive randomizations) or, more generally, probability contents (finitely additive randomizations) as mixed strategies. By means of a very general minimax theorem for such finitely additive randomizations it can be shown that the problem of strict determinateness of -additive randomizations is equivalent to an integral representation problem. The latter is investigated in the last paragraph.

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Diese Arbeit enthält einen Teil der Ergebnisse der Habilitationsschrift des Verfassers.     

Matrix Units for Signed Brauer’s Algebras

Brauers centerlizer algebras have a basis consisting of undirected graphs. Signed Brauers algebras have a basis consisting of directed graphs, which generalizes Brauers algebras. In this paper, we compute a complete set of matrix units of Signed Brauers algebras.AMS Subject Classification: 99c:16028, 16S99(16K20).