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.     

Invariant Subspaces for Positive Operators Acting on a Banach Space with Markushevich Basis

We introduce weak quasinilpotence for operators. Then, by substituting Markushevich basis and weak quasinilpotence at a nonzero vector for Schauder basis and quasinilpotence at a nonzero vector, respectively, we answer a question on the invariant subspaces of positive operators in [3].     

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.     

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.     

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).     

Parallel Composition of Graph Grammars

The specification of complex systems is usually done by the divide and conquer idea: the system is divided into smaller, less complex components that are developed separately and then merged in some way to form the specification of the whole system. The main aim of this paper is to provide an approach to the parallel composition of graph grammars, formalizing the intuitive idea of divide and conquer described above. This parallel composition of graph grammars provides a suitable formalism for the specification of concurrent systems based on the specifications of their components. Dividing is formalized by special graph grammar morphisms, called specialization morphisms. These morphisms also describe structural and behavioural compatibilities between graph grammars. As a main result, we characterize the parallel composition as the pullback in the category of graph grammars.     

Discrete Series Characters for GL(n, q)

The discrete series characters of the finite general linear group GL(n, q) are expressed as uniquely defined integral linear combinations of characters induced from linear characters on certain subgroups Hd, n of GL(n, q). The coefficients in these linear combinations are determined (for all n, q) by a family of polynomials r(T) Z[T] indexed by the set of all partitions .     

Central Limit Theorems for dependent variables. I

Summary This paper gives a flexible approach to proving the Central Limit Theorem (C.L.T.) for triangular arrays of dependent random variables (r.v.s) which satisfy a weak mixing condition called -mixing. Roughly speaking, an array of real r.v.s is said to be -mixing if linear combinations of its past and future are asymptotically independent. All the usual mixing conditions (such as strong mixing, absolute regularity, uniform mixing, -mixing and -mixing) are special cases of -mixing. Linear processes are shown to be -mixing under weak conditions. The main result makes no assumption of stationarity. A secondary result generalises a C.L.T. that Rosenblatt gave for strong mixing samples which are nearly second order stationary.     

OnU ϕ-sets of trigonometric integrals

, (t) >0 E(–, +),E<, , ¦f(t)¦ (t) xE, f(t)=0 (–, +).     

Foundational Isomorphisms in Continuous Differentiation Theory

We provide an elementary proof of existence for the Foundational Isomorphism in each of the categories of convergence spaces, compactly generated topological spaces and sequential convergence spaces. This isomorphism embodies the germ of differentiation and its inverse the germ of integration.     

A Numerical Comparison of Some Modified Controlled Random Search Algorithms

In this paper we propose a new version of the Controlled Random Search(CRS) algorithm of Price. The new algorithmhas been tested on thirteen global optimization test problems. Numericalexperiments indicate that the resulting algorithm performs considerablybetter than the earlier versions of the CRS algorithms. The algorithm,therefore, could offer a reasonable alternative to many currently availablestochastic algorithms, especially for problems requiring direct searchtype methods. Also a classification of the CRS algorithms is made based onglobal technique – local technique and the relative performance ofclasses is numerically explored.     

Isogeny Covariant Differential Modular Forms and the Space of Elliptic Curves up to Isogeny

The purpose of this article is to develop the theory of differential modular forms introduced by A. Buium. The main points are the construction of many isogeny covariant differential modular forms and some auxiliary (nonisogeny covariant) forms and an extension of the classical theory of Serre differential operators on modular forms to a theory of -Serre differential operators on differential modular forms. As an application, we shall give a geometric realization of the space of elliptic curves up to isogeny.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the biest I. The Walsh case

We prove L^p estimates (Theorem 1.8) for the Walsh model of the biest, a trilinear multiplier with singular symbol. The corresponding estimates for the Fourier model will be obtained in the sequel [11] biest of this paper.     

A Euclidean interpretation of Dynkin diagrams and its relation to root systems

A simple metric property satisfied by bases of (finite, not necessarily reduced) root systems is used to define sets in Euclidean space that provide models for Dynkin diagrams and their positive semidefinite one-vertex extensions. The theory of root systems can be founded on the study of these Dynkin sets, and conversely the Dynkin sets representing connected diagrams can be characterized as the bases and extended bases of root systems. (By an extended base, we mean a base together with the lowest root of a given length.) In this correspondence the role of nonreduced root systems is natural and important.     

Orthonormal systems satisfying an inequality of S. M. Nikol'skii

N- (p, q) (1 pN-, L _p - L _q -. , , , L L _q - , , .     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the biest II. The Fourier case

We prove L^p estimates (Theorem 1.2) for the biest, a trilinear multiplier operator with singular symbol. The methods used are based on the treatment of the Walsh analogue of the biest in the prequel [13] of this paper, but with additional technicalities due to the fact that in the Fourier model one cannot obtain perfect localization in both space and frequency.     

Symmetric Spectra and Topological Hochschild Homology

A functor is defined which detects stable equivalences of symmetric spectra. As an application, the definition of topological Hochschild homology on symmetric ring spectra using the Hochschild complex is shown to agree with Bökstedts original ad hoc definition. In particular, this shows that Bökstedts definition is correct even for nonconnective, nonconvergent symmetric ring spectra.     

‘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.     

Continuation of functionals on ultradifferentiable function spaces

, c _k b _k . . . .

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This work is supported by N.B.H.M. grant No. 48/1/94-R&D-II.