cubic correspondences arising from g 2 we use the automorphic realization of the minimal representation the theta representation of the three fold cover of g 2 to construct a correspondence of automorphic forms between members of dual pairs inside g 2 the dual pairs under consideration are sl2 sl2 and sl3 z 3 in the first case we obtain the shimura correspondence between the three fold cover of sl2 and sl2 through explicit integral formulae in the second case we decompose theta over the three fold cover of sl3 both locally and globally the constituents are parametrized by their central characters and are cuspidal except essentially when the central character is trivial we thus obtain cuspidal theta representations and the unramified theta representation of the three fold cover of sl3

oscillations of delay difference systems this paper is concerned with the oscillatory behavior of a linear difference system either autonomous or nonautonomous criteria for oscillations are obtained in a way that is either dependent on or independent of the delays the structure of the family of delays for which the system exhibits an oscillatory behavior is also analyzed

reasoning with partially ordered information in a possibilistic logic framework in many applications the reliability relation associated with available information is only partially defined while most of existing uncertainty frameworks deal with totally ordered pieces of knowledge partial pre orders offer more flexibility than total pre orders to represent incomplete knowledge possibilistic logic which is an extension of classical logic deals with totally ordered information it offers a natural qualitative framework for handling uncertain information priorities are encoded by means of weighted formulas where weights are lower bounds of necessity measures this paper proposes an extension of possibilistic logic for dealing with partially ordered pieces of knowledge we show that there are two different ways to define a possibilistic logic machinery which both extend the standard one

an assumption based tms abstract this paper presents a new view of problem solving motivated by a new kind of truth maintenance system unlike previous truth maintenance systems which were based on manipulating justifications this truth maintenance system is in addition based on manipulating assumption sets as a consequence it is possible to work effectively and efficiently with inconsistent information context switching is free and most backtracking and all retraction is avoided these capabilities motivate a different kind of problem solving architecture in which multiple potential solutions are explored simultaneously this architecture is particularly well suited for tasks where a reasonable fraction of the potential solutions must be explored

on the nature of the nonoscillatory solutions of a class of neutral delay differential equations consider the neutral delay differential equation ddt x t px t q x t 1 x t 2 0 e where p q 1 and 2 are nonnegative constants for 2 we prove that all nonoscillatory solutions of e are bounded if and only if c the characteristic equation p e q e 1 e 2 0 of e has no positive roots and zero is a simple root if we also prove that condition c is equivalent to 1 p q 1 2 if 2 moreover for the case where 2 we show that c is a necessary and sufficient condition for every nonoscillatory solution x of e to be bounded or such that 0 lim inft 1t 01 x s ds lim supt 1t 01 x s ds

global attractivity in delay differential equations using a mixed monotone technique abstract we derive new sufficient conditions for global attractivity in nonlinear delay differential equations using a mixed monotone technique the equations considered include the equation of the form d dt x t ax t x t bx t f x t where a b and are nonnegative numbers such that a 0 1 b 0 and 1 ae be has a negative root moreover f x is a mixed monotone function that is f x x x where x y is monotone decreasing in x and increasing in y our results are applied to some delay differential equations from mathematical biology

possibilistic logic a retrospective and prospective view possibilistic logic is a weighted logic introduced and developed since the mid 1980s in the setting of artificial intelligence with a view to develop a simple and rigorous approach to automated reasoning from uncertain or prioritized incomplete information standard possibilistic logic expressions are classical logic formulas associated with weights interpreted in the framework of possibility theory as lower bounds of necessity degrees possibilistic logic handles partial inconsistency since an inconsistency level can be computed for each possibilistic logic base logical formulas with a weight strictly greater than this level are immune to inconsistency and can be safely used in deductive reasoning this paper first recalls the basic features of possibilistic logic including information fusion operations then several extensions that mainly deal with the nature and the handling of the weights attached to formulas are suggested or surveyed the leximin based comparison of proofs the use of partially ordered scales for the weights or the management of fuzzily restricted variables inference principles that are more powerful than the basic possibilistic inference in case of inconsistency are also briefly considered the interest of a companion logic based on the notion of guaranteed possibility functions and working in a way opposite to the one of usual logic is also emphasized its joint use with standard possibilistic logic is briefly discussed this position paper stresses the main ideas only and refers to previous published literature for technical details

an extension of the characterization of oscillations to arbitrary functional differential equations via the laplace transform in this paper we consider a functional differential equation of general form using the laplace transform we prove that such an equation has a nonoscillatory solution if and only if the characteristic equation has a real zero

a rankin selberg integral for the adjoint representation of gl3 in this paper we construct steps 1 4 and par t of 2 as formulated at g sh p 19 for the funct ion l s r here is a cusp form on g l a and r is the eight dimensional adjoint representa t ion of g l a the l group of g l 3 to do so we construct a rankin selberg integral using the embedding of sl 3 in gz let us ment ion tha t the langland s conjucture for this l function can not be obta ined by the langlands shahid i method the paper is organized as follows in the first section we collect some informat ion on the s t ructure of gz and compute the space of double cosets p gz sl3 where p is a maximal parabol ic subgroup of g2 in sect two the global integral is const ructed and is shown to be euler ian with whi t t ake r model finally in sect three we carry out the unramif ied computa t ion using the local computa t ion of the integral for gl3 x gl3 as const ructed in i j s for simplicity we shall assume tha t rc has a trivial central character

oscillations of differential difference systems of neutral type this note is concerned with the oscillatory behavior of a linear differential difference system of neutral type criteria for oscillations are obtained for autonomous and nonautonomous systems

a necessary and sufficient condition for oscillation of neutral type hyperbolic equations abstract in the present paper a necessary and sufficient condition is obtained for oscillation of the solutions of neutral type linear hyperbolic differential equations of the form u tt x t l a i u tt x t i u x t j b j t u x j t cu x t k c k u x t k 0 x t 0 g where is a bounded domain in r n with a piecewise smooth boundary and u x t ni 1uxtxt x t

solving conflicts in information merging by a flexible interpretation of atomic propositions although many techniques for merging conflicting propositional knowledge bases have already been proposed most existing work is based on the idea that inconsistency results from the presence of incorrect pieces of information which should be identified and removed in contrast we take the view in this paper that conflicts are often caused by statements that are inaccurate rather than completely false suggesting to restore consistency by interpreting certain statements in a flexible way rather than ignoring them completely in accordance with this view we propose a novel approach to merging which exploits extra logical background information about the semantic relatedness of atomic propositions several merging operators are presented which are based on different formalizations of this background knowledge ranging from purely qualitative approaches related to possibilistic logic to quantitative approaches with a probabilistic flavor both syntactic and semantic characterizations are provided for each merging operator and the computational complexity is analyzed

oscillations caused by several retarded and advanced arguments in this paper we study the oscillatory behavior of equations of the forms y t i 1npiy t i 0 and y t i 1npiy t i 0 where piand i i 1 2 n are positive constants we prove that each one of the following conditions 1 pi i1 e for some i i 1 2 n 2 i 1npi 1 e where min 1 2 n 3 i 1npi 1 n i 1n i 1 e or 4 1 n i 1n pi i 1 2 21 e implies that every solution of and oscillates a generalization in the case where the coefficientspi i 1 2 n are positive and continuous functions is also presented

multiple integral average conditions for oscillation of delay differential equations we obtain some multiple integral average conditions for oscillation and nonoscillation of the first order nonautonomous delay equations our theorems improve several previous well known results

oscillatory retarded functional systems this note is concerned with the oscillatory behavior of a linear retarded system several criteria are obtained for having the system oscillatory conditions regarding the existence of nonoscillatory solutions are also given

linearized oscillations for odd order neutral delay differential equations abstract consider the n th order nonlinear neutral delay differential equation d n dt n x t p t g x t q t h x t 0 1 where n 1 is an odd integer we prove that under appropriate hypotheses eq 1 oscillates provided that the same is true for an associated linear equation with constant coefficients of the form d n dt n y t p 0 y t q 0 y t 0 a partial converse is also presented where we show that under appropriate hypotheses eq 1 has a positive solution

on a rankin selberg integral of the l function for widetilde mathrm sl _2 times mathrm gl _2 sl 2 gl2 we present a rankin selberg integral on the exceptional group g 2 which represents the l function for generic cuspidal representations of widetilde mathrm sl 2 times mathrm gl 2 as an application we show that certain fourier jacobi type periods on g 2 are non vanishing

necessary and sufficient condition for oscillation of a neutral differential system with several delays abstract in this paper we prove that a general neutral differential system with several delays has a nonoscillatory solution if and only if its characteristic equations has a real root

nonoscillations for odd dimensional systems of linear retarded functional differential equations this paper is concerned with the nonoscillatory problems of odd dimensional systems of linear retarded functional differential equations based upon the corresponding characteristic equations we get some criteria for nonoscillations by utilizing the matrix measures

a linguistic multi criteria decision making approach based on logical reasoning in real decision making problems it is always more natural for decision makers to use linguistic terms to express their preferences opinions in a qualitative way among alternatives than to provide quantitative values additionally many of these decision making problems are under uncertain environments with vague and imprecise information involved following the idea of computing with words cww methodology we propose in this paper a linguistic valued qualitative aggregation and reasoning framework for multi criteria decision making problems where a linguistic valued algebraic structure is constructed for modelling the linguistic information involved in multi criteria decision making problems and a linguistic valued logic based approximate reasoning method is developed to infer the final decision making result this method takes the advantage of handling the linguistic information no matter totally ordered or partially ordered directly without numerical approximation and having a non classical logic as its formal foundation for decision making process

pseudo almost periodicity of some nonautonomous evolution equations with delay abstract this paper is concerned with pseudo almost periodicity of the solutions to the nonautonomous evolution equation with delay u t a t u t f t u t h some sufficient conditions which ensure the existence and uniqueness of pseudo almost periodic mild solutions to the evolution equation with delay are given an example is shown to illustrate our results

oscillatory behavior in linear retarded functional differential equations abstract this paper is devoted to the investigation of when all solutions of autonomous and nonautonomous linear retarded functional differential equations are oscillatory