generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries abstract this paper deals with relational databases which are extended in the sense that fuzzily known values are allowed for attributes precise as well as partial imprecise uncertain knowledge concerning the value of the attributes are represented by means of 0 1 valued possibility distributions in zadeh s sense thus we have to manipulate ordinary relations on cartesian products of sets of fuzzy subsets rather than fuzzy relations besides vague queries whose contents are also represented by possibility distributions can be taken into account the basic operations of relational algebra union intersection cartesian product projection and selection are extended in order to deal with partial information and vague queries approximate equalities and inequalities modeled by fuzzy relations can also be taken into account in the selection operation then the main features of a query language based on the extended relational algebra are presented an illustrative example is provided this approach which enables a very general treatment of relational databases with fuzzy attribute values makes an extensive use of dual possibility and necessity measures

laplacian and homology of free two step nilpotent lie algebras abstract in this paper we determine the homology with trivial coefficients of the free two step nilpotent lie algebras over the complex numbers this is done by working out the structure of the homology as a module under the general linear group the main tool is a laplacian for the free two step nilpotent lie algebras which turns out to be closely related to the casimir operator of the general linear group we are able to compute all eigenvalues of the laplacian on the chain complex

extreme growth rate of periodic orbits for equivalent differentiable flows abstract we prove that the extreme growth rate of periodic orbits of differentiable flows is preserved by lipschitz equivalence when all the fixed points are hyperbolic and thus it is an invariant in an open dense subset x h r of the set of c r 1 r flows by contrast for any 1 r there exist two infinite dimensional connected subsets of equivalent c r flows disjoint from x h r such that the growth rate of periodic orbits attains infinity and zero respectively

aggregating constraint satisfaction degrees expressed by possibilistic truth values in information systems one often has to deal with constraints in order to compel the semantics and integrity of the stored information or to express some querying criteria hereby different constraints can be of different importance a method to aggregate the information about the satisfaction of a finite number of constraints for a given data instance is presented central to the proposed method is the use of extended possibilistic truth values to express the degree of satisfaction of a constraint and the use of residual implicators and residual coimplicators to model the impact and relevance of a constraint the proposed method can be applied to any constraint based system a database application is discussed and illustrated

mixing for the time changes of heisenberg nilflows we consider reparametrizations of heisenberg nilflows we show that if a heisenberg nilflow is uniquely ergodic all non trivial time changes within a dense subspace of smooth time changes are mixing equivalently in the language of special flows we consider special flows over linear skew shifts over an irrational rotation of the circle without assuming any diophantine condition on the frequency we define a dense class of smooth roof functions for which the corresponding special flows are mixing mixing is produced by a mechanism known as stretching of birkhoff sums the set of mixing timechanges or equivalently roof functions has countable codimension and can be explicitely described in terms of invariant distributions for the nilflow allowing to produce concrete examples of mixing time changes

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

topological entropy of fixed point free flows topological entropy was introduced as an invariant of topological conjugacy and also as an analogue of measure theoretic entropy topological entropy for one parameter flows on a compact metric spaces is defined by bowen general statements are proved about this entropy but it is not easy to calculate the topological entropy and to show it is invariant under conjugacy for all this i would like to try to pose a new direction and study a definition for the topological entropy that involves handling the technical difficulties that arise from allowing reparametrizations of orbits some well known results are proved as well using this definition these results enable us to prove some results which seem difficult to prove using bowen s definition also we show here that this definition is equivalent to bowen s definition for any flow without fixed points on a compact metric space finally it is shown that the topological entropy of an expansive flow can be defined globally on a local cross sections

flexible querying in a relational framework supported by possibilistic logic traditionally flexible querying systems are supported by a logical framework that is based on satisfaction degrees alternatively certainty about query satisfaction can also be modelled by possibility and necessity measures this approach was extended by our group in order to handle the cases of missing information more adequately in this paper it is presented how our extended logical framework can be used to support flexible querying on conventional relational databases the handling of preferences both inside elementary query conditions and between query conditions is presented as well as the extension of the traditional selection projection and join operators motivated examples are provided to illustrate the used concepts

combinatorial vector fields and dynamical systems in this paper we introduce the notion of a combinatorial dynamical system on any cw complex earlier in fo3 and fo4 we presented the idea of a combinatorial vector field see also fo1 for the one dimensional case and studied the corresponding morse theory equivalently we studied the homological properties of gradient vector fields these terms were defined precisely in fo3 see also sect 2 of this paper in this paper we broaden our investigation and consider general combinatorial vector fields we first study the homological properties of such vector fields generalizing the morse inequalities of fo3 we then introduce various zeta functions which keep track of the closed orbits of the corresponding flow and prove that these zeta functions initially defined only on a half plane can be analytically continued to meromorphic functions on the entire complex plane lastly we review the notion of reidemeister torsion of a cw complex introduced in re fr and show that the torsion is equal to the value at z 0 of one of the zeta functions introduced earlier much of this paper can be viewed as a combinatorial analogue of the work on smooth dynamical systems presented in p p fra fri1 2 and elsewhere

birth of homoclinic intersections a model for the central dynamics of partially hyperbolic systems creation d intersection homoclines un modele pour la dynamique centrale des systemes partiellement hyperboliques nous montrons une conjecture de j palis tout diffeomorphisme d une variete compacte peut etre approche en topologie c 1 par un diffeomorphisme morse smale ou par un diffeomorphisme ayant une intersection homocline transverse

on the homology of free 2 step nilpotent lie algebras abstract we find an explicit formula for the total dimension of the homology of a free 2 step nilpotent lie algebra we analyse the asymptotics of this formula and use it to find an improved lower bound on the total dimension of the homology of any 2 step nilpotent lie algebra

topological entropies of equivalent smooth flows we construct two equivalent smooth flows one of which has positive topological entropy and the other has zero topological entropy this provides a negative answer to a problem posed by ohno

impact of weights on conjunctive and disjunctive aggregation of extended possibilistic truth values extended possibilistic truth values are a flexible means to model the certainty or uncertainty about the truth value of a proposition with respect to flexible database querying they are suited to express the extent to which a database instance satisfies a query condition since a flexible query can impose several conditions each with different importance weighted aggregation is necessary in this paper weighted aggregation of extended possibilistic truth values is presented the impact of the weights on extended possibilistic truth values in both conjunctive and disjunctive aggregation is handled it is illustrated that the different aggregation types require a different approach special care is given to the case where both conjunctive and disjunctive aggregation are mixed together it is shown that the weights will have to be propagated throughout the calculations but that this can cause basic properties like associativity to get lost the problems that can arise are illustrated and solutions are proposed

cohomology operations for lie algebras if l is a lie algebra over r and z its centre the natural inclusion z l extends to a representation i z end h l r of the exterior algebra of z in the cohomology of l we begin a study of this representation by examining its poincare duality properties its associated higher cohomology operations and its relevance to the toral rank conjecture in particular by using harmonic forms we show that the higher operations presented by goresky kottwitz and macpherson 1998 form a subalgebra of end h l r and that they can be assembled to yield an explicit hirsch brown model for the borel construction associated to 0 z l l z 0

topology of bounded degree graph complexes abstract the bounded degree graph complexes were first introduced by reiner and roberts j algebraic combin 11 2000 135 154 they arise from the finite free resolution of quadratic veronese rings and modules we prove various results about the homotopy types of these complexes and deduce corresponding characteristic free results about the quadratic veronese resolutions in particular we characterize the set of multidegrees which support at least one higher syzygy in this resolution the answer turns out to be independent of the field characteristic

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

on the cohomology of galois groups determined by witt rings let f denote a field of characteristic different from two in this paper we describe the mod 2 cohomology of a galois group gf called the w group of f which is known to essentially characterize the witt ring wf of anisotropic quadratic modules over f we show that h gf f2 contains the mod 2 galois cohomology of f and that its structure will reflect important properties of the field we construct a space xf endowed with an action of an elementary abelian group e such that the computation of the cohomology of gf reduces to calculating the equivariant cohomology h e xf f2 for the case of a field which is not formally real this amounts to computing the cohomology of an explicit euclidean space form an object which is interesting in its own right we provide a number of examples and a substantial combinatorial computation for the cohomology of the universal w groups