even continuity and equicontinuity in fuzzy topology we study the notion of even continuity in the category fcs of fuzzy convergence spaces and in fns the category of fuzzy neighborhood spaces we further compare this notion to equicontinuity in fus the category of fuzzy uniform spaces

conditional exponential moments for iterated wiener integrals we provide sharp exponential moment bounds for stratonovich iterated stochastic integrals under conditioning by certain small balls including balls in certain holder like norms of exponent greater than 1 3 the proof uses a control of the variation of the levy area under conditioning the results are applied to the computation of the onsager machlup functional of diffusion processes with constant diffusion matrix

p closedness in l fuzzy topological spaces a good definition of p closedness is introduced and studied in l fuzzy topological spaces where l is a fuzzy lattice

a complete axiomatization of fuzzy functional dependencies using fuzzy function the notion of functional dependency in classical relational databases corresponds to a partial function therefore it appears natural that the notion of fuzzy functional dependency should correspond to the notion of partial fuzzy function following this approach we introduce the notion of fuzzy functional dependency in fuzzy relational databases and show that the classical inference rules for functional dependencies form a sound and complete formal system in our case

the categorical topology approach to fuzzy topology and fuzzy convergence it is the purpose of this paper to have a look at fuzzy topology from the point of view of categorical topology we first look at interesting subcategories of fts and determine whether they are bireflective and or coreflective we also describe the set of all subcategories of fts which are at the same time bireflective and coreflective due to the fact that top is one of these subcategories of fts ffs itself can be neither cartesian closed nor extensional we therefore secondly construct a supercategory of bts which is a topological quasitopos the construction of this quasitopos is based on the theory of convergence in fts

symmetric sign pattern matrices that require unique inertia abstract a sign pattern matrix is a matrix whose entries are from the set 0 the purpose of this paper is to characterize symmetric sign patterns that require unique inertia that is all the real symmetric matrices with the given sign pattern must have the same inertia further some constructions to obtain sign patterns that require unique inertia are provided sign patterns corresponding to some special graphs are also considered finally extensions to complex sign patterns are mentioned

a convex log concave correlation inequality for gaussian measure and an application to abstract wiener spaces this paper deals with a generalization of a result due to brascamp and lieb which states that in the space of probabilities with log concave density with respect to a gaussian measure on open image in new window this gaussian measure is the one which has strongest moments we show that this theorem remains true if we replace x by a general convex function then we deduce a correlation inequality for convex functions quite better than the one already known finally we prove results concerning stochastic analysis on abstract wiener spaces through the notion of approximate limit

onsager machlup functionals for non trace class spde s an onsager machlup functional limit is derived for a class of spde s whose principal part is not trace class both nondegenerate and degenerate limits are obtained and are illustrated by examples the proof uses fkg type inequalities

possibilistic functional dependencies and their relationship to possibility theory this paper introduces possibilistic functional dependencies these dependencies are associated with a particular possibility distribution over possible worlds of a classical database the possibility distribution reflects a layered view of the database the highest layer of the classical database consists of those tuples that certainly belong to it while the other layers add tuples that only possibly belong to the database with different levels of possibility the relation between the confidence levels associated with the tuples and the possibility distribution over possible database worlds is discussed in detail in the setting of possibility theory a possibilistic functional dependency is a classical functional dependency associated with a certainty level that reflects the highest confidence level where the functional dependency no longer holds in the layered database moreover the relationship between possibilistic functional dependencies and possibilistic logic formulas is established related work is reviewed and the intended use of possibilistic functional dependencies is discussed in the conclusion

nested sequences of principal minors and potential stability abstract sufficient conditions are determined for an n by n zero nonzero pattern to allow a nested sequence of nonzero principal minors a method is then given to sign such a pattern so that it allows a nested sequence of k by k principal minors with sign 1 k for 1 k n it is a classical result that a sign pattern with such a sequence is potentially stable thus classes of potentially stable sign patterns can be identified a necessary and sufficient condition for a certain tree sign pattern class to be potentially stable is also given

positive definite completions of partial hermitian matrices abstract the question of which partial hermitian matrices some entries specified some free may be completed to positive definite matrices is addressed it is shown that if the diagonal entries are specified and principal minors composed of specified entries are positive then if the undirected graph of the specified entries is chordal a positive definite completion necessarily exists furthermore if this graph is not chordal then examples exist without positive definite completions in case a positive definite completion exists there is a unique matrix in the class of all positive definite completions whose determinant is maximal and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original partial hermitian matrix additional observations regarding positive definite completions are made

onsager machlup functional for the fractional brownian motion let x be the solution of the stochastic differential equation where b h is a fractional brownian motion with hurst parameter h in this paper we compute the onsager machlup functional of x for the supremum norm and holder norms of order with in the case and for holder norms of order with when

on the inertia set of a signed graph with loops abstract a signed graph is a pair g where g v e is a graph in which parallel edges and loops are permitted with v 1 n and e the edges in are called odd edges and the other edges of e even by s g we denote the set of all n n real symmetric matrices a a i j such that if a i j 0 then among the edges connecting i and j there must be at least one even edge if a i j 0 then among the edges connecting i and j there must be at least one odd edge and if a i j 0 then either there must be at least one odd edge and at least one even edge connecting i and j or there are no edges connecting i and j here we allow i j for a real symmetric matrix a the partial inertia of a is the pair p q where p and q are the number of positive and negative eigenvalues of a respectively if g is a signed graph we define the inertia set of g as the set of the partial inertias of all matrices a s g by mr g we denote max rank a a s g we say that a signed graph g satisfies the northeast property if for each p q with p q mr g in the inertia set of g also p 1 q p q 1 belong to the inertia set of g in this paper we show that if g is a signed graph where g is a tree with possibly loops attached at some of the vertices then g satisfies the northeast property furthermore we present a formula for calculating the inertia set of a signed graph g where g is a tree with possibly loops attached at some of the vertices

the reduction of the fuzzy data domain and fuzzy consistent join abstract in this paper fuzzy functional dependencies are represented by means of fuzzy similarity relations we show that the inference rules for fuzzy functional dependencies which are similar to armstrong s axioms for the classical case are sound and complete making use of fuzzy functional dependencies we can compress the domain of the fuzzy data and make the fuzzy data clearer an algorithm for testing the satisfiability of a fuzzy instance for the set of fuzzy functional dependencies is given furthermore we discuss the decomposition and join of relation schemes we define the fuzzy consistent join and give its properties lastly we obtain an algorithm for determining lossless consistent join

a generalised form of compactness in fuzzy topological spaces the n compactness of wang 13 extended in 151 provides the first theory of compactness which is applicable to arbitrary fuzzy subsets many of the standard properties associated with compactness are valid for n compactness including the product theorem furthermore n compactness reduces to ordinary compactness in the topologically generated case on closer inspection one finds evidence that a concept weaker than n compactness might also be desirable for example n compactness does not reduce to any of the standard fuzzified versions of compactness 1 2 6 73 in the case where the fuzzy subset under consideration is the whole space in particular when applied to the whole space n compactness is substantially stronger than fuzzy compactness as fuzzy compactness seems to be a good working concept for the whole space an extension of this notion to arbitrary fuzzy subsets might well have applications not accessible to the much stronger n compactness as a consequence of the definition an n compact fuzzy set is forced to attain a maximum value as a result it is possible to have fuzzy sets which are never n compact even if the fuzzy topology has only a finite number of open fuzzy sets our intuition based on the case of general topology would expect every fuzzy set to be compact in such a case in this paper we introduce a weaker generalisation of compactness which we call f compactness it is shown that ficompactness is inherited by closed fuzzy subsets continuous images finite suprema and products it reduces to compactness or to fuzzy compactness in all cases where

modal trajectory estimation using maximum gaussian mixture this technical note deals with the estimation of the whole trajectory of a stochastic dynamic system with highest probability conditionally upon the past observation process using a maximum gaussian mixture we first recall the gaussian sum technique applied to minimum variance filtering it is then shown that the same concept of gaussian mixture can be applied in that context provided we replace the sum operator by the max operator

doubly robust smoothing of dynamical processes via outlier sparsity constraints coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice in this context the present paper develops novel fixed lag and fixed interval smoothing algorithms that are robust to outliers simultaneously present in the measurements and in the state dynamics outliers are handled through auxiliary unknown variables that are jointly estimated along with the state based on the least squares criterion that is regularized with the l1 norm of the outliers in order to effect sparsity control the resultant iterative estimators rely on coordinate descent and the alternating direction method of multipliers are expressed in closed form per iteration and are provably convergent additional attractive features of the novel doubly robust smoother include i ability to handle both types of outliers ii universality to unknown nominal noise and outlier distributions iii flexibility to encompass maximum a posteriori optimal estimators with reliable performance under nominal conditions and iv improved pcoping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice in this context the present paper develops novel fixed lag and fixed interval smoothing algorithms that are robust to outliers simultaneously present in the measurements and in the state dynamics outliers are handled through auxiliary unknown variables that are jointly estimated along with the state based on the least squares criterion that is regularized with the l1 norm of the outliers in order to effect sparsity control the resultant iterative estimators rely on coordinate descent and the alternating direction method of multipliers are expressed in closed form per iteration and are provably convergent additional attractive features of the novel doubly robust smoother include i ability to handle both types of outliers ii universality to unknown nominal noise and outlier distributions iii flexibility to encompass maximum a posteriori optimal estimators with reliable performance under nominal conditions and iv improved performance relative to competing alternatives at comparable complexity as corroborated via simulated tests erformance relative to competing alternatives at comparable complexity as corroborated via simulated tests

on the inertia of sums of hermitian matrices abstract given n n hermitian matrices h1 hp a complete description is found for the possible inertias of the sum h1 hp in terms of the inertias of hi i 1 p we also consider and solve other related problems

maximum a posteriori state path estimation discretization limits and their interpretation continuous discrete models with dynamics described by stochastic differential equations are used in a wide variety of applications for these systems the maximum a posteriori map state path can be defined as the curves around which lie the infinitesimal tubes with greatest posterior probability which can be found by maximizing a merit function built upon the onsager machlup functional a common approach used in the engineering literature to obtain the map state path is to discretize the dynamics and obtain the map state path for the discretized system in this paper we prove that if the trapezoidal scheme is used for discretization then the discretized map state path estimation converges hypographically to the continuous discrete map state path estimation as the discretization gets finer however if the stochastic euler scheme is used instead then the discretized estimation converges to the minimum energy estimation the minimum energy estimates are in turn proved to be the state paths associated with the map noise paths which in some cases differ from the map state paths therefore the discretized map state paths can have different interpretations depending on the discretization scheme used

the partial sum process of orthogonal expansions as geometric rough process with fourier series as an example an improvement of menshov rademacher theorem abstract the partial sum process of orthogonal expansion n 0 c n u n is a geometric 2 rough process for any orthonormal system u n n 0 in l 2 and any sequence of numbers c n satisfying n 0 log 2 n 1 2 c n 2 since being a geometric 2 rough process implies the existence of a limit function up to a null set our theorem could be treated as an improvement of menshov rademacher theorem for fourier series the condition can be strengthened to n 0 log 2 n 1 c n 2 which is equivalent to f u f v 2 sin u v 2 d u d v with f the limit function

cubature kalman filtering for continuous discrete systems theory and simulations in this paper we extend the cubature kalman filter ckf to deal with nonlinear state space models of the continuous discrete kind to be consistent with the literature the resulting nonlinear filter is referred to as the continuous discrete cubature kalman filter cd ckf we use the ito taylor expansion of order 1 5 to transform the process equation modeled in the form of stochastic ordinary differential equations into a set of stochastic difference equations building on this transformation and assuming that all conditional densities are gaussian distributed the solution to the bayesian filter reduces to the problem of how to compute gaussian weighted integrals to numerically compute the integrals we use the third degree cubature rule for a reliable implementation of the cd ckf in a finite word length machine it is structurally modified to propagate the square roots of the covariance matrices the reliability and accuracy of the square root version of the cd ckf are tested in a case study that involves the use of a radar problem of practical significance the problem considered herein is challenging in the context of radar in two respects high dimensionality of the state and increasing degree of nonlinearity the results presented herein indicate that the cd ckf markedly outperforms existing continuous discrete filters

stochastic calculus with respect to gaussian processes in this paper we develop a stochastic calculus with respect to a gaussian process of the form b t int t 0 k t s dw s where w is a wiener process and k t s is a square integrable kernel using the techniques of the stochastic calculus of variations we deduce change of variable formulas for the indefinite integrals and we study the approximation by riemann sums the particular case of the fractional brownian motion is discussed

degrees of compactness in fuzzy convergence spaces we develop a theory of compactness in the category of fuzzy convergence spaces in the spirit of lowen i e we define for each fuzzy subset of a fuzzy convergence space a degree of being compact these degrees of compactness generalize at the same time the theory of compactness in the category of fuzzy convergence spaces and some known measures of compactness in fuzzy topological spaces together with degrees of closedness and of even continuity they prove useful in the development of a theory of compactness for fuzzy function spaces

onsager machlup functional for some smooth norms on wiener space in this paper we determine onsager machlup functionals for a variety of norms on wiener space which includes among others holder norms for every 0 1 2 as well as besov or sobolev type norms we basically require the knowledge of the small ball probabilities for the wiener measure and use versions of the norms which are rotationaly invariant on the range of the brownian paths a property of crucial importance in our approach

stochastic area for brownian motion on the sierpinski gasket we construct a levy stochastic area for brownian motion on the sierpinski gasket the standard approach via ito integrals fails because this diffusion has sample paths which are far rougher than those of semimartingales we thus provide an example demonstrating the restrictions of the semimartingale framework as a consequence of the existence of the area one has a stochastic calculus and can solve stochastic differential equations driven by brownian motion on the sierpinski gasket

pointwise convergence continuous convergence and even continuity in fns we discuss the notions of pointwise convergence continuous convergence and even continuity which were previously defined for fuzzy convergence spaces using prefilters in fuzzy neighborhood spaces and show that these concepts can there be described entirely using ordinary filters

the onsager machlup functional for a class of anticipating processes consider the solution xt 0 t 1 of the equation x t x 0 w t mathop smallint limits 0 t b x s d s wherew wt 0 t 1 is ad dimensional wiener process b is a lipschitz function from d into d andx0 is ad dimensional functional of the wiener process

functional limit theorems for the increments of d dimensional gaussian processes in a holder type norm in this paper estimating upper bounds of large deviation probabilities for the increments of d dimensional gaussian processes in holder type norm we obtain functional limit results for the increments of d dimensional gaussian processes in the holder type norm

an ell _ 1 laplace robust kalman smoother robustness is a major problem in kalman filtering and smoothing that can be solved using heavy tailed distributions e g l1 laplace this paper describes an algorithm for finding the maximum a posteriori map estimate of the kalman smoother for a nonlinear model with gaussian process noise and l1 laplace observation noise the algorithm uses the convex composite extension of the gauss newton method this yields convex programming subproblems to which an interior point path following method is applied the number of arithmetic operations required by the algorithm grows linearly with the number of time points because the algorithm preserves the underlying block tridiagonal structure of the kalman smoother problem excellent fits are obtained with and without outliers even though the outliers are simulated from distributions that are not l1 laplace it is also tested on actual data with a nonlinear measurement model for an underwater tracking experiment the l1 laplace smoother is able to construct a smoothed fit without data removal from data with very large outliers

sign patterns requiring a unique inertia abstract a sign pattern requires a unique inertia if every real matrix in the sign pattern class has the same inertia several sufficient or necessary conditions are given for a sign pattern to require a unique inertia it is proved that a sign pattern requires a unique inertia if and only if it requires a unique refined inertia all sign patterns of orders 2 and 3 that require a unique inertia are characterized if the underlying graph of a sign pattern is a tree then it is shown that any skew symmetric sign pattern requires a unique inertia and a linear time algorithm is given to determine whether or not a symmetric sign pattern requires a unique inertia

an inequality constrained nonlinear kalman bucy smoother by interior point likelihood maximization kalman bucy smoothers are often used to estimate the state variables as a function of time in a system with stochastic dynamics and measurement noise this is accomplished using an algorithm for which the number of numerical operations grows linearly with the number of time points all of the randomness in the model is assumed to be gaussian including other available information for example a bound on one of the state variables is non trivial because it does not fit into the standard kalman bucy smoother algorithm in this paper we present an interior point method that maximizes the likelihood with respect to the sequence of state vectors satisfying inequality constraints the method obtains the same decomposition that is normally obtained for the unconstrained kalman bucy smoother hence the resulting number of operations grows linearly with the number of time points we present two algorithms the first is for the affine case and the second is for the nonlinear case neither algorithm requires the optimization to start at a feasible sequence of state vector values both the unconstrained affine and unconstrained nonlinear kalman bucy smoother are special cases of the class of problems that can be handled by these algorithms

relationships between l ordered convergence structures and strong l topologies by making use of the intrinsic fuzzy inclusion orders on the fuzzy power set the relationships between l ordered convergence spaces and strong l topological spaces are researched where l is a commutative unital quantale it is shown that the category of strong l topological spaces can be embedded in the category of l ordered convergence spaces as a reflective subcategory as a result we observe that there is a galois correspondence between the category of l ordered convergence spaces and the category of strong l topological spaces further it is proved that the class of all strong l topological l ordered convergence spaces precisely is the class of all strong l topological spaces and the class of spaces with non idempotent l ordered interior operators is characterized as a subclass of the class of l ordered convergence spaces

fuzzy uniform convergence and equicontinuity abstract in our earlier papers we investigated function space structures in fts the category of fuzzy topological spaces and in fcs the category of fuzzy convergence spaces this paper is devoted to the study of function space structures in fus the category of fuzzy uniform spaces due to lowen we develop the basic theory and give examples of such structures such as pointwise and compact convergence we consider separation axioms in these fuzzy function spaces and show that the fuzzy uniformity of uniform convergence is conjoining for c x y we define a notion of equicontinuous sets of mappings on which pointwise and compact convergence coincide

tail estimates for markovian rough paths we work in the context of markovian rough paths associated to a class of uniformly subelliptic dirichlet forms 26 and prove a better than exponential tail estimate for the accumulated local p variation functional which has been introduced and studied in 17 we comment on the significance of these estimates to a range of currently studied problems including the recent results of ni hao 32 and chevyrev and lyons 18

stratified l ordered convergence structures in this paper a new kind of lattice valued convergence structures on a universal set called stratified l ordered convergence structures are presented by modifying the axiom for stratified l generalized convergence structures in the fuzzy setting so as to make use of the intrinsic fuzzy inclusion order on the fuzzy power set the category of stratified l ordered convergence spaces described here is shown to be a reflective full subcategory in the category of stratified l generalized convergence spaces and hence it is topological and cartesian closed as preparation a further investigation of stratified l filters is presented from the viewpoint that latticed valued filters should be compatible with the intrinsic fuzzy inclusion order on the fuzzy power set

inertia sets of two classes of symmetric sign patterns abstract a sign pattern is a matrix whose entries are from the set 0 for a symmetric sign pattern a of order n the inertia set of a is the set of inertias of all real symmetric matrices with the same sign pattern as a the purpose of this paper is to characterize the inertia sets of symmetric star and nonnegative symmetric tridiagonal sign patterns

fuzzy data dependencies and implication of fuzzy data dependencies abstract in this paper we give the definitions of fuzzy functional dependency ffd fuzzy multivalued dependency fmvd and fuzzy join dependency fjd we show that the inference rules of ffds and fmvds which are similar to armstrong s axioms for classical case are sound and complete furthermore we show that a classical data dependency satisfies the definition of a fuzzy data dependency we also show that ffd can be viewed as an fmvd and an fmvd can be viewed as an fjd we discuss the test for implication of fuzzy data dependencies a series of results which are similar to the classical result is obtained in this paper

unscented rauch tung striebel smoother this note considers the application of the unscented transform to optimal smoothing of nonlinear state space models in this note a new rauch tung striebel type form of the fixed interval unscented kalman smoother is derived the new smoother differs from the previously proposed two filter formulation based unscented kalman smoother in the sense that it is not based on running two independent filters forward and backward in time instead a separate backward smoothing pass is used which recursively computes corrections to the forward filtering result the smoother equations are derived as approximations to the formal bayesian optimal smoothing equations the performance of the new smoother is demonstrated with a simulation

compactness in fuzzy convergence spaces abstract lowen and lowen applications of category theory to fuzzy subsets kluwer 1992 p 153 and lowen et al fuzzy sets and systems 40 1991 347 recently introduced the category fcs of fuzzy convergence spaces a topological quasitopos which is a supercategory of fts the category of fuzzy topological spaces in this paper compactness in fcs is examined doing so we found that to define compactness as an absolute property we had to generalize the definition of fuzzy convergence space to fuzzy subsets all basic theorems are proved including the tychonoff product theorem based on the theory developed here in a following publication a richardson compactification for fuzzy convergence spaces will be given

multivalued dependencies in fuzzy relational databases abstract we show that by using the theory of possibility distribution multivalued dependencies in fuzzy relations can be expressed in the frame work of particularization another definition of functional dependencies in a fuzzy relation is given in terms of fuzzy hamming weight we have also discussed the validity of inference rules for multivalued dependencies in fuzzy relations

traces of random variables on wiener space and the onsager machlup functional abstract let f be a square integrable random variable on the classical wiener space and let us denote by f n the symmetric kernels appearing in its chaos expansion we give sufficient conditions for the unambiguous definition of f at the points of the cameron martin space we also give conditions for the existence of approximate limits in the sense of denjoy these results are first proved for multiple integrals i n f n before they are extended to the general random variables f the conditions are given in terms of the l p norms of the kernels f n the last section of the paper is devoted to an original application of our estimates to the proof of the existence of the onsager machlup functional for a nonanticipative stochastic differential equation of a special type

the inertia of a hermitian matrix having prescribed complementary principal submatrices abstract for i 1 2 let hi be a given ni ni hermitian matrix we characterize the set of inertias in h 1 x x h 2 x is n 1 n 2 in terms of in h1 and in h2

various topologies in the wiener space and levy s stochastic area in this paper we observe how levy s stochastic area looks when we see it through various topologies in the wiener space our theorem implies that it is quite natural from the viewpoint of topology to define a distinct skeleton of levy s stochastic areas w for each distinct topology in the wiener space or equivalently for each distinct abstract wiener space on which the wiener measure ands w are realized thus we cannot determine its intrinsic skeleton in the theory of abstract wiener spaces

the iterated kalman smoother as a gauss newton method the kalman smoother is known to be the maximum likelihood estimator when the measurement and transition functions are affine i e a linear function plus a constant a new proof of this result is presented that shows that the kalman smoother decomposes a large least squares problem into a sequence of much smaller problems the iterated kalman smoother is then presented and shown to be a gauss newton method for maximizing the likelihood function in the nonaffine case this method takes advantage of the decomposition obtained with the kalman smoother

on the mortensen equation for maximum likelihood state estimation the main purpose of the paper is to formulate the maximum likelihood state estimation problem correctly for a continuous time nonlinear stochastic dynamical system by using the onsager machlup functional a modified likelihood is introduced the basic equation for the maximum likelihood state estimate is derived with the aid of a dynamic programming approach the numerical procedure for realizing the recursive filtering is also proposed with some numerical results

joint maximum a posteriori state path and parameter estimation in stochastic differential equations abstract in this article we introduce the joint maximum a posteriori state path and parameter estimator jme for continuous time systems described by stochastic differential equations sdes this estimator can be applied to nonlinear systems with discrete time sampled measurements with a wide range of measurement distributions we also show that the minimum energy state path and parameter estimator mee obtains the joint maximum a posteriori noise path initial conditions and parameters these estimators are demonstrated in simulated experiments in which they are compared to the prediction error method pem using the unscented kalman filter and smoother the experiments show that the mee is biased for the damping parameters of the drift function furthermore for robust estimation in the presence of outliers the jme attains lower state estimation errors than the pem

the inertia sets of symmetric tridiagonal sign patterns abstract we give a complete description of the possible inertias of real symmetric matrices with a given arbitrarily prescribed tridiagonal symmetric sign pattern the inertia set of such a pattern is a subset of z 2 given by a system of linear inequalities whose parameters are determined from the sign sequence of the pattern s diagonal entries

the inertia of certain hermitian skew triangular block matrices abstract let n1 n2 n3 be nonnegative integers we consider hermitian matrices h of the form h h 11 h 12 h 13 h 21 h 22 h 23 h 31 h 32 h 33 where each hij is ni nj we characterize the set of inertias in h in hii i vi i and r1 i 1 rank h1 i 1 r1 i 1 for i 1 2 in terms of 1 v1 1 2 v2 2 n3 r12 r13 r12 r 12 and we discuss the implications of this characterization for the determination of the inertia of other types of hermitian skew triangular block matrices

fuzzy neighborhood spaces abstract in this paper we introduce a subcategory of the category of fuzzy topological spaces and we prove basic properties of this subcategory the main idea behind these spaces is the notion of fuzzy neighborhoods which enables us to introduce a local theory of fuzzy topologies

on the onsager machlup functional of diffusion processes around non c2 curves abstract the onsager machlup function namely the fictitious density of diffusions paths in function space is considered where the density is evaluated around non c2 curves thus extending earlier results the extension holds also for the case of diffusions evolving on a manifold

qualitative stability of linear systems abstract this paper provides a finitely computable graph theoretic answer to the following question concerning linear dynamical systems when given only the signs of entries or 0 in a real square matrix a can one be certain that all positive trajectories of the system ax are bounded matrices having such sign patterns are called sign quasistable with bounded replaced by convergent to the origin the matrices are called sign stable and were fully described in earlier papers however when a s digraph has several strong components so that the system is actually a hierarchy of subsystems and when some of those subsystems fail to be sign stable the recognition of sign quasistability is a very delicate matter by means of certain graph color tests it is possible to identify the system variables that are capable for some choice of matrix entry magnitudes and initial conditions of emitting nonzero constant

closures of database hypergraphs a hypergraph formalism is introduced to represent database schemata in particular a database schema b described by one full join dependency and a set of functional dependencies is represented by a database hypergraph h containing both undirected and directed hyperedges undirected hyperedges correspond to the relations in the join dependency and directed hyperedges correspond to the functional dependencies in addition two classes of database hypergraphs are defined e acyclic hypergraphs and e independent hypergraphs a hypergraph is e acyclic if it is equivalent to some acyclic hypergraph it is e independent if it is equivalent to some independent i e cover embedding hypergraph furthermore the closure of a database hypergraph is defined as the extension of the transitive closure of a graph by using a lower bound and an upper bound of the hypergraph closure called l closure and u closure respectively it is proved that two e acyclic e independent hypergraphs are equivalent if and only if they have the same closure moreover a hypergraph is e acyclic e independent if and only if its closure is acyclic independent and in most cases such a recognition can be done in polynomial time finally it is shown how to use the database hypergraph closure to solve some database design problems

some exact equivalents for the brownian motion in holder norm some exact equivalents of small probabilities are given for the wiener measure on spaces of holder paths it turns out that most of them are easier to derive than their counterparts in the uniform norm because of a classical result of z ciesielski which makes the brownian motion on these spaces easy to handle in particular we study the equivalents of the probability of eb in a fixed ball ofb in a small ball and we give applications to the speed of clustering in strassen law

fuzzy uniform spaces in this paper we introduce the notion of fuzzy uniform spaces in section 2 we give some basic results and show how a fuzzy topology is derived from a fuzzy uniformity in sections 3 and 4 we prove that the notions which are introduced are good extensions and we prove that the category of uniform spaces is nicely injected in the category of fuzzy uniform spaces finally in section 5 we prove some basic results