strongest strong cycles and theta fuzzy graphs in this paper new concepts are introduced to enhance the process of block identification in fuzzy graphs since reduction in the strength of the connectedness between two nodes occurs more frequently than total disconnection of a network block identification in fuzzy graph networks is very important a special type of cycle which is called a strongest strong cycle and a new connectivity parameter which is called cycle connectivity are introduced in fuzzy graphs a subclass of fuzzy graphs known as fuzzy graphs is identified in which all the existing characterizations of blocks in graphs are true a set of necessary conditions is obtained for a fuzzy graph to be a block as well as a set of necessary and sufficient conditions for a fuzzy graph to be a block

bipolar fuzzy graphs in this paper we introduce the notion of bipolar fuzzy graphs describe various methods of their construction discuss the concept of isomorphisms of these graphs and investigate some of their important properties we then introduce the notion of strong bipolar fuzzy graphs and study some of their properties we also discuss some propositions of self complementary and self weak complementary strong bipolar fuzzy graphs

types of arcs in a fuzzy graph the concept of connectivity plays an important role in both theory and applications of fuzzy graphs depending on the strength of an arc this paper classifies arcs of a fuzzy graph into three types namely a strong b strong and d arcs the advantage of this type of classification is that it helps in understanding the basic structure of a fuzzy graph completely we analyze the relation between strong paths and strongest paths in a fuzzy graph and obtain characterizations for fuzzy bridges fuzzy trees and fuzzy cycles using the concept of a strong b strong and d arcs an arc of a fuzzy tree is a strong if and only if it is an arc of its unique maximum spanning tree also we identify different types of arcs in complete fuzzy graphs

notes on bipolar fuzzy graphs in this note we show by examples that definitions 3 1 5 6 and 5 7 example 5 8 propositions 5 9 and 5 10 and partial proof of propositions 5 11 and 5 12 in a previous paper by akram muhammad akram bipolar fuzzy graphs inform sci 181 2011 5548 5564 contain some flaws and then provide the correct versions finally we introduce a generalized bipolar fuzzy graph

semigroup kernels poisson bounds and holomorphic functional calculus letlbe the generator of a continuous holomorphic semigroupswhose action is determined by an integral kernelkon a scale of spaceslp x under mild geometric assumptions on x we prove that iflhas a boundedh functional calculus onl2 x andksatisfies bounds typical for the poisson kernel thenlhas a boundedh functional calculus onlp x for eachp 1 moreover if x is of polynomial type andksatisfies second order gaussian bounds we establish criteria forlto have a bounded hormander functional calculus or a bounded davies helffer sjostrand functional calculus

a preparation theorem for weierstrass systems it is shown that lion and rolin s preparation theorem for globally subanalytic functions holds for the collection of definable functions in any expansion of the real ordered field by a weierstrass system

cartan decomposition subgroups of 2 for g sl 3 r and g so 2 n we give explicit practical conditions that determine whether or not a closed connected subgroup h of g has the property that there exists a compact subset c of g with chc g to do this we fix a cartan decomposition g ka k of g and then carry out an approximate calculation of khk n a for each closed connected subgroup h of g

approximate generalizations and computational experiments in this paper i demonstrate how one can generalize finitely many examples to statements about infinite classes of economic models if there exist upper bounds on the number of connected components of one dimensional linear subsets of the set of parameters for which a conjecture is true one can conclude that it is correct for all parameter values in the class considered except for a small residual set once one has verified the conjecture for a predetermined finite set of points i show how to apply this insight to computational experiments and spell out assumptions on the economic fundamentals that ensure that the necessary bounds on the number of connected components exist

menger s theorem for fuzzy graphs the concept of the strongest path plays a crucial role in fuzzy graph theory in classical graph theory all paths in a graph are strongest with a strength value of one in this article we introduce menger s theorem for fuzzy graphs and discuss the concepts of strength reducing sets and t connected fuzzy graphs we also characterize t connected and t arc connected fuzzy graphs

weighted lp estimates for powers of selfadjoint operators abstract we prove l p and weighted l p estimates for bounded functions of a selfadjoint operator satisfying a pointwise gaussian estimate for its heat kernel as an application we obtain weighted estimates for fractional powers of an electromagnetic schrodinger operator with singular coefficients the proofs are based on a modification of techniques due to hebisch 1990 17 and auscher and martell 2006 4

definable sets in ordered structures i this paper introduces and begins the study of a well behaved class of linearly ordered structures the minimal structures the definition of this class and the corresponding class of theories the strongly dlminlmal theories is made in analogy with the notions from stability theory of minimal structures and strongly minimal theories theorems 2 1 and 2 3 respectively provide characterizations of 41 minimal ordered groups and rings several other simple results are collected in 3 the primary tool in the analysis of minimal structures is a strong analogue of ii forking symmetry given by theorem 4 2 this result states that any parametri cally definable unary function in an yminimal structure is piecewise either constant or an ore er preserving or reversing bijection of intervals the results that follow include the existence and uniqueness of prime models over sets theorem 5 1 and a characterization of all bto categorical aminimal structures theorem 6 1 1 introduction the class of linearly ordered structures has long been an im portant subject of concern to model theorists impressive results have been obtained in the study of models of several particular theories that extend the theory of linear order among those theories that have been approached successfully are peano arithmetic the theory of ordered abelian groups that of real closed fields and that of linear order itself yet very little has been done in the way of developing a general model theory for ordered structures in this paper we develop the model theory for a class of linearly ordered structures that we isolate by demanding that a structure in this class satisfy a condition whose effect is that the linear ordering and the algebraic part of the structure behave quite well with respect to one another let l be a finitary first order language and w an l structure a set of n tuples a c x is said to be parametrically definable if there is some l formula

tangent cones and c 1 regularity of definable sets abstract let x r n be a connected locally closed set which is definable in an o minimal structure we prove that the following three statements are equivalent i x is a c 1 manifold ii the tangent cone and the paratangent cone of x coincide at every point in x iii for every x x the tangent cone of x at the point x is a k dimensional linear subspace of r n k does not depend on x varies continuously in x and the density x x 3 2

the field of reals with multisummable series and the exponential function we show that the field of real numbers with multisummable real power series is model complete o minimal and polynomially bounded further expansion by the exponential function yields again a model complete and o minimal structure which is exponentially bounded and in which the gamma function on the positive real line is definable 2000 mathematics subject classification primary 03c10 32b05 32b20 secondary 26e05

weighted norm inequalities off diagonal estimates and elliptic operators part i general operator theory and weights this is the first part of a series of four articles in this work we are interested in weighted norm estimates we put the emphasis on two results of different nature one is based on a good inequality with two parameters and the other uses calderon zygmund decomposition these results apply well to singular non integral operators and their commutators with bounded mean oscillation functions singular means that they are of order 0 non integral that they do not have an integral representation by a kernel with size estimates even rough so that they may not be bounded on all lp spaces for 1 p 8 pointwise estimates are then replaced by appropriate localized lp lq estimates we obtain weighted lp estimates for a range of p that is different from 1 8 and isolate the right class of weights in particular we prove an extrapolation theorem a la rubio de francia for such a class and thus vector valued estimates

second order riesz transforms associated with magnetic schrodinger operators abstract let a 1 i a 2 v be a magnetic schrodinger operator on r n where a l loc 2 r n n and 0 v l loc 1 r n we show that l p r n boundedness of l j l k a 1 and v a 1 for some interval of p automatically implies boundedness of the same operators and their commutators on l w p r n for certain muckenhoupt weights w and on the musielak orlicz hardy type spaces

quasi analytic solutions of analytic ordinary differential equations and o minimal structures it is well known that the non spiraling leaves of real analytic foliations of codimension 1 all belong to the same o minimal structure naturally the question arises if the same statement is true for non oscillating trajectories of real analytic vector fields we show under certain assumptions that such a trajectory generates an o minimal and model complete structure together with the analytic functions the proof uses the asymptotic theory of irregular singular ordinary differential equations in order to establish a quasi analyticity result from which the main theorem follows as applications we present an infinite family of o minimal structures such that any two of them do not admit a common extension and we construct a non oscillating trajectory of a real analytic vector field in dimension 5 that is not definable in any o minimal extension of the reals

fuzzy planar graphs fuzzy planar graph is a very important subclass of fuzzy graph in this paper two types of edges are mentioned for fuzzy graphs effective edges and considerable edges in addition a comparative study between kuratowski s graphs and fuzzy planar graph is made a new concept of a strong fuzzy planar graph is introduced some related results are established these results have certain applications in subway tunnels routes oil gas pipelines representation etc it is also shown that an image can be represented by a fuzzy planar graph and contraction of such an image can be made with the help of a fuzzy planar graph

strong arcs in fuzzy graphs an arc of a fuzzy graph is called strong if its weight is at least as great as the strength of connectedness of its end nodes when it is deleted an arc is strong iff its weight is equal to the strength of connectedness of its end nodes a bridge is strong but a strong arc need not be a bridge an arc of maximum weight is strong but a strong arc need not have maximum weight in a connected graph there is a strong path a path consisting of strong arcs between any two nodes a fuzzy graph is a fuzzy tree iff there is a unique strong path between any two of its nodes in a fuzzy tree an arc is strong iff it is a bridge and a strong path between two nodes is a path of maximum strength between them

maximal inequalities and riesz transform estimates on lp spaces for magnetic schrodinger operators i the paper concerns the magnetic schrodinger operator h a v j 1n 1i xj aj 2 v on rn under certain conditions given in terms of the reverse holder inequality on the magnetic field and the electric potential we prove some lp estimates on the riesz transforms of h and we establish some related maximal inequalities

fuzzy end nodes in fuzzy graphs we define a fuzzy end node in a fuzzy graph and show that no node can be both a cut node and a fuzzy end node in a fuzzy tree every node is either a cut node or a fuzzy end node but the converse is not true we also show that any nontrivial fuzzy tree has at least two fuzzy end nodes and we characterize fuzzy cycles that have no cut nodes or no fuzzy end nodes

connectivity index of a fuzzy graph and its application to human trafficking abstract connectivity is a high priority concept in fuzzy graphs the stability of a fuzzy graph is determined by the strength of connectedness of each pair of its nodes this paper introduces two measures of connectivity called as connectivity index and average connectivity index of fuzzy graphs several results related to these parameters are obtained these measures can be used to determine the potential flow of a fuzzy graph certain special types of nodes called cen crn and neutral nodes are also introduced and algorithms for finding these nodes are provided applications of these concepts in two different type of networks are provided

definable sets in ordered structures on introduit la notion de theorie o minimale des structures ordonnees une telle theorie etant telle que les sous ensembles definissables de ses modeles soient particulierement simples

smooth functions in o minimal structures abstract fix an o minimal expansion of the real exponential field that admits smooth cell decomposition we study the density of definable smooth functions in the definable continuously differentiable functions with respect to the definable version of the whitney topology this implies that abstract definable smooth manifolds are affine moreover abstract definable smooth manifolds are definably c diffeomorphic if and only if they are definably c 1 diffeomorphic

complements of subanalytic sets and existential formulas for analytic functions we show that the complement of a subanalytic set defined by real analytic functions from any subalgebra closed under differentiation is a subanalytic set defined by the functions from the same subalgebra this result has an equivalent formulation in logic consider an expression built from functions as above using equalities and inequalities as well as existential and universal quantifiers such an expression is equivalent to an existential expression involving functions from the same class provided that the variables approach neither infinity nor the boundary of the domain

o minimal hauptvermutung for polyhedra i milnor discovered two compact polyhedra which are homeomorphic but not pl homeomorphic a counterexample to the hauptvermutung he constructed the homeomorphism by a finite procedure repeated infinitely often informally we call a procedure constructive if it consists of an explicit procedure that is repeated only finitely many times in this sense milnor did not give a constructive procedure to define the homeomorphism between the two polyhedra in the case where the homeomorphism is semialgebraic the author and yokoi proved that the polyhedra in r n are pl homeomorphic in that article the required pl homeomorphism was not constructively defined from the given homeomorphism in the present paper we obtain the pl homeomorphism by a constructive procedure starting from the homeomorphism we prove in fact that for any ordered field r equipped with any o minimal structure two definably homeomorphic compact polyhedra in r n are pl homeomorphic the o minimal hauptvermutung theorem 1 1 together with the fact that any compact definable set is definably homeomorphic to a compact polyhedron we can say that o minimal topology is tame

a game theoretic approach to fault diagnosis and identification of hybrid systems physical systems can fail for this reason the problem of identifying and reacting to faults has received a lot of attention in the control and computer science communities in this paper we study the fault diagnosis problem for hybrid systems from a game theoretical point of view a hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modelled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics we model hybrid systems as hybrid automata and add distinguished actions to describe faults we define a fault identification game on them using two players the environment and the identifier the environment controls the evolution of the system and chooses whether and when a fault occurs the identifier observes the external behaviour of the system and announces whether a fault has occurred or not existence of a winning strategy for the identifier implies that faults can be detected correctly while computing such a winning strategy corresponds to implementing an identifier for the system we will show how to determine the existence of a winning strategy and how to compute it for all decidable classes of hybrid automata that admit a finite bisimulation quotient

the real field with convergent generalized power series we construct a model complete and o minimal expansion of the field of real numbers in which each real function given on 0 1 by a series cnxn with 0 n and cn r n 1 is definable this expansion is polynomially bounded

riesz transform gaussian bounds and the method of wave equation for an abstract self adjoint operator l and a local operator a we study the boundedness of the riesz transform al on lp for some 0 a very simple proof of the obtained result is based on the finite speed propagation property for the solution of the corresponding wave equation we also discuss the relation between the gaussian bounds and the finite speed propagation property using the wave equation methods we obtain a new natural form of the gaussian bounds for the heat kernels for a large class of the generating operators we describe a surprisingly elementary proof of the finite speed propagation property in a more general setting than it is usually considered in the literature

resolution of a semilinear equation in l1 let n or be a bounded regular open set of n and let x s be a continuous nondecreasing function in s measurable in x such that x 0 0 almost everywhere we solve for f l 1 the problem p u u f in u 0 on in fact for this result instead of assuming that is nondecreasing in s we need only that x s s 0 we deduce an almost necessary and sufficient condition on in order that p has a solution roughly speaking this condition is f v g with g l 1 and v l 1

characteristic cycles of constructible sheaves in his paper k kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds let x be a real analytic manifold and f a complex of sheaves of c vector spaces on x whose cohomology is constructible with respect to a subanalytic strati cation the characteristic cycle cc f is a subanalytic lagrangian cycle with in nite support and with values in the orientation sheaf of x in the cotangent bundle t x the de nition of cc f is morse theoretic heuristically cc f encodes the in nitesimal change of the euler characteristic of the stalks of f along the various directions in x it tends to be di cult in practice to calculate cc f explicitly for all but the simplest complexes f on the other hand the characteristic cycle construction has good functorial properties the behavior of cc f with respect to the operations of proper direct image verdier duality and non characteristic inverse image of f is well understood ks in this paper we describe the e ect of the operation of direct image by an open embedding combining our result with those that were previously known we obtain descriptions of cc rf f and cc f f analogous to those in ks for arbitrary morphisms f x y in the semi algebraic category and complexes f with semi algebraically constructible cohomology in e ect this provides an axiomatic characterization of the functor cc at least in the semi algebraic context our arguments do apply more generally in the subanalytic case but because statements become quite convoluted we shall not strive for the greatest degree of generality as a concrete application we consider the case of the ag manifold x of a complex semisimple lie algebra g here the weyl group w of g operates

ax lindemann for mathcal a _g we prove the ax lindemann theorem for the coarse moduli space a g of principally polarized abelian varieties of dimension g 1 we affirm the andre oort conjecture unconditionally for a g for g 6 and under grh for all g

on m strong fuzzy graphs the cartesian product and disjoint sum of graphs play a prominent role and have numerous interesting algebraic properties in this note we consider operations on fuzzy graphs under which m strong property is preserved if g1 and g2 are m strong fuzzy graphs then we prove that g1 g2 g1 g2 and g1 g2 are also m strong but g1 g2 need not be m strong if g1 g2 is m strong then we show that at least one factor must be m strong we show that the product of a m strong fuzzy graph g1 with a non m strong fuzzy graph g2 remains m strong if and only if g2 satisfies special condition for any fuzzy graph g gcc is the smallest m strong fuzzy graph that contains g and g gcc if and only if g is m strong we further show that m strong fuzzy graph g is a fuzzy tree if and only if the support g is a tree

eigenvalue asymptotics and exponential decay of eigenfunctions for schrodinger operators with magnetic fields we consider the schr6dinger operator with magnetic field h va x 2 v x in rj assuming that v 0 and icurl a i v 1 is locally in certain reverse holder class we study the eigenvalue asymptotics and exponential decay of eigenfunctions introduction consider the schrodinger operator with magnetic field 0 1 h h a v jv a x v x inlr n 3 where i 1 v rn r is the electric scalar potential and a rn rn is the magnetic vector potential under some natural conditions on a and v h admits a self adjoint realization which is still denoted by h in l2 ir1n in this paper we shall study its eigenvalue asymptotics and exponential decay of its eigenfunctions let n a h denote the number of eigenvalues counting multiplicity of h smaller than a or the dimension of the spectral projection for h corresponding to x a in the case a x 0 the following phase space volume estimate due to cwickel lieb rosenbljum sil theorem 9 3 p 95 is classical 0 2 n a a v cnl i x e r n x r n 1h12 v x l where cn is a constant depending on n on the other hand there exist some simple degenerate potentials v x i e potentials which do not tend to infinity in all direction as lxi oo e g v x v xi x2 xn x2x n xn for which the right hand side of 0 2 is infinite and nevertheless a v x has a discrete spectrum furthermore in the case where a x 0 and v x 0 the phase space volume of the set where the symbol of h is less than a n i x e nr x r n e ijaj x l2 l j 1 received by the editors may 19 1995 1991 mathematics subject classification primary 35p20 35j10

transitive blocks and their applications in fuzzy interconnection networks abstract in any network the problem of reduction of flow is more important and frequent than the disconnection of the network problems related with maximum bandwidth paths and maximal flows are also very significant in this article the authors discuss connectivity concepts related with paths and flows in interconnection networks in a fuzzy framework some of the properties and applications of a stable structure called transitive block are discussed blocks in fuzzy graphs generalize the concept of blocks in graphs the existence of a strongest strong cycle in any fuzzy block having at least three vertices is established four characterizations previously proposed for a class of blocks in fuzzy graphs are found to be true for a larger class two subclasses of fuzzy graphs namely connectivity transitive and cyclically transitive fuzzy graphs are introduced to get a better understanding of blocks in fuzzy graphs an application of transitive blocks in interconnection networks is also proposed

tauberian theorems for k summability with respect to an analytic germ abstract the goal of this article is to establish tauberian theorems for the k summability processes defined by germs of analytic functions in several complex variables the proofs are based on the tauberian theorems for k summability in one variable and in monomials and a method of monomialization of germs of analytic functions

interval valued fuzzy graphs we define the cartesian product composition union and join on interval valued fuzzy graphs and investigate some of their properties we also introduce the notion of interval valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval valued fuzzy complete graphs

canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant this article contains an elementary constructive proof of resolution of singularities in characteristic zero our proof applies in particular to schemes of finite type and to analytic spaces so we recover the great theorems of hironaka we introduce a discrete local invariant rm inv x a whose maximum locus determines a smooth centre of blowing up leading to desingularization to define rm inv x we need only to work with a category of local ringed spaces x x cal o x satisfying certain natural conditions if a in x then rm inv x a depends only on widehat cal o x a more generally rm inv x is defined inductively after any sequence of blowings up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of rm inv x cdot the paper is self contained and includes detailed examples one of our goals is that the reader understand the desingularization theorem rather than simply know it is true

approximate solutions and micro regularity in the denjoy carleman classes abstract we begin with a sequence m of positive real numbers and we consider the denjoy carleman class c m we show how to construct m approximate solutions for complex vector fields with c m coefficients we then use our construction to study micro local properties of boundary values of approximate solutions in general m involutive structures of codimension one where the approximate solution is defined in a wedge whose edge where the boundary value exists is a maximally real submanifold we also obtain a c m version of the edge of the wedge theorem

connectivity concepts in fuzzy incidence graphs abstract connectivity concepts in fuzzy incidence graphs are discussed in this article fuzzy incidence graphs are important in interconnection networks with influenced flows thus it is of primary importance to analyze their connectivity properties the existence of a strong path between any node arc pair of a fuzzy incidence graph is established cut pairs and fuzzy incidence trees are characterized using the concept of strong pairs several other structural properties of fuzzy incidence graphs are also obtained

the rational points of a definable set let x r n be a set that is definable in an o minimal structure over r this article shows that in a suitable sense there are very few rational points of x which do not lie on some connected semialgebraic subset of x of positive dimension

o minimality and the andre oort conjecture for mathbb c n we give an unconditional proof of the andre oort conjecture for arbitrary products of modular curves we establish two generalizations the first includes the manin mumford conjecture for arbitrary products of elliptic curves defined over q as well as lang s conjecture for torsion points in powers of the multiplicative group the second includes the manin mumford conjecture for abelian varieties defined over q our approach uses the theory of o minimal structures a part of model theory and follows a strategy proposed by zannier and implemented in three recent papers a new proof of the manin mumford conjecture by pila zannier a proof of a special but new case of pink s relative manin mumford conjecture by masser zannier and new proofs of certain known results of andre oort manin mumford type by pila 2010 mathematics subject classification 11g18 03c64

node connectivity and arc connectivity of a fuzzy graph the fuzzy graph approach is more powerful in cluster analysis than the usual graph theoretic approach due to its ability to handle the strengths of arcs effectively the concept of node strength sequence is introduced and is studied in a complete fuzzy graph two new connectivity parameters in fuzzy graphs namely fuzzy node connectivity k and fuzzy arc connectivity k are introduced and obtained the fuzzy analogue of whitney s theorem fuzzy node cut fuzzy arc cut and fuzzy bond are defined fuzzy bond is a special type of a fuzzy bridge it is proved that at least one of the end nodes of a fuzzy bond is a fuzzy cutnode it is shown that k k for a fuzzy tree and it is the minimum of the strengths of its strong arcs the relationships of the new parameters with already existing vertex and edge connectivity parameters are studied and is shown that the value of all these parameters are equal in a compete fuzzy graph also a new clustering technique based on fuzzy arc connectivity is introduced

remez type inequality on sets with cusps abstract a remez type inequality is proved for a large family of sets with cusps in r n including compact fat and semialgebraic or subanalytic sets

hardy spaces associated with magnetic schrodinger operators on strongly lipschitz domains abstract let p 0 1 be a strongly lipschitz domain in r n and a i a i a v a magnetic schrodinger operator on l 2 satisfying the dirichlet boundary condition where a a 1 a n l loc 2 r n and 0 v l loc 1 in this paper the authors introduce the hardy space h a p by the lusin area function associated with a and establish its equivalent characterization via the non tangential maximal function associated with e t a t 0 as applications the authors obtain the boundedness of the riesz transforms l k a 1 2 k 1 n from h a p to l p for p 0 1 and the fractional integral a from h a p to h a q for 0 p q 1 and n 2 1 p 1 q where l k is the closure of x k i a k in l 2

a note on divisible points of curves let c be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3 we partially answer a question posed by levin on points on c for which a non trivial power lies again on c our results have connections to zilber s conjecture on intersections with tori and yield to methods arising in transcendence theory and the theory of o minimal structures

semiclassical analysis for the ground state energy of a schrodinger operator with magnetic wells abstract motivated by a recent paper by montgomery mon we give the asymptotic behavior in the semi classical sense of the ground state energy for the schrodinger operator with a magnetic field we consider the case when the locus of the minima of the intensity of the magnetic field is compact and our study is sharper when this locus is an hypersurface or a finite union of points

counting special points logic diophantine geometry and transcendence theory we expose a theorem of pila and wilkie on counting rational points in sets definable in o minimal structures and some applications of this theorem to problems in diophantine geometry due to masser peterzil pila starchenko and

inclusion dynamics hybrid automata hybrid systems are dynamical systems with the ability to describe mixed discrete continuous evolution of a wide range of systems consequently at first glance hybrid systems appear powerful but recalcitrant neither yielding to analysis and reasoning through a purely continuous time modeling as with systems of differential equations nor open to inferential processes commonly used for discrete state transition systems such as finite state automata a convenient and popular model called hybrid automata was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting intuitively a hybrid automaton is simply a finite state automaton with each state augmented by continuous variables which evolve according to a set of well defined continuous laws each specified separately for each state this article investigates both the notion of hybrid automaton and the model checking problem over such a structure in particular it relates first order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions x f x t to a decidability problem for first order formulaeover the reals furthermore the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first order formulaeover the reals despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite we show that our techniques permit effective model checking for a nontrivial fragment of ctl

quasianalytic denjoy carleman classes and o minimality we show that the expansion of the real field generated by the functions of a quasianalytic denjoy carleman class is model complete and o minimal provided that the class satisfies certain closure conditions some of these structures do not admit analytic cell decomposition and they show that there is no largest o minimal expansion of the real field

schubert calculus on the grassmannian of hermitian lagrangian spaces abstract with an eye towards index theoretic applications we describe a schubert like stratification on the grassmannian of hermitian lagrangian spaces in c n c n this is a natural compactification of the space of hermitian n n matrices the closures of the strata define integral cycles and we investigate their intersection theoretic properties we achieve this by blending morse theoretic ideas with techniques from o minimal or tame geometry and geometric integration theory

wiener index of a fuzzy graph and application to illegal immigration networks abstract connectivity parameters have important role in the study of networks in the physical world wiener index is one such parameter with several applications in chemistry and network theory in this article wiener index of various fuzzy graph structures like fuzzy trees and fuzzy cycles are discussed relationship between connectivity index and wiener index of a fuzzy graph is also studied for the effective computation of wiener index of a fuzzy graph an algorithm is proposed a real life application related with human trafficking and illegal immigration is presented towards the end