moment estimate and existence for solutions of stochastic functional differential equations abstract in this paper we give the existence uniqueness theorems and the moment estimates of solutions for a large class of sfdes these estimates improve and extend some related results including exponential stability decay stability and asymptotic behavior their corollaries improve and extend the classical halanay inequality and some of its generalizations moreover the stochastic version of the wintner theorem in continuous function space is established by the compare principle which improves and extends the main results of xu et al 2008 2013 when the methods presented are applied to the sfdes with impulses and sfdes in hilbert spaces we extend the related results of govindan and ahmed 2013 liu et al 2007 2010 vinodkumar 2010 and xu et al 2012 two examples are provided to illustrate the effectiveness of our results

on b function spectrum and rational singularity by duality 18 because r tr ccy 0 for i 0 by 6 31 this follows also from 13 21 23 where rc is assumed projective here coy denotes the dualizing sheaf i e the dualizing complex 18 shifted by the dimension to the right the trace morphism 0 2 is injective and its image is independent of the choice of resolution because 0 2 is an isomorphism if y is smooth we will denote by csy the image of 0 2 see 2 4 8 below now assume y is a reduced divisor d on a complex manifold x of dimension n let f be a reduced defining equation of d on a neighborhood of a c d the b function i e bernstein polynomial of f is a monic polynomial bf s in s with rational coefficients and is a generator of the ideal whose element b s satisfies the relation

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

stability analysis for neutral stochastic delay systems with markovian switching abstract this paper considers the exponential stability in p th p 1 moment and the almost sure exponential stability for neutral stochastic delay systems with markovian switching by using the generalized integral inequality and the nonnegative local martingale convergence theorem the lyapunov stability results on the exponential stability in p th p 1 moment and the almost sure exponential stability for such systems are given when the time varying delay is a bounded measurable function and the coefficients in the monotonicity condition are time varying the derived results are illustrated by two examples

structural properties of large scale systems the role of the structural properties of large scale systems for the synthesis of feasible control schemes is investigated the feasibility of considering a state variable as an output control objective of a system is expressed via the concepts of multi input connectability and structural functional controllability it is shown that these concepts can be formulated as mixed integer linear programming milp problems and efficient algorithms are presented for the determination of the above notions as well as for accessibility structural controllability and observability several examples illustrate the concepts and the proposed approach

the canonical sheaf of du bois singularities we prove that a cohen macaulay normal variety x has du bois singularities if and only if x g x for a log resolution x x where g is the reduced exceptional divisor of many basic theorems about du bois singularities become transparent using this characterization including the fact that cohen macaulay log canonical singularities are du bois we also give a straightforward and self contained proof that generalizations of semi log canonical singularities are du bois in the cohen macaulay case it also follows that the kodaira vanishing theorem holds for semi log canonical varieties and that cohen macaulay semi log canonical singularities are cohomologically insignificant in the sense of dolgachev

non fragile observer based sliding mode control for markovian jump systems with mixed mode dependent time delays and input nonlinearity this paper is concerned with the state estimation and the sliding mode control smc for a class of markovian jump systems with mixed mode dependent time delays and input nonlinearity a non fragile observer is designed to estimate the system states and an observer based smc is synthesized to ensure the reachability of the sliding surfaces in the state estimation space by constructing a novel mode dependent lyapunov krasovskii functional some new criteria are established for the existence and the solvability of the desired observer based sliding mode controller finally numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results

stability of highly nonlinear neutral stochastic differential delay equations abstract stability criteria for neutral stochastic differential delay equations nsddes have been studied intensively for the past several decades most of these criteria can only be applied to nsddes where their coefficients are either linear or nonlinear but bounded by linear functions this paper is concerned with the stability of hybrid nsddes without the linear growth condition to which we will refer as highly nonlinear ones the stability criteria established in this paper will be dependent on delays

delay dependent exponential stability of stochastic systems with time varying delay nonlinearity and markovian switching the problem of delay dependent stability in the mean square sense for stochastic systems with time varying delays markovian switching and nonlinearities is investigated both the slowly time varying delays and fast time varying delays are considered based on a linear matrix inequality approach delay dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature

log canonical singularities are du bois a recurring difficulty in the minimal model program mmp is that while log terminal singularities are quite well behaved for instance they are rational log canonical singularities are much more complicated they need not even be cohenmacaulay the aim of this paper is to prove that as conjectured in kol92 1 13 log canonical singularities are du bois the concept of du bois singularities abbreviated as db was introduced by steenbrink in ste83 as a weakening of rationality it is not clear how to define du bois singularities in positive characteristic so we work over a field of characteristic 0 throughout the paper the precise definition is rather involved see 1 10 but our main applications rely only on the following consequence

stabilization of delay systems delay dependent impulsive control the stabilization problem of delay systems is studied under the delay dependent impulsive control the main contributions of this technical note are that for one thing it shows that time delays in impulse term may contribute to the stabilization of delay systems that is a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks for another it shows the robustness of impulsive control that is the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization in this technical note from impulsive control point of view we firstly propose an impulsive delay inequality then we apply it to the delay systems which may be originally unstable and derive some delay dependent impulsive control criteria to ensure the stabilization of the addressed systems the effectiveness of the proposed strategy is evidenced by two illustrative examples

f injective singularities are du bois in this paper we prove that singularities of f injective type are du bois this extends the correspondence between singularities associated to the minimal model program and singularities defined by the action of frobenius in positive characteristic

mixed hodge complexes on algebraic varieties using the theory of mixed hodge modules we introduce the notion of mixed hodge complex on an algebraic variety and establish the relation between the filtered complex of du bois and the corresponding complex of mixed hodge modules some application to the du bois singularity is given

lyapunov conditions for finite time stability of time varying time delay systems in this paper we develop the lyapunov razumikhin method to finite time stability fts and finite time contractive stability ftcs of time delay systems several lyapunov based sufficient conditions for establishing these fts properties are obtained then the theoretical results are applied to fts and ftcs for a class of linear time varying ltv time delay system the efficiency of the proposed criteria is illustrated by three numerical examples where a stabilizing memoryless controller for ftcs of a second order ltv system with time delay is proposed

characteristic classes of symmetric products of complex quasi projective varieties we prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi projective variety more concretely we study homology hirzebruch classes for motivic coefficients as well as for complexes of mixed hodge modules as a special case we obtain a generating series formula for the intersection homology hirzebruch classes of symmetric products in some cases the latter yields a similar formula for twisted homology l classes generalizing results of hirzebruch zagier and moonen our methods also apply to the study of todd classes of complexes of coherent sheaves as well as chern classes of complexes of constructible sheaves generalizing to arbitrary coefficients results of moonen and resp ohmoto

deligne s conjecture on 1 motives we reformulate a conjecture of deligne on 1 motives by using the integral weight filtration of gillet and soule on cohomology and prove it this implies the original conjecture up to isogeny if the degree of cohomology is at most two we can prove the conjecture for the hodge realization without isogeny and even for 1 motives with torsion

determination of the generic rank of structural matrices abstract a new algorithm for determining the generic rank of structural matrices is presented the use of the algorithm in determining whether a system is structurally controllable is discussed and it is found to be adaptable to the much wider problem of control system synthesis such as the elimination of excess manipulated variables or control objectives

the decomposition theorem perverse sheaves and the topology of algebraic maps we give a motivated introduction to the theory of perverse sheaves culminating in the decomposition theorem of beilinson bernstein deligne and gabber a goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties while most proofs are omitted we discuss several approaches to the decomposition theorem indicate some important applications and examples

mixed hodge complexes on algebraic varieties and t structures abstract the aim of this paper is to provide some complements on the categories of mixed q hodge complexes introduced by m saito in 17 in particular we prove that the category of pure diagrams has a t structure that lifts the perverse t structure and derive some consequences of this fact we also compare the category of mixed hodge complexes defined by m saito with a more naive version these complements are used in 12 to provide a partial generalization to higher dimension of a result of a be linson 1 2 which shows that the derived category of polarizable mixed hodge structures is equivalent to the more flexible triangulated category of polarizable mixed hodge complexes

new criteria on p th moment input to state stability of impulsive stochastic delayed differential systems by employing the razumikhin technique the uniformly exponentially stable function and the average dwell time adt approach some razumikhin type theorems on input to state stability iss for time varying impulsive stochastic delay differential systems isdds are obtained it is shown that if the time varying continuous stochastic delayed dynamics is iss and the impulsive effects are destabilizing then the isdds is input to state stable iss with respect to a lower bound of the average dwell time adt the existing results on iss of impulsive systems in the literature require the coefficients of the estimated upper bound for the diffusion operator of a lyapunov function to be constant numbers while the results in this note allow us the coefficients of the estimated upper bound of the diffusion operator to be sign changing time varying function an example is given to illustrate the effectiveness of our results from the example one can see the existing results fail to be used to determine the iss for some type of isdds

hodge genera of algebraic varieties ii we study the behavior of hodge genera under algebraic maps we prove thatthemotivic c y genussatisfiesthe stratifiedmultiplicativeproperty whichshows how to compute the invariant of the source of a morphism from its values on varieties arising from the singularities of the map by considering morphisms to a curve we obtain a hodge theoretic version of the riemann hurwitz formula we also study the monodromy contributions to the y genus of a family of compact complex manifolds and prove an atiyah meyer type formula in the algebraic and analytic contexts this formula measures the deviation from multiplicativity of the y genus and expresses the correction terms as higher genera associated to the period map these higher gen era are hodge theoretic extensions of novikov higher signatures to analytic and alge braic settings characteristic class formulae of atiyah meyer type are also obtained by making use of saito s theory of mixed hodge modules

stability of nonlinear differential systems with state dependent delayed impulses we consider nonlinear differential systems with state dependent delayed impulses impulses which involve the delayed state of the system for which the delay is state dependent such systems arise naturally from a number of applications and the stability issue is complex due to the state dependence of the delay we establish general and applicable results for uniform stability uniform asymptotic stability and exponential stability of the systems by using the impulsive control theory and some comparison arguments we show how restrictions on the change rates of states and impulses should be imposed to achieve system s stability in comparison with general impulsive delay differential systems with state dependent delay in the nonlinearity or the differential systems with constant delays in our approach the boundedness of the state dependent delay is not required but derives from the stability result obtained examples are given to demonstrate the sharpness and applicability of our general results and the proposed approach

characteristic classes of complex hypersurfaces abstract the milnor hirzebruch class of a locally complete intersection x in an algebraic manifold m measures the difference between the poincare dual of the hirzebruch class of the virtual tangent bundle of x and respectively the brasselet schurmann yokura homology hirzebruch class of x in this note we calculate the milnor hirzebruch class of a globally defined algebraic hypersurface x in terms of the corresponding hirzebruch invariants of vanishing cycles and singular strata in a whitney stratification of x our approach is based on schurmann s specialization property for the motivic hirzebruch class transformation of brasselet schurmann yokura the present results also yield calculations of todd chern and l type characteristic classes of hypersurfaces

optimization model for generic rank determination of structural matrices abstract a simple and rigorous approach that determines the generic rank of a structural matrix is presented this approach is based upon an integer linear programming ilp formulation which features the property of total unimodularity in the set of constraints the integer linear programming formulation of the proposed approach with the addition of integer cuts can be used to identify all the structurally redundant equations and or excess columns of a system this approach can also be used as a systematic tool to search for all the possible not necessarily feasible sets of controlled and manipulated variables of large scale control systems the features of the proposed algorithm are illustrated through a representative set of example problems

sufficient stability conditions of nonlinear differential systems under impulsive control with state dependent delay in this technical note we study the delayed impulsive control of nonlinear differential systems where the impulsive control involves the delayed state of the system for which the delay is state dependent since the state dependence of the delay makes the impulsive transients dependent on the historical information of the states which means that it is hard to know exactly a priori how far in the history the information is needed the main challenge is how to determine the historical states we resolve this challenge and establish some sufficient conditions for local stability of nonlinear differential systems with state dependent delayed impulsive control based on impulsive control theory two examples are given to show the effectiveness of the proposed approach

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

further results on exponential stability for impulsive switched nonlinear time delay systems with delayed impulse effects this paper is concerned with the problem of exponential stability for a class of impulsive switched nonlinear time delay systems with delayed impulse effects by using the multiple lyapunov krasovskii functionals technique some exponential stability criteria are obtained respectively for two kinds of impulsive signals destabilizing impulsive signal and stabilizing impulsive signal the derived results not only characterise the effects of delayed impulse time delay and switching on nonlinear systems but also remove some restriction conditions furthermore a more precise bound of system state is given compared with existing results on related problems the obtained results are less conservative three examples are provided to illustrate the effectiveness and the generality of the proposed results

exponential stability of neutral stochastic delay differential equation with delay dependent impulses abstract in this paper we mainly consider exponential stability es for a type of neutral stochastic delay differential equations with delay dependent impulses nsddewdi by means of the average dwell time adt condition a new sufficient criterion for es is given the infinitesimal operator of lyapunov functions is controlled by two time variant coefficients furthermore these new conditions are calculated through an example so as to verify the validity of our results

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

a new algorithm for determining structural controllability the physical meaning of structural controllability is explored and is used as the basis for deriving a now algorithm for determining the controllability of linear multi input time invariant processes with ill defined parameter values the algorithm can be used in system design studies to specify the number of inputs required and their points of application to ensure plant controllability a flow chart is provided for implementing the algorithm on a digital computer however it is shown that in many cases structural controllability can be determined without computational aids and this is an advantage compared with the techniques suggested by earlier workers

control objective reduction in single input single output control schemes abstract structural analysis techniques have been applied to the problem of eliminating excess control objectives when developing single input single output regulatory control schemes an algorithm is presented for determining whether a control scheme involving fewer observations than control objectives is possible and if so what are feasible minimum sots of observations

effect of delayed impulses on input to state stability of nonlinear systems abstract this paper studies the input to state stability iss and integral input to state stability iiss of nonlinear systems with delayed impulses by using lyapunov method and the analysis technique proposed by hespanha et al 2005 some sufficient conditions ensuring iss iiss of the addressed systems are obtained those conditions establish the relationship between impulsive frequency and the time delay existing in impulses and reveal the effect of delayed impulses on iss iiss an example is provided to illustrate the efficiency of the obtained results

equivariant characteristic classes of singular complex algebraic varieties homology hirzebruch characteristic classes for singular varieties have been recently defined by brasselet schuurmann and yokura as an attempt to unify previously known characteristic class theories for singular spaces e g macpherson chern classes baum fulton macpherson todd classes and goresky macpherson l classes in this paper we define equivariant analogues of these classes for singular quasi projective varieties acted upon by a finite group of algebraic automorphisms and show how these can be used to calculate the homology hirzebruch classes of global quotient varieties we also compute the new classes in the context of monodromy problems e g for varieties that fiber equivariantly in the complex topology over a connected algebraic manifold as another application we discuss atiyah meyer type formulae for twisted hirzebruch classes of global orbifolds 2012 wiley periodicals inc

characteristic classes of singular toric varieties in this paper we compute the motivic chern classes and homology hirzebruch characteristic classes of possibly singular toric varieties which in the context of complete toric varieties fit nicely with a generalized hirzebruch riemann roch theorem as important special cases we obtain new or recover well known formulae for the baum fulton macpherson todd or macpherson s chern classes of toric varieties as well as for the thom milnor l classes of simplicial projective toric varieties we present two different perspectives for the computation of these characteristic classes of toric varieties first we take advantage of the torus orbit decomposition and the motivic properties of the motivic chern and respectively homology hirzebruch classes to express the latter in terms of dualizing sheaves and respectively the dual todd classes of closures of orbits this method even applies to torus invariant subspaces of a given toric variety the obtained formula is then applied to weighted lattice point counting in lattice polytopes and their subcomplexes yielding generalized pick type formulae second in the case of simplicial toric varieties we compute our characteristic classes by using the lefschetz riemann roch theorem of edidin graham in the context of the geometric quotient description of such varieties in this setting we define mock hirzebruch classes of simplicial toric varieties which specialize to the mock chern mock todd and mock l classes of such varieties and investigate the difference between the actual homology hirzebruch class and the mock hirzebruch class we show that this difference is localized on the singular locus and we obtain a formula for it in which the contribution of each singular cone is identified explicitly finally the two methods of computing characteristic classes are combined for proving several characteristic class formulae originally obtained by cappell and shaneson in the early 1990s 2015 wiley periodicals inc

stabilization of hybrid neutral stochastic differential delay equations by delay feedback control abstract this paper is concerned with the problem of exponential mean square stabilization of hybrid neutral stochastic differential delay equations with markovian switching by delay feedback control a delay feedback controller is designed in the drift part so that the controlled system is mean square exponentially stable we discussed two types of structure controls that is state feedback and output injection the stabilization criteria are derived in terms of linear matrix inequalities

input to state stability of impulsive stochastic delayed systems under linear assumptions in this paper the input to state stability iss integral iss iiss and stochastic iss siss are investigated for impulsive stochastic delayed systems by means of the lyapunov krasovskii function and the average impulsive interval approach the conditions for iss type properties are derived under linear assumptions respectively for destabilizing and stabilizing impulses it is shown that if the continuous stochastic delayed system is iss and the impulsive effects are destabilizing then the hybrid system is iss with respect to a lower bound of the average impulsive interval moreover it is unveiled that if the continuous stochastic delayed system is not iss the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval an improved comparison principle is developed for impulsive stochastic delayed systems which facilitates the derivations of our results for iss iiss siss an example of networked control systems is provided to illustrate the effectiveness of the proposed results

hirzebruch milnor classes of complete intersections abstract we prove a new formula for the hirzebruch milnor classes of global complete intersections with arbitrary singularities describing the difference between the hirzebruch classes and the virtual ones this generalizes a formula for the chern milnor classes in the hypersurface case that was conjectured by s yokura and was proved by a parusinski and p pragacz it also generalizes a formula of j seade and t suwa for the chern milnor classes of complete intersections with isolated singularities

hodge genera of algebraic varieties i the aim of this paper is to study the behavior of hodge theoretic intersection homology genera and their associated characteristic classes under proper morphisms of complex algebraic varieties we obtain formulae that relate parametrized families of global invariants of a complex algebraic variety x to such invariants of singularities of proper algebraic maps defined on x such formulae severely constrain both topologically and analytically the singularities of complex maps even between smooth varieties similar results were announced by the first and third author in 13 32 2007 wiley periodicals inc

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

comments on determining structural controllability abstract focusing on the determination of the generic rank of structural matrices deficiencies in burrows and sahinkaya s 1981 algorithm for determining structural controllability are highlighted

a characterization of seminormal schemes abstract given a noetherian and mori ring a we show that the seminormalization of a is exactly the subring of p spec a p consisting of pointwise functions which vary algebraically along dvrs this characterization allows easy navigation among the various definitions of the seminormalization we discuss applications to the chow variety functor of algebraic cycles