self dual instantons and holomorphic curves a gradient flow of a morse function on a compact riemannian manifold is said to be of morse smale type if the stable and unstable manifolds of any two critical points intersect transversally for such a morse smale gradient flow there is a chain complex generated by the critical points and graded by the morse index the boundary operator has as its x y entry the number of gradient flow lines running from x to y counted with appropriate signs whenever the difference of the morse indices is 1 the homology of this chain complex agrees with the homology of the underlying manifold m and this can be used to prove the morse inequalities cf 33 26 around 1986 floer generalized this idea to infinite dimensional variational problems in which every critical point has infinite morse index but the moduli spaces of connecting orbits form finite dimensional manifolds for every pair of critical points the dimensions of these spaces give rise to a relative morse index and the boundary operator is defined by counting connecting

localization and diagonalization a review of functional integral techniques for low dimensional gauge theories and topological field theories localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low dimensional gauge theories are reviewed these are the functional integral counterparts of the mathai quillen formalism the duistermaat heckman theorem and the weyl integral formula respectively in each case the necessary mathematical background euler classes of vector bundles equivariant cohomology topology of lie groups is introduced and the finite dimensional integration formulae described then some applications to path integrals are discussed and an overview of the relevant literature is given the applications include supersymmetric quantum mechanics cohomological field theories phase space path integrals and two dimensional yang mills theory

the randomization technique as a modeling tool and solution procedure for transient markov processes we present a randomization procedure for computing transient solutions to discrete state space continuous time markov processes this procedure computes transient state probabilities it is based on a construction relating a continuous time markov process to a discrete time markov chain modifications and extensions of the randomization method allow for computation of distributions of first passage times and sojourn times in markov processes and also the computation of expected cumulative occupancy times and expected number of events occurring during a time interval several implementations of the randomization procedure are discussed in particular we present an implementation for a general class of markov processes that can be described in terms of state space s event set e rate vectors r and target vectors t abbreviated as sert this general approach can handle systems whose state spaces are quite large if they have sparse generators

higher gauge theory differential versus integral formulation the term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels essentially given by 1 and 2 forms so far there have been two approaches to this subject the differential picture uses non abelian 1 and 2 forms in order to generalize the connection 1 form of a conventional gauge theory to the next level the integral picture makes use of curves and surfaces labeled with elements of non abelian groups and generalizes the formulation of gauge theory in terms of parallel transports we recall how to circumvent the classic no go theorems in order to define non abelian surface ordered products in the integral picture we then derive the differential picture from the integral formulation under the assumption that the curve and surface labels depend smoothly on the position of the curves and surfaces we show that some aspects of the no go theorems are still present in the differential but not in the integral picture this implies a substantial structural

an improved result on reachable set estimation and synthesis of time delay systems in this paper the problems of reachable set estimation and synthesis of time delay systems are investigated by introducing the non uniform delay partitioning method and the triple integral technique an improved reachable set estimation condition is proposed in terms of linear matrix inequality based on the criterion a sufficient condition for the existence of a state feedback controller is established to render the reachable set of the closed loop system be bounded by a given ellipsoid two numerical examples are given to demonstrate the effectiveness of the obtained results

a vanishing result for a casson type instanton invariant casson type invariants emerging from donaldson theory over certain negative definite 4 manifolds were recently suggested by andrei teleman these are defined by a count of a zero dimensional moduli space of flat instantons motivated by the cobordism program of proving witten s conjecture we use a moduli space of pu 2 seiberg witten monopoles to exhibit an oriented one dimensional cobordism of the instanton moduli space to the empty space the casson type invariant must therefore vanish

technical communique new conditions for delay derivative dependent stability two recent lyapunov based methods have significantly improved the stability analysis of time delay systems the delay fractioning approach of gouaisbaut and peaucelle 2006 for systems with constant delays and the convex analysis of systems with time varying delays of park and ko 2007 in this paper we develop a convex optimization approach to stability analysis of linear systems with interval time varying delay by using the delay partitioning based lyapunov krasovskii functionals lkfs novel lkfs are introduced with matrices that depend on the time delays these functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives

existence of irreducible representations for knot complements with nonconstant equivariant signature mathematics subject classi cation 1991 57m25 57m05 58g03 57r571 introductionthe purpose of this paper is to establish the existence of irreducible su 2 repre sentations of knot complement fundamental groups near abelian representationswhere the equivariant knot signature changes for knots in s

on the phase of chern simons theory with complex gauge group we compute the eta function for chern simons quantum field theory with complex gauge group the calculation is performed using the schwinger expansion technique we discuss in particular the role of the metric on the field configuration space and demonstrate that for a certain class of acceptable metrics the one loop phase contribution to the effective action can be calculated explicitly the result is found to be proportional to a gauge invariant part of the action

bλf theory and flat spacetimes we propose a reduced constrained hamiltonian formalism for the exactly solubleb f theory of flat connections and closed two forms over manifolds with topology 3 0 1 the reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group 1 3 and elements of the second cohomology group of 3 with value in the lie algebral g wheng so 3 1 and if the two form can be expressed asb e e for some vierbein fielde then the variables represent a flat spacetime this is not always possible we show that the solutions of the theory generally represent spacetimes with global torsion we describe the dynamical evolution of spacetimes with and without global torsion and classify the flat spacetimes which admit a locally homogeneous foliations following thurston s classification of geometric structures

new finite sum inequalities with applications to stability of discrete time delay systems this paper is concerned with the problem of stability analysis of discrete time delay systems new finite sum inequalities which encompass the ones based on abel lemma or wirtinger type inequality are first proposed the potential capability of the newly derived inequalities is then demonstrated by establishing less conservative stability conditions for some classes of linear discrete time systems with delay the derived stability criteria are theoretically and numerically proved to be less conservative than existing results

exactly soluble diffeomorphism invariant theories a class of diffeomorphism invariant theories is described for which the hilbert space of quantum states can be explicitly constructed these theories can be formulated in any dimension and include witten s solution to 2 1 dimensional gravity as a special case higher dimensional generalizations exist which start with an action similar to the einstein action inn dimensions many of these theories do not involve a spacetime metric and provide examples of topological quantum field theories one is a version of yang mills theory in which the only quantum states ons3 r are the vacua finally it is shown that the three dimensional chern simons theory which witten has shown is intimately connected with knot theory arises naturally from a four dimensional topological gauge theory

inexact uniformization method for computing transient distributions of markov chains the uniformization method also known as randomization is a numerically stable algorithm for computing transient distributions of a continuous time markov chain when the solution is needed after a long run or when the convergence is slow the uniformization method involves a large number of matrix vector products despite this the method remains very popular due to its ease of implementation and its reliability in many practical circumstances because calculating the matrix vector product is the most time consuming part of the method overall efficiency in solving large scale problems can be significantly enhanced if the matrix vector product is made more economical in this paper we incorporate a new relaxation strategy into the uniformization method to compute the matrix vector products only approximately we analyze the error introduced by these inexact matrix vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications

topological higher gauge theory from bf to bfcg theory we study generalizations of three and four dimensional bf theories in the context of higher gauge theory first we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of yetter mackaay and porter under certain conditions we can present their corresponding continuum counterparts in terms of classical lagrangians we then explain that two of these models are already familiar from the literature the ea model of three dimensional gravity coupled to topological matter and also a four dimensional model of bf theory coupled to topological matter

dressing symmetries of holomorphic bf theories we consider holomorphic bf theories their solutions and symmetries the equivalence of cech and dolbeault descriptions of holomorphic bundles is used to develop a method for calculating hidden nonlocal symmetries of holomorphic bf theories a special cohomological symmetry group and its action on the solution space are described

dirichlet and neumann boundary value problems for yang mills connections the yang mills equations have been extensively studied on compact riemannian manifolds without boundary a substantial amount of work has also been done on non compact examples with a boundary component at infinity see 5 10 11 14 15 here we define and describe a solution of dirichlet and neumann boundary value problems for yang mills connections on a compact four dimensional manifold with smooth boundary the equations in the interior are the full yang mills equations we do not restrict ourselves to self dual or anti self dual solutions in the case where the structure group in the gauge theory is abelian our results are contained in the hodge de rham theory for manifolds with boundary see 6 9 4 3 in the general case our results describe a non linear version of this theory the base manifold m of the theory is a compact orientable four dimensional manifold with smooth boundary m we assume that m is endowed with a riemannian metric we consider a principal fiber bundle p over m with structure group g a compact lie group which will have a metric invariant under the adjoint action in the usual example this comes from trace the unknown in the problem is the connection a i e a differential form in p ad g where g is the lie algebra of g there are two natural boundary value problems one of them requires fixing the tangential part of the connection a on the bundle restricted to m if m is locally described as x 0 this amounts to prescribing a1 x dx a2 x dx 2 a3 x dx 3 on m the connection is fixed in the sense that a particular choice is fixed in the gauge equivalence class of a on the boundary the yang mills equations are satisfied in the interior this corresponds to the dirichlet problem in the other boundary value problem we consider a is free at the boundary but the normal part of the curvature is set equal to zero we call this the neumann problem for the dirichlet problem we consider a sequence of l1 connections that minimizes the yang mills functional with prescribed admissible tangential boundary data we show that there exists a weak limiting connection a by finding local good gauges the limiting connection is only locally defined we show that a solves the yang mills equations and satisfies the boundary conditions up to

higher dimensional bf theories in the batalin vilkovisky formalism the bv action and generalized wilson loops this paper analyzes in detail the batalin vilkovisky quantization procedure for bf theories on an n dimensional manifold and describes a suitable superformalism to deal with the master equation and the search of observables in particular generalized wilson loops for bf theories with additional polynomial b interactions are discussed in any dimensions the paper also contains the explicit proofs to the theorems stated in 16

abelian bf theory and turaev viro invariant the u 1 bf quantum field theory is revisited in the light of deligne beilinson cohomology we show how the u 1 chern simons partition function is related to the bf one and how the latter on its turn coincides with an abelian turaev viro invariant significant differences compared to the non abelian case are highlighted

delay dependent stability criteria for generalized neural networks with two delay components this paper investigates the delay dependent stability for generalized continuous neural networks with time varying delays a novel lyapunov krasovskii functional lkf that considers more information on activation functions of delayed neural networks and delay upper bounds is developed simultaneously most commonly used techniques for treating the derivative of the lkf are reviewed and compared with each other with the way of introducing slack matrices those techniques are classified into two categories including free weighting matrix fwm based techniques and reciprocally convex combination based techniques it is found that the introduced slack matrices play an important role in conservatism reducing and those four types of fwm based methods lead to same results and are equivalent moreover the obtained criteria are extended to the system with a single time varying delay two numerical examples are given to verify the effectiveness of the proposed method

spectral flow and bifurcation of critical points of strongly indefinite functionals abstract our main results here are as follows let x be a family of 2 periodic hamiltonian vectorfields that depend smoothly on a real parameter in a b and has a known trivial branch s of 2 periodic solutions let p be the poincare map of the linearization of x at s if the conley zehnder index of the path p does not vanish then any neighborhood of the trivial branch of periodic solutions contains 2 periodic solutions not on the branch moreover if each solution s is constant and each linearization a of x at s is time independent then bifurcation of 2 periodic orbits from the branch of equilibria arises whenever i a b i a b where i a is the index of the linear hamiltonian system ju au

technical communique further result on reachable set bounding for linear uncertain polytopic systems with interval time varying delays the problem of reachable set estimation of linear uncertain polytopic time varying delay systems subject to bounded peak inputs is studied in this paper the delays considered in this paper are assumed to be non differentiable and vary within an interval where the lower and upper bounds are known based on the lyapunov krasovskii method and delay decomposition technique a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one dimensional search method and matlab s lmi toolbox and allow us to find the smallest radius a numerical example is given to illustrate the effectiveness of the proposed result

an extended reciprocally convex matrix inequality for stability analysis of systems with time varying delay abstract the reciprocally convex combination lemma rccl is an important technique to develop stability criteria for the systems with a time varying delay this note develops an extended reciprocally convex matrix inequality which reduces the estimation gap of the rccl based matrix inequality and reduces the number of decision variables of the recently proposed delay dependent rccl a stability criterion of a linear time delay system is established through the proposed matrix inequality finally a numerical example is given to demonstrate the advantage of the proposed method

chern simons functional and the homology cobordism group for each integral homology sphere y we construct a function y on the set of integers we establish that y depends only on the homology cobordism class of y and that it recovers the froyshov invariant we state a relation between y and fintushel and stern s r invariant we show that the value of y at each integer is related to the critical values of the chern simons functional and we give some topological applications of y in particular we show that if y is trivial then there is no simply connected homology cobordism from y to itself

letter to the editor stability analysis on delayed neural networks based on an improved delay partitioning approach in this paper the asymptotical stability is investigated for a class of delayed neural networks dnns in which one improved delay partitioning idea is employed by choosing an augmented lyapunov krasovskii functional and utilizing general convex combination method two novel conditions are obtained in terms of linear matrix inequalities lmis and the conservatism can be greatly reduced by thinning the partitioning of delay intervals moreover the lmi based criteria heavily depend on both the upper and lower bounds on time delay and its derivative which is different from the existent ones though the results are not presented via standard lmis they still can be easily checked by resorting to matlab lmi toolbox finally three numerical examples are given to demonstrate that our results can be less conservative than the present ones

robust h state feedback control for linear systems this paper investigates the problem of robust h control for linear systems first the state feedback closed loop control algorithm is designed second by employing the geometric progression theory a modified augmented lyapunov krasovskii functional lkf with the geometric integral interval is established then parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill this technique can eliminate the unnecessary enlargement of the lkf derivative estimation which gives less conservatism in addition the designed controller can ensure that the linear systems are globally asymptotically stable with a guaranteed h performance in the presence of a disturbance input and parameter uncertainties a liquid monopropellant rocket motor with a pressure feeding system is evaluated in a simulation example it shows that this proposed state feedback control approach achieves the expected results for linear systems in the sense of the prescribed h performance

a geometric proof of the fintushel stern formula abstract the fintushel stern formula asserts that the casson invariant of a brieskorn homology sphere p q r equals 1 8 the signature of its milnor fiber we give a geometric proof of this formula as opposite to computational methods used in the original proof the formula is also refined to relate equivariant casson invariants to equivariant signatures

self adjoint elliptic operators and manifold decompositions part iii determinant line bundles and lagrangian intersection the theory of spectral flows developed in the series 10 11 12 and the present paper has a wide range of applications to important geometric operators on compact manifolds to present our results on spectral flow and manifold decomposition the present paper develops a theory of determinant line bundles and infinitedimensional lagrangians associated to self adjoint elliptic operators on compact manifolds the trace class properties of these infinite lagrangians established here and the precise uniform estimates relating them to finite lagrangians are crucial for such a determinant line bundle approach to analytical questions as an application we elucidate the walker s and other generalizations of casson s su 2 representation theoretic invariant of 3 manifolds in terms of the invariant of certain dirac operators this is carried out by introducing the technique of canonical perturbations of singular lagrangian subvarieties in symplectic geometry at the end of part ii of this series we obtained a formulation of the spectral flow of a family of self adjoint elliptic operators d u l2 e l2 e in terms

three dimensional quantum gravity chern simons theory and the a polynomial we study three dimensional chern simons theory with complex gauge group sl 2 which has many interesting connections with three dimensional quantum gravity and geometry of hyperbolic 3 manifolds we show that in the presence of a single knotted wilson loop in an infinite dimensional representation of the gauge group the classical and quantum properties of such theory are described by an algebraic curve called the a polynomial of a knot using this approach we find some new and rather surprising relations between the a polynomial the colored jones polynomial and other invariants of hyperbolic 3 manifolds these relations generalize the volume conjecture and the melvin morton rozansky conjecture and suggest an intriguing connection between the sl 2 partition function and the colored jones polynomial

n 2 topological gauge theory the euler characteristic of moduli spaces and the casson invariant we discuss gauge theory with a topologicaln 2 symmetry this theory captures the de rham complex and riemannian geometry of some underlying moduli space and the partition function equals the euler number of we explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions to motivate our constructions we explain the relation between the mathai quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the gauss codazzi equations we interpret the gauge theory actions from the atiyah jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of connections as a consequence of these considerations we propose the euler number of the moduli space of flat connections as a generalization to arbitrary three manifolds of the casson invariant we also comment on the possibility of constructing a topological version of the penner matrix model

a knot invariant via representation spaces a beautiful construction of a casson on the representation spaces corresponding to a heegard splitting of an oriented homology 3 sphere m gives rise to an integer invariant m of m this invariant generalizes the rohlin invariant and gives stricking corollaries in low dimension al topology defined as an intersection number of appropriate subspaces this invariant m can be roughly thought of as the number of conjugacy classes of irreducible representations of n m into su2 counted with signs a detailed discussion of this invariant can be found in an expose by s akbulut and j mccarthy 1 further works on casson s invariant include the generalizations by k walker as well as s boyer and a nicas to rational homology 3 spheres 14 3 and by s cappell r lee and e miller to representatio ns into sun 4 the works of c taubes 13 and a flore 6 interpret casson s invariant as the euler number of the instanton homology or flore homology of m in this paper analogous to casson s original construction we will define an intersection number of the representation spaces corresponding to a braid representative of a knot k in s this intersection number turns out to be an integer knot invariant see theorem 1 8 the representations of the knot group s k used in our construction seem to be mysterious they are representations of s3 k into su2 such that all meridians of k are represented by trace zero matrices call such a representation of the knot group a trace free representation then roughly speaking our knot invariant h k is the number of conjugacy classes of irreducible trace free representations of s3 k counted with signs our knot invariant h k can be computed via knot diagrams it turns out that our algorithm of computing h k by using the skein model is the same as the algorithm of computing sgn k given by j h conway 5

an instanton invariant for 3 manifolds to an oriented closed 3 dimensional manifoldm withh1 m 0 we assign a 8 graded homology groupi m whose euler characteristic is twice casson s invariant the definition uses a construction on the space of instantons onm

topological quantum field theories on manifolds with a boundary we consider a class of exactly soluble topological quantum field theories on manifolds with a boundary that are invariant on shell under diffeomorphisms which preserve the boundary after showing that the functional integral of the two point function with boundary conditions yields precisely the linking number we use it to derive topological properties of the linking number considering gauge fixing we obtain exact results of the partition function ray singer torsion of manifolds with a boundary and then point functions in closed expressions

implicit ode solvers with good local error control for the transient analysis of markov models obtaining the transient probability distribution vector of a continuous time markov chain ctmc using an implicit ordinary differential equation ode solver tends to be advantageous in terms of run time computational cost when the product of the maximum output rate of the ctmc and the largest time of interest is large in this paper we show that when applied to the transient analysis of ctmcs many implicit ode solvers are such that the linear systems involved in their steps can be solved by using iterative methods with strict control of the 1 norm of the error this allows the development of implementations of those ode solvers for the transient analysis of ctmcs that can be more efficient and more accurate than more standard implementations

chern simons field theories with non semisimple gauge group of symmetry the subject of this work is a class of chern simons field theories with non semisimple gauge group which may well be considered as the most straightforward generalization of an abelian chern simons field theory as a matter of fact these theories which are characterized by a non semisimple group of gauge symmetry have cubic interactions like those of non abelian chern simons field theories but are free from radiative corrections moreover at the tree level in the perturbative expansion there are only two connected tree diagrams corresponding to the propagator and to the three vertex originating from the cubic interaction terms for such theories it is derived here a set of brst invariant observables which lead to metric independent amplitudes the vacuum expectation values of these observables can be computed exactly from their expressions it is possible to isolate the gauss linking number and an invariant of the milnor type which describes the topological relations among three or more closed curves

link invariants for flows in higher dimensions linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of bf theories the linking numbers associated with n manifolds with smooth flows generated by divergence free p vector fields endowed with an invariant flow measure are computed in the context of quantum field theory they constitute invariants of smooth dynamical systems for nonsingular flows and generalize previous proposals of invariants in particular they generalize arnold s asymptotic hopf invariant from three to higher dimensions this invariant is generalized by coupling with a non abelian gauge flat connection with nontrivial holonomy the computation of the asymptotic jones witten invariants for flows is naturally extended to dimension n 2p 1 finally we give a possible interpretation and implementation of these issues in the context of 11 dimensional supergravity and string theory

non trivial involutions on floer homology we construct the first examples of irreducible 3 manifolds with the homology of s1 s2 admitting an involution acting non trivially on their floer homology the examples are obtained by 0 surgery along certain composite amphicheiral knots whose su 2 representation variety satisfies a non degeneracy condition

fundamental limits on uncertain delays when is a delay system stabilizable by lti controllers this paper concerns the stabilization of linear time invariant lti systems subject to uncertain possibly time varying delays the fundamental issue under investigation referred to as the delay margin problem addresses the question what is the largest range of delay such that there exists a single lti feedback controller capable of stabilizing all the plants for delays within that range drawing upon analytic interpolation and rational approximation techniques we derive fundamental bounds on the delay margin within which the delay plant is guaranteed to be stabilizable by a certain lti output feedback controller our contribution is threefold first for single input single output siso systems with an arbitrary number of plant unstable poles and nonminimum phase zeros we provide an explicit computationally efficient bound on the delay margin which requires computing only the largest real eigenvalue of a constant matrix second for multi input multi output mimo systems we show that estimates on the variation ranges of multiple delays can be obtained by solving lmi problems and further by finding bounds on the radius of delay variations third we show that these bounds and estimates can be extended to systems subject to time varying delays when specialized to more specific cases e g to plants with one unstable pole but possibly multiple nonminimum phase zeros our results give rise to analytical expressions exhibiting explicit dependence of the bounds and estimates on the pole and zeros thus demonstrating how fundamentally unstable poles and nonminimum phase zeros may limit the range of delays over which a plant can be stabilized by a lti controller

a unified proof for the convergence of jacobi and gauss seidel methods we present a new unified proof for the convergence of both the jacobi and the gauss seidel methods for solving systems of linear equations under the criterion of either a strict diagonal dominance of the matrix or b diagonal dominance and irreducibility of the matrix these results are well known the proof for criterion a makes use of gersgorin s theorem while the proof for criterion b uses taussky s theorem that extends gersgorin s work hence the topic is interesting for teaching purposes

gauge invariant factorization and canonical quantization of topologically massive gauge theories in any dimension abelian topologically massive gauge theories tmgt provide a topological mechanism to generate mass for a bosonic p tensor field in any spacetime dimension these theories include the 2 1 dimensional maxwell chern simons and 3 1 dimensional cremmer scherk actions as particular cases within the hamiltonian formulation the embedded topological field theory tft sector related to the topological mass term is not manifest in the original phase space however through an appropriate canonical transformation a gauge invariant factorisation of phase space into two orthogonal sectors is feasible the first of these sectors includes canonically conjugate gauge invariant variables with free massive excitations the second sector which decouples from the total hamiltonian is equivalent to the phase space description of the associated non dynamical pure tft within canonical quantisation a likewise factorisation of quantum states thus arises for the full spectrum of tmgt in any dimension this new factorisation scheme also enables a definition of the usual projection from tmgt onto topological quantum field theories in a most natural and transparent way none of these results rely on any gauge fixing procedure whatsoever comment 1 25 pages no figures

further refinements in stability conditions for time varying delay systems abstract this paper addresses the problem of assessing the stability of linear time invariant lti systems with time varying delay the first contribution is a new stability criterion specified as a negativity condition for a quadratic function parameterized by the delay this result mainly follows from an augmented affine parameter dependent lyapunov krasovskii functional which in turn takes advantages of convexity properties then as a second contribution we invoke a result from robust control literature to show how the proposed stability condition can be checked exactly in terms of linear matrix inequality lmi conditions the improvements obtained by the proposed refinements are illustrated via numerical examples drawn from the literature

floer homology and homotopy planes we compute the floer homology of a certain family of homology 3spheres occuring as the boundary of a compactification of complex homotopy planes the floer complex turns out to be concentrated in even degrees and 2 periodic this is proved by using suitable bordisms to seifert fibred spaces

generalized reciprocally convex combination lemmas and its application to time delay systems various efficient matrix inequalities have recently been proposed to deal with the stability analysis of linear systems with time varying delays this paper provides more insights on the relationship between some of them we present an equivalent formulation of moon et al s inequality allowing us to discover strong links not only with the most recent and efficient matrix inequalities such as the reciprocally convex combination lemma and also its relaxed version but also with some previous inequalities such as the approximation inequality introduced in 14 or free matrix based inequality more especially it is proved that these existing inequalities can be captured as particular cases of moon et al s inequality examples show the best tradeoff between the reduction of conservatism and the numerical complexity

a quantum field theoretic description of linking numbers and their generalization it is shown that the linking number of two surfaces of dimensionp andn p 1 in ann dimensional manifold has a natural description in terms of the two point funciton of a simple topological field theory the two point function of a more general theory whose partition function yields the ray singer torsion provides a definition for a generalized linking number

loop and path spaces and four dimensional bf theories connections holonomies and observables we study the differential geometry of principal g bundles whose base space is the space of free paths loops on a manifold m in particular we consider connections defined in terms of pairs a b where a is a connection for a fixed principal bundle p m g and b is a 2 form on m the relevant curvatures parallel transports and holonomies are computed and their expressions in local coordinates are exhibited when the 2 form b is given by the curvature of a then the so called non abelian stokes formula follows

gauge theories on four dimensional riemannian manifolds this paper develops the riemannian geometry of classical gauge theories yang mills fields coupled with scalar and spinor fields on compact four dimensional manifolds some important properties of these fields are derived from elliptic theory regularity an energy gap theorem the manifold structure of the configuration space and a bound for the supremum of the field in terms of the energy it is then shown that finite energy solutions of the coupled field equations cannot have isolated singularities this extends a theorem of k uhlenbeck

instanton homology of seifert fibred homology three spheres for an oriented integral homology 3 sphere 2 a casson has introduced an integer invariant a 2 that is defined by using the space 2 of conjugacy classes of irreducible representations of 2 into su 2 see 1 this invariant a 2 can be computed from a surgery or heegard description of 2 and satisfies a 2 ju 2 mod 2 where i 2 is the kervaire milnor rochlin invariant of 2 this powerful new invariant was used to settle an outstanding problem in 3 manifold topology namely showing that if 2 is a homotopy 3 sphere then ju 2 o c taubes 17 utilizing gauge theoretic considerations has reinterpreted casson s invariant in terms of flat connections refining this approach a floer 13 has recently defined another invariant of 2 its instanton homology which takes the form of an abelian group 2 with a natural z8 grading that is an enhancement of a 2 in that

the integer valued su 3 casson invariant for brieskorn spheres we develop techniques for computing the integer valued su 3 casson in variant defined in 6 our method involves resolving the singularities in the flat moduli space using a twisting perturbation and analyzing its effect on the topology of the per turbed flat moduli space these techniques together with bott morse theory and the splitting principle for spectral flow are applied to calculatesu 3 for all brieskorn homology spheres

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

the su 3 casson invariant for integral homology 3 spheres we derive a gauge theoretic invariant of integral homology 3 spheres which counts gauge orbits of irreducible perturbed flat su 3 connections with sign given by spectral flow to compensate for the dependence of this sum on perturbations the invariant includes contributions from the reducible perturbed flat orbits our formula for the correction term generalizes that given by walker in his extension of casson s su 2 invariant to rational homology 3 spheres

self adjoint elliptic operators and manifold decompositions part i low eigenmodes and stretching this paper is the first of a three part investigation into the behavior of analytical invariants of manifolds that can be split into the union of two submanifolds in this article we will show how the low eigensolutions of a self adjoint elliptic operator over such a manifold can be studied by a splicing construction this construction yields an approximated solution of the operator whenever we have two l2 solutions on both sides and a common limiting value of two extended l2 solutions in part 11 the present analytic mayer vietoris results on low eigensolutions and further analytic work will be used to obtain a decomposition theorem for spectral flows in terms of maslov indices of lagrangians in part i11 after comparing infinite and finite dimensional lagrangians and determinant line bundles and then introducing canonical perturbations of lagrangian subvarieties of symplectic varieties we will study invariants of 3 manifolds including casson s invariant 0 1996 john wiley sons inc

technical communique new stability criteria for linear systems with interval time varying delay this paper investigates robust stability of uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and is a fast time varying function the uncertainty under consideration includes polytopic type uncertainty and linear fractional norm bounded uncertainty a new lyapunov krasovskii functional which makes use of the information of both the lower and upper bounds of the interval time varying delay is proposed to drive some new delay dependent stability criteria in order to obtain much less conservative results a tighter bounding for some term is estimated moreover no redundant matrix variable is introduced finally three numerical examples are given to show the effectiveness of the proposed stability criteria

delay partitioning approach for systems with interval time varying delay and nonlinear perturbations this paper considers the problem of robust stability for a class of linear systems with interval time varying delay and nonlinear perturbations less conservative stability criteria was put forward by using delay partitioning approach by decomposing the delay interval into multiple equidistant subintervals new lyapunov krasovskii l k functional contains some triple integral terms and augment terms which are introduced on these intervals thus resulting in being much less conservative than most existing results in the literature in addition in deriving the stability conditions in linear matrix inequality lmi framework neither model transformations nor superfluous free weighting matrix are employed for dealing the cross terms that emerge from the time derivative of the l k functional instead they are dealt using tighter integral inequalities which only contain a minimal number of slack matrix variables numerical examples are given to demonstrate the effectiveness of the proposed approach

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

combined convex technique on delay dependent stability for delayed neural networks in this brief by employing an improved lyapunov krasovskii functional lkf and combining the reciprocal convex technique with the convex one a new sufficient condition is derived to guarantee a class of delayed neural networks dnns to be globally asymptotically stable since some previously ignored terms can be considered during the estimation of the derivative of lkf a less conservative stability criterion is derived in the forms of linear matrix inequalities whose solvability heavily depends on the information of addressed dnns finally we demonstrate by two numerical examples that our results reduce the conservatism more efficiently than some currently used methods

stability analysis of linear systems with time varying delay via intermediate polynomial based functions abstract this note is devoted to stability analysis for linear system with time varying delay by advisably introducing slack matrices novel fractional order intermediate polynomial based functions ipfs are proposed then the stability condition is derived for the time delay system from configuration on fractional order polynomials the relationships among system states are taken into account and consolidated via slack variables and the characteristics for integral inequality are synthetically considered while avoiding higher order time delays more remarkably adjusting tunable parameters also contributes to reduction of conservatism the comparisons of computational complexity and stability region on a well known numerical example are provided to validate the advantages of the resulting stability criterion

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

on backwards and forwards reachable sets bounding for perturbed time delay systems linear systems with interval time varying delay and unknown but bounded disturbances are considered in this paper we study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system firstly two definitions on forwards and backwards reachable sets where initial state vectors are not necessary to be equal to zero are introduced then by using the lyapunov krasovskii method two sufficient conditions for the existence of i the smallest possible outer bound of forwards reachable sets and ii the largest possible inter bound of backwards reachable sets are derived these conditions are presented in terms of linear matrix inequalities with two parameters need to tuned which therefore can be efficiently solved by combining existing convex optimization algorithms with a two dimensional search method to obtain optimal bounds lastly the obtained results are illustrated by four numerical examples

stability analysis for linear delayed systems via an optimally dividing delay interval approach this paper addresses the problem of stability for linear systems with time varying delay a novel augmented lyapunov krasovskii functional is constructed by using the idea of optimally dividing the delay interval 0 t into some variable sub intervals and line integral technology using the novel augmented functional the new delay dependent stability criteria are proposed for linear systems with time varying delay the gain is that this stability criterion can lead to much less conservative stability results compared to other methods for linear systems with delay two numerical examples are provided to verify the effectiveness of the proposed criteria

even dimensional generalization of chern simons action and new gauge symmetry we propose a new even dimensional action which shares close algebraic similarities with the chern simons action and thus possesses a topological nature this action has a new type of gauge symmetry in the sense that adjoint representation is not enough to close the gauge transformation and gauge fermions are incorporated quaternionic structure emerges as a natural algebra to control the different natures of even forms odd forms bosons and fermions we claim that the bundle structure in consideration is mathematically a new object

local symmetries of the non abelian two form an inhomogeneous gauge transformation law for non abelian two forms in b f type theories is proposed and corresponding invariant actions are discussed the auxiliary one form required for maintaining vector gauge symmetry in some of these theories transforms like a gauge field and hence cannot be set to zero by a gauge choice it can be set equal to the usual gauge field by a gauge choice leading to gauge equivalences between different types of theories those with the auxiliary field and those without a new type of symmetry also appears in some of these theories one which depends on local functions but cannot be generated by local constraints the corresponding conserved currents and brst charges are parametrized by the space of flat connections

notes on stability of time delay systems bounding inequalities and augmented lyapunov krasovskii functionals the bounding inequalities and the lyapunov krasovskii functionals lkfs are important for the stability analysis of time delay systems much attention has been paid to develop tighter inequalities for improving stability criteria while the contribution of the lkfs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria this note is concerned with this issue firstly it is proved that when a simple lkf is applied the stability criteria obtained by the wirtinger based inequality and the jensen inequality are equivalent although the wirtinger based inequality is tighter it means that the tighter inequality does not always lead to a less conservative criterion secondly it is found that a suitable augmented lkf with necessary integral vectors in its derivative is required to achieve the advantage of the wirtinger based inequality based on this observation two delay product type terms are introduced into the lkf to establish new stability criteria finally a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria

lie symmetries and particular solutions of seiberg witten equations in r3 it is shown that the conformal group of three dimensional euclidean space so 4 1 is a maximal group of lie symmetries of the seiberg witten and freund s equations in r3 particular explicit solutions which are invariant under some subgroups of so 4 1 are constructed