on sufficient conditions for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems the specific notion under consideration is asymptotic stability independent of delay as an attempt to achieve a compromise between the complexity and tightness of various stability tests we present a number of sufficient stability conditions which improve several previously available sufficient conditions and which are also much easier to verify than the known necessary and sufficient conditions

an algorithm for computing some heegaard floer homologies in this paper we give an algorithm to compute the hat version of heegaard floer homology of a closed oriented three manifold this method also allows us to compute the filtration coming from a null homologous link in a three manifold

oscillation and global attractivity in a delay periodic host macroparasite model abstract in this paper we shall consider the nonlinear delay host macroparasite model with periodic coefficients with common period by means of a continuation theorem in coincidence degree theory we establish a sufficient condition for the existence of a positive periodic solution m t with strictly positive components also we establish some sufficient conditions for oscillation of all positive solutions about the positive periodic solution m t and establish a sufficient condition for the global attractivity of m t

stability analysis for continuous time positive systems with time varying delays this note addresses the stability problem of continuous time positive systems with time varying delays it is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a hurwitz matrix the result is a time varying version of the widely known asymptotic stability criterion for constant delay positive systems a numerical example illustrates the correctness of our result

combinatorial cobordism maps in hat heegaard floer theory in a previous article sarkar and wang 15 gave a combinatorial description of the hat version of heegaard floer homology for three manifolds given a cobordism between two connected three manifolds there is an induced map between their heegaard floer homologies assume that the first homology group of each boundary component surjects onto the first homology group of the cobordism modulo torsion under this assumption we present a procedure for finding the rank of the induced heegaard floer map combinatorially in the hat version

delay independent stability conditions for time varying nonlinear uncertain systems a new stability criterion for time varying systems consisting of linear and norm bounded nonlinear terms with uncertain time varying delays is formulated an explicit delay independent sufficient stability condition is formulated in the terms of the transition matrix of the given linear part without delay and the bounds for the uncertain terms the obtained condition turns out to be also necessary if the matrix of the linear part is time invariant and symmetric it is shown that these systems satisfy the well known aizerman s conjecture the obtained criterion is contrasted by some of stability estimates available in the literature for these kinds of systems in all cases the proposed criterion provides less conservative stability bounds

novel criteria for exponential stability of nonlinear differential systems with delay general nonlinear differential systems with time varying delay are considered several explicit criteria for global exponential stability are presented two examples are given to illustrate the obtained results

geometry of batalin vilkovisky quantization the geometry ofp manifolds odd symplectic manifolds andsp manifolds p manifolds provided with a volume element is studied a complete classification of these manifolds is given this classification is used to prove some results about batalin vilkovisky procedure of quantization in particular to obtain a very general result about gauge independence of this procedure

algebraic formulation of higher gauge theory in this paper we present a purely algebraic formulation of higher gauge theory and gauged sigma models based on the abstract theory of graded commutative algebras and their morphisms the formulation incorporates naturally becchi rouet stora tyutin brst symmetry and is also suitable for alexandrov kontsevich schwartz zaboronsky aksz type constructions it is also shown that for a full fledged batalin vilkovisky formulation including ghost degrees of freedom higher gauge and gauged sigma model fields must be viewed as internal smooth functions on the shifted tangent bundle of a space time manifold valued in a shifted l algebroid encoding symmetry the relationship to other formulations where the l algebroid arises from a higher lie groupoid by lie differentiation is highlighted

existence uniqueness and stability of stochastic neutral functional differential equations of sobolev type in this paper we are mainly concerned with a class of stochastic neutral functional differential equations of sobolev type with poisson jumps under two different sets of conditions we establish the existence of the mild solution by applying the leray schauder alternative theory and the sadakovskii s fixed point theorem respectively furthermore we use the bihari s inequality to prove the osgood type uniqueness also the mean square exponential stability is investigated by applying the gronwall inequality finally two examples are given to illustrate the theory results

exponential stability of coupled linear delay time varying differential difference equations coupled linear delay time varying differential difference equations are considered explicit criteria for exponential stability of such equations are presented the obtained results are used to derive sufficient conditions for exponential stability in linear time varying differential equations of neutral type and in singular linear delay time varying differential equations some illustrative examples are given

sufficient conditions for the existence of global solutions of delayed differential equations the purpose of this contribution is to give sufficient conditions for the existence of global solutions or left semi global solutions for some classes of delayed functional differential equations the principle of monotone sequences is used as a main tool of investigation inequalities for coordinates of global solutions are derived as a consequence of used method examples illustrate the results

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

stability analysis of nonlinear neutral functional differential equations we present a novel approach to analyze the exponential stability of nonlinear neutral functional differential equations our approach is simple and based on a system transformation the comparison principle and the spectral properties of metzler matrices consequently we derive some new explicit criteria for the exponential stability of general nonlinear neutral functional differential equations it is important to note that our approach leads to both delay dependent and delay independent stability criteria several illustrative examples with simulations and a brief comparison between the obtained results with some existing results in the literature are presented

a combinatorial description of knot floer homology given a grid presentation of a knot or link k in the three sphere we describe a heegaard diagram for the knot complement in which the heegaard surface is a torus and all elementary domains are squares using this diagram we obtain a purely combinatorial description of the knot floer homology of k

tour of bordered floer theory heegaard floer theory is a kind of topological quantum field theory tqft assigning graded groups to closed connected oriented 3 manifolds and group homomorphisms to smooth oriented four dimensional cobordisms bordered heegaard floer homology is an extension of heegaard floer homology to 3 manifolds with boundary with extended tqft type gluing properties in this survey we explain the formal structure and construction of bordered floer homology and sketch how it can be used to compute some aspects of heegaard floer theory

scalar criteria for exponential stability of functional differential equations abstract using a novel approach we present some scalar criteria for the exponential stability of general functional differential equations both delay independent and delay dependent stability criteria are provided a discussion of the obtained results is given

global stability for separable nonlinear delay differential systems abstract in this paper we consider separable nonlinear delay differential systems and we establish conditions for global asymptotic stability of the zero solution applying these we offer improved 3 2 type criteria for global asymptotic stability of nonautonomous lotka volterra systems with delays

global attractivity in delayed hopfield neural network models two different approaches are employed to investigate the global attractivity of delayed hopfield neural network models without assuming the monotonicity and differentiability of the activation functions liapunov functionals and functions combined with the razumikhin technique are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays in the case of monotone and smooth activation functions the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model such criteria depend on the magnitude of delays and show that self inhibitory connections can contribute to the global convergence

combinatorial heegaard floer homology and nice heegaard diagrams abstract we consider a stabilized version of hf of a 3 manifold y i e the u 0 variant of heegaard floer homology for closed 3 manifolds we give a combinatorial algorithm for constructing this invariant starting from a heegaard decomposition for y and give a topological proof of its invariance properties

exact renormalization group and effective action a batalin vilkovisky algebraic formulation in this article taking inspiration from costello s work on renormalization in batalin vilkovisky bv theory k j costello e print arxiv 0706 1533 math qa we present an abstract formulation of exact renormalization group rg in the framework of bv algebra theory in the first part we work out a general algebraic and geometrical theory of bv algebras canonical maps flows and flow stabilizers in the second part relying on this formalism we build a bv algebraic theory of the rg in line with the graded geometric outlook of our approach we adjoin the rg scale with an odd parameter and analyze in depth the implications of the resulting rg supersymmetry and find that the rg equation takes polchinski s form j polchinski nucl phys b 231 269 1984 finally we study abstract purely algebraic odd symplectic free models of rg flow and effective action and the perturbation theory thereof to illustrate and exemplify the general theory in this article taking inspiration from costello s work on renormalization in batalin vilkovisky bv theory k j costello e print arxiv 0706 1533 math qa we present an abstract formulation of exact renormalization group rg in the framework of bv algebra theory in the first part we work out a general algebraic and geometrical theory of bv algebras canonical maps flows and flow stabilizers in the second part relying on this formalism we build a bv algebraic theory of the rg in line with the graded geometric outlook of our approach we adjoin the rg scale with an odd parameter and analyze in depth the implications of the resulting rg supersymmetry and find that the rg equation takes polchinski s form j polchinski nucl phys b 231 269 1984 finally we study abstract purely algebraic odd symplectic free models of rg flow and effective action and the perturbation theory thereof to illustrate and exemplify the general theory

a path integral approach to the kontsevich quantization formula we give a quantum field theory interpretation of kontsevich s deformation quantization formula for poisson manifolds we show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory its batalin vilkovisky quantization yields a superconformal field theory the associativity of the star product and more generally the formality conjecture can then be understood by field theory methods as an application we compute the center of the deformed algebra in terms of the center of the poisson algebra

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

six dimensional 1 0 superconformal models and higher gauge theory we analyze the gauge structure of a recently proposed superconformal field theory in six dimensions we find that this structure amounts to a weak courant dorfman algebra which in turn can be interpreted as a strong homotopy lie algebra this suggests that the superconformal field theory is closely related to higher gauge theory describing the parallel transport of extended objects indeed we find that under certain restrictions the field content and gauge transformations reduce to those of higher gauge theory we also present a number of interesting examples of admissible gauge structures such as the structure lie 2 algebra of an abelian gerbe differential crossed modules the 3 algebras of m2 brane models and string lie 2 algebras

sharp conditions for global stability of lotka volterra systems with distributed delays abstract we give a criterion for the global attractivity of a positive equilibrium of n dimensional non autonomous lotka volterra systems with distributed delays for a class of autonomous lotka volterra systems we show that such a criterion is sharp in the sense that it provides necessary and sufficient conditions for the global asymptotic stability independently of the choice of the delay functions the global attractivity of positive equilibria is established by imposing a diagonal dominance of the instantaneous negative feedback terms and relies on auxiliary results showing the boundedness of all positive solutions the paper improves and generalizes known results in the literature namely by considering systems with distributed delays rather than discrete delays

stability of perturbed systems with time varying delays abstract this paper gives easily verifiable sufficient conditions of robust asymptotic stability of linear time delay systems subject to parametric unstructured or highly structured perturbations the criteria given in this paper are delay independent or delay dependent the considered delay may be time varying an estimation of the transient behaviour of the studied systems is also provided exponential rate of convergence scalar or vectorial inequalities involving hurwitz matrices matrix measures and norms constitute the mathematical foundations of the exposed results

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

the embedding tensor leibniz loday algebras and their higher gauge theories we show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a leibniz algebra with one of its induced quotient lie algebras embedded into a rigid symmetry lie algebra that provides an additional representation constraint every leibniz algebra gives rise to a lie n algebra in a canonical way for every n in mathbb n cup infty it is the gauging of this l infty algebra that explains the tensor hierarchy of the bosonic sector of gauged supergravity theories the tower of p from gauge fields corresponds to lyndon words of the universal enveloping algebra of the free lie algebra of an odd vector space in this construction truncation to some n yields the reduced field content needed in a concrete spacetime dimension

exponential stability and periodic oscillatory solution in bam networks with delays both exponential stability and periodic oscillatory solution of bidirectional associative memory bam networks with axonal signal transmission delays are considered by constructing suitable lyapunov functional and some analysis techniques some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of bam with delays these conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for bam with delays in addition two examples are given to illustrate the results

delay independent stability conditions and decay estimates for time varying functional differential equations this paper presents sufficient delay independent conditions that guarantee stability of nonlinear time varying functional differential equations fde s estimates on the rate of decay of solutions are also obtained

simple stability criteria for single and composite linear systems with time delays easy ways to test the stability of systems involving time delays have been sought in this paper several stability conditions with an extremely simple form are provided first some criteria for single linear systems with time delays are presented then these results are extended to the composite linear systems with time delays which exist in each subsystem and in the interconnections between subsystems among these criteria those which are expressed by scalar inequalities also permit us to assess the transient behaviour of systems

global linearized stability theory for delay differential equations abstract for nonlinear delay differential equations where nonlinearities are approximated by linear functions we discuss a rather general global stability principle several examples which extend and improve known global stability results are presented

differential geometry of gerbes abstract we define in a global manner the notion of a connective structure for a gerbe on a space x when the gerbe is endowed with trivializing data with respect to an open cover of x we describe this connective structure in two separate ways which extend from abelian to general gerbes the corresponding descriptions due to j l brylinski and n hitchin we give a global definition of the 3 curvature of this connective structure as a 3 form on x with values in the lie stack of the gauge stack of the gerbe we also study this notion locally in terms of more traditional lie algebra valued 3 forms the bianchi identity which the curvature of a connection on a principal bundle satisfies is replaced here by a more elaborate equation

global dynamics of one class of nonlinear nonautonomous systems with time varying delays abstract a class of nonautonomous systems of nonlinear delay differential equations was studied via construction of matrix inequalities and comparison techniques the results for the nonautonomous systems with time varying delays are novel e g the global stability of differential equations with nonlinear casual volterra operators is considered for the first time in the literature criteria obtained for permanence and global attractivity are explicit and hence are convenient for applying verifying in practice we illustrate applications of the results obtained to the nonautonomous and asymptotically autonomous nicholson type models