adaptive fuzzy output feedback control for switched nonstrict feedback nonlinear systems with input nonlinearities this paper studies adaptive fuzzy output feedback tracking control problem for nonstrict feedback switched nonlinear systems the switched systems under consideration contain unknown nonlinearities unmeasured states and unknown deadzones fuzzy logic systems are utilized to approximate the unknown nonlinearities and a switched fuzzy state observer is designed and thus the immeasurable states are estimated via it in the framework of observer based output feedback control and by using the certainty equivalence deadzone inverse a novel adaptive fuzzy output feedback control design method with the parameters adaptation laws is developed the stability of the closed loop system and the convergence of the tracking error are proved based on lyapunov function and the average dwell time methods two simulation examples are provided to check the effectiveness of the proposed approach

an improved global asymptotic stability criterion for delayed cellular neural networks a new lyapunov krasovskii functional is constructed for delayed cellular neural networks and the s procedure is employed to handle the nonlinearities an improved global asymptotic stability criterion is also derived that is a generalization of and an improvement over previous results numerical examples demonstrate the effectiveness of the criterion

a 3d non newtonian fluid structure interaction model for blood flow in arteries the mathematical modelling and numerical simulation of the human cardiovascular system is playing nowadays an important role in the comprehension of the genesis and development of cardiovascular diseases in this paper we deal with two problems of 3d modelling and simulation in this field which are very often neglected in the literature on the one hand blood flow in arteries is characterized by travelling pressure waves due to the interaction of blood with the vessel wall on the other hand blood exhibits non newtonian properties like shear thinning viscoelasticity and thixotropy the present work is concerned with the coupling of a generalized newtonian fluid accounting for the shear thinning behaviour of blood with an elastic structure describing the vessel wall to capture the pulse wave due to the interaction between blood and the vessel wall we provide an energy estimate for the coupling and compare the numerical results with those obtained with an equivalent fluid structure interaction model using a newtonian fluid

fibers of tropicalization we use functoriality of tropicalization and the geometry of projections of subvarieties of tori to show that the fibers of the tropicalization map are dense in the zariski topology for subvarieties of tori over fields of generalized power series points in each tropical fiber are obtained constructively using kedlaya s transfinite version of newton s method

functorial tropicalization of logarithmic schemes the case of constant coefficients the purpose of this article is to develop foundational techniques from logarithmic geometry in order to define a functorial tropicalization map for fine and saturated logarithmic schemes in the case of constant coefficients our approach crucially uses the theory of fans in the sense of kato and generalizes thuillier s retraction map onto the non archimedean skeleton in the toroidal case for the convenience of the reader many examples as well as an introductory treatment of the theory of kato fans are included

a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

holonomic and perverse logarithmic d modules abstract we introduce the notion of a holonomic d module on a smooth idealized logarithmic scheme and show that verdier duality can be extended to this context in contrast to the classical case the pushforward of a holonomic module along an open immersion is in general not holonomic we introduce a perverse t structure on the category of coherent logarithmic d modules which makes the dualizing functor t exact on holonomic modules conversely this t exactness characterizes holonomic modules among all coherent logarithmic d modules we also introduce logarithmic versions of the gabber and kashiwara malgrange filtrations

exponential h synchronization of switching fuzzy systems with time varying delay and impulses abstract this paper studies the problem of exponential h synchronization of switching fuzzy systems with time varying delay and impulses via maximum minimum dwell time the switching fuzzy model has locally takagi and sugeno t s fuzzy models and switches them according to states external variables and or time by introducing the concept of maximum minimum dwell time and a modified two side direction relation between the number of switchings and the maximum minimum dwell time a normal l 2 norm bound constraint is derived by using the matrix decomposition method and reciprocal convex combination and combining with the wirtinger based inequality which gives a sharper upper bound than the jensen s inequality some new sufficient criteria are obtained to guarantee that the error system without impulses and with impulses is globally exponentially stable with an h performance index respectively three illustrative examples are provided to show the effectiveness of the results

delay dependent exponential stabilization of positive 2d switched state delayed systems in the roesser model this paper deals with the controller synthesis for a class of positive two dimensional 2d switched delay systems described by the roesser model this kind of systems has the property that the states take nonnegative values whenever the initial boundaries are nonnegative some delay dependent sufficient conditions for the exponential stability of positive 2d switched systems with state delays are given furthermore the design of positive state feedback controller under which the resulting closed loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities lmis an example is included to illustrate the effectiveness of the proposed approach

exponential stability analysis for delayed neural networks with switching parameters average dwell time approach this paper is concerned with the problem of exponential stability analysis of continuous time switched delayed neural networks by using the average dwell time approach together with the piecewise lyapunov function technique and by combining a novel lyapunov krasovskii functional which benefits from the delay partitioning method with the free weighting matrix technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time varying delays respectively moreover the decay estimates are explicitly given the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

delay dependent criteria for global robust periodicity of uncertain switched recurrent neural networks with time varying delay in this paper we introduce some ideas of switched systems into the field of neural networks and a large class of switched recurrent neural networks srnns with time varying structured uncertainties and time varying delay is investigated some delay dependent robust periodicity criteria guaranteeing the existence uniqueness and global asymptotic stability of periodic solution for all admissible parametric uncertainties are devised by taking the relationship between the terms in the leibniz newton formula into account because free weighting matrices are used to express this relationship and the appropriate ones are selected by means of linear matrix inequalities lmis the criteria are less conservative than existing ones reported in the literature for delayed neural networks with parameter uncertainties some examples are given to show that the proposed criteria are effective and are an improvement over previous ones

stability and synchronization of discrete time neural networks with switching parameters and time varying delays this paper is concerned with the problems of exponential stability analysis and synchronization of discrete time switched delayed neural networks using the average dwell time approach together with the piecewise lyapunov function technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time delays benefitting from the delay partitioning method and the free weighting matrix technique the conservatism of the obtained results is reduced in addition the decay estimates are explicitly given and the synchronization problem is solved the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

observer design for switched recurrent neural networks an average dwell time approach this paper is concerned with the problem of observer design for switched recurrent neural networks with time varying delay the attention is focused on designing the full order observers that guarantee the global exponential stability of the error dynamic system based on the average dwell time approach and the free weighting matrix technique delay dependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities the error state decay estimate is also given then the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results finally four illustrative examples are provided to demonstrate the effectiveness and the superiority of the proposed methods

finite element error estimation for quasi newtonian fluid structure interaction problems we consider a monolithic scheme for fluid structure interaction problems involving an incompressible quasi newtonian fluid the monolithic formulation is obtained using the arbitrary lagrangian eulerian ale method with matching conditions at the fluid structure interface the stability and error analysis are performed for the finite element approximation finally some numerical experiments that confirm the theoretical analysis are presented

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

h_ infty state estimation for discrete time complex networks with randomly occurring sensor saturations and randomly varying sensor delays in this paper the state estimation problem is investigated for a class of discrete time delay nonlinear complex networks with randomly occurring phenomena from sensor measurements the randomly occurring phenomena include randomly occurring sensor saturations rosss and randomly varying sensor delays rvsds that result typically from networked environments a novel sensor model is proposed to describe the rosss and the rvsds within a unified framework via two sets of bernoulli distributed white sequences with known conditional probabilities rather than employing the commonly used lipschitz type function a more general sector like nonlinear function is used to describe the nonlinearities existing in the network the purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that for all probabilistic sensor saturations and sensor delays the dynamics of the estimation error is guaranteed to be exponentially mean square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an h norm in terms of a novel lyapunov krasovskii functional and the kronecker product sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method a simulation example is provided to show the usefulness of the proposed state estimation conditions

estimation of domain of attraction for aperiodic sampled data switched delayed neural networks subject to actuator saturation in this paper for the case of the asynchronous switching caused by that subsystem s switching occuring during a sampling interval the domain of attraction estimation problem is investigated for aperiodic sampled data switched delayed neural networks asdsdnns subject to actuator saturation a parameters dependent time scheduled lyapunov functional consisting of a novel looped functional is constructed using segmentation technology and linear interpolation by employing this novel functional and using an average dwell time adt approach exponential stability criteria are proposed for polytopic uncertain asdsdnns subject to actuator saturation and a relationship between adt and sampling period is revealed for asdsdnns as a corollary exponential stability criteria are proposed for nominal asdsdnns subject to actuator saturation furthermore by describing the domain of attraction as a time varying ellipsoid determined by the time scheduled lyapunov matrix the proposed theoretical conditions are transformed into a linear matrix inequality lmi based multi objective optimization problem the dynamic estimates of the domain of attraction for asdsdnns are solved numerical simulation examples are provided to illustrate the effectiveness of the proposed method

passivity of switched recurrent neural networks with time varying delays this paper is concerned with the passivity analysis for switched neural networks subject to stochastic disturbances and time varying delays first using the multiple lyapunov functions method a state dependent switching law is designed to present a stochastic passivity condition second a hysteresis switching law involving both the current state and the previous value of the switching signal are presented to avoid chattering resulted from the state dependent switching third based on the average dwell time approach a class of switching signals is determined to guarantee the switched neural network stochastically passive finally three numerical examples are provided to illustrate the characteristics of three proposed switching laws

robust control of linear systems via switching the standard approach to the problem of controlling linear systems with large parameter uncertainty is to seek a controller that stabilizes the system and achieves a required performance over the whole polytope of uncertainty in the case where the latter polytope is large the design may become very conservative we present an alternative approach where the uncertainty polytope is divided into overlapping smaller regions and where each of these regions is assigned to a separate subsystem assuming that there is online information on which of the regions the parameters of the system move to a recently developed method for h design of switched system with dwell time is applied a lyapunov function lf in a quadratic form which is non increasing at the switching instants is assigned to each subsystem this function is used to determine the stability and to find a bound on the l2 gain of the switched system the obtained results are used to solve the corresponding robust h state feedback and static output feedback control problems

a new result on h_ infty state estimation of delayed static neural networks this brief presents a new guaranteed h infty performance state estimation criterion for delayed static neural networks to facilitate the use of the slope information about activation function the estimation error of activation function is separated into two parts for the first time then a novel lyapunov krasovskii functional lkf is constructed which has fully captured the slope information of the activation based on the new lkf a less conservative design criterion of estimator is derived to ensure the asymptotic stability of estimation error system with h infty performance the desired estimator gain matrices and the performance index are obtained by solving a convex optimization problem the simulation results show that the proposed method has much better performance than the most recent results

global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays by employing the lyapunov krasovskii functional and linear matrix inequality lmi approach the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time varying delays and distributed time varying delays some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time varying delay the proposed lmi result is computationally efficient as it can be solved numerically using standard commercial software two examples are given to show the usefulness of the results

tropical geometry of genus two curves abstract we exploit three classical characterizations of smooth genus two curves to study their tropical and analytic counterparts first we provide a combinatorial rule to determine the dual graph of each algebraic curve and the metric structure on its minimal berkovich skeleton our main tool is the description of genus two curves via hyperelliptic covers of the projective line with six branch points given the valuations of these six points and their differences our algorithm provides an explicit harmonic 2 to 1 map to a metric tree on six leaves second we use tropical modifications to produce a faithful tropicalization in dimension three starting from a planar hyperelliptic embedding finally we consider the moduli space of abstract genus two tropical curves and translate the classical igusa invariants characterizing isomorphism classes of genus two algebraic curves into the tropical realm while these tropical igusa functions do not yield coordinates in the tropical moduli space we propose an alternative set of invariants that provides new length data

stable pair tropical and log canonical compactifications of moduli spaces of del pezzo surfaces we give a functorial normal crossing compactification of the moduli space of smooth cubic surfaces entirely analogous to the grothendieck knudsen compactification m 0 n subset overline m 0 n

geometry of chow quotients of grassmannians we consider kapranov s chow quotient compactification of the moduli space of ordered n tuples of hyperplanes in p r 1 in linear general position for r 2 t his is canonically identified with the grothendieck knudsen compactification of m0 n which has among others the following nice properties 1 modular meaning stable pointed rational curves 2 canonical description of limits of one parameter degenerations 3 natural mori theoretic meaning log canonical compactification we generalize 1 and 2 to all r n but we show that 3 which we view as the deepest fails except possibly in the cases 2 n 3 6 3 7 3 8 where we conjecture that it holds

design of state dependent switching laws for stability of switched stochastic neural networks with time delays we study the stability properties of switched stochastic neural networks ssnns with time varying delays whose subsystem is not necessarily stable we introduce state dependent switching sds as a tool for stability analysis some sds laws for asymptotic stability and p th moment exponentially stable are designed by employing lyapunov krasovskii l k functional and lyapunov razumikhin l r method respectively it is shown that the stability of ssnns with time varying delays composed of unstable subsystems can be achieved by using sds law the control gains in the designed sds laws can be derived by solving the lmis in derived stability criteria two numerical examples are provided to demonstrate the effectiveness of the proposed sds laws

local h polynomials invariants of subdivisions and mixed ehrhart theory abstract there are natural polynomial invariants of polytopes and lattice polytopes coming from enumerative combinatorics and ehrhart theory namely the h and h polynomials respectively in this paper we study their generalization to subdivisions and lattice subdivisions of polytopes by abstracting constructions in mixed hodge theory we introduce multivariable polynomials which specialize to the h h polynomials these polynomials the mixed h polynomial and the refined limit mixed h polynomial have rich symmetry non negativity and unimodality properties which both refine known properties of the classical polynomials and reveal new structure for example we prove a lower bound theorem for a related invariant called the local h polynomial we introduce our polynomials by developing a very general formalism for studying subdivisions of eulerian posets that extends the work of stanley brenti and athanasiadis on local h vectors in particular we prove a conjecture of nill and schepers and answer a question of athanasiadis

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

the cox ring of a spherical embedding abstract let g be a connected reductive group and g h a spherical homogeneous space we show that the ideal of relations between a natural set of generators of the cox ring of a g embedding of g h can be obtained by homogenizing certain equations which depend only on the homogeneous space using this result we describe some examples of spherical homogeneous spaces such that the cox ring of any of their g embeddings is defined by one equation

h control of switched delayed systems with average dwell time this paper considers the problems of stability analysis and h controller design of time delay switched systems with average dwell time in order to obtain less conservative results than what is seen in the literature a tighter bound for the state delay term is estimated based on the scaled small gain theorem and the model transformation method an improved exponential stability criterion for time delay switched systems with average dwell time is formulated in the form of convex matrix inequalities the aim of the proposed approach is to reduce the minimal average dwell time of the systems which is made possible by a new lyapunov krasovskii functional combined with the scaled small gain theorem it is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature moreover the exponential h controller can be constructed by solving a set of conditions which is developed on the basis of th

log concavity of characteristic polynomials and the bergman fan of matroids in a recent paper the first author proved the log concavity of the coefficients of the characteristic polynomial of a matroid realizable over a field of characteristic 0 answering a long standing conjecture of read in graph theory we extend the proof to all realizable matroids making progress towards a more general conjecture of rota heron welsh our proof follows from an identification of the coefficients of the reduced characteristic polynomial as answers to particular intersection problems on a toric variety the log concavity then follows from an inequality of hodge type

the influence of the non newtonian properties of blood on the flow in large arteries unsteady flow in a 90 curved tube a numerical and experimental investigation of unsteady entry ow in a 903 curved tube is presented to study the impact of the non newtonian properties of blood on the velocity distribution the time dependent ow rate for the newtonian and the nonnewtonian blood analog uid were identical for the numerical computation a carreau yasuda model was employed to accommodate the shear thinning behavior of the xanthan gum solution the viscoelastic properties were not taken into account the experimental results indicate that signi cant di erences between the newtonian and non newtonian uid are present the numerical results for both the newtonian and the non newtonian uid agree well with the experimental results since viscoelasticity was not included in the numerical code shear thinning behavior of the blood analog uid seems to be the dominant non newtonian property even under unsteady ow conditions finally a comparison between the non newtonian uid model and a newtonian uid at a rescaled reynolds number is presented the rescaled reynolds number based on a characteristic rather than the high shear rate viscosity of the xanthan gum solution was about three times as low as the original reynolds number comparison reveals that the character of ow of the non newtonian uid is simulated quite well by using the appropriate reynolds number 1999 elsevier science ltd all rights reserved

pinning distributed synchronization of stochastic dynamical networks a mixed optimization approach this paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances two kinds of pinning schemes are considered 1 pinned nodes are fixed along the time evolution and 2 pinned nodes are switched from time to time according to a set of bernoulli stochastic variables using lyapunov function methods and stochastic analysis techniques several easily verifiable criteria are derived for the problem of pinning distributed synchronization for the case of fixed pinned nodes a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm for the case of switching pinning scheme upper bounds of the convergence rate and the mean control gain are obtained theoretically simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results

event triggered state estimation for discrete time multidelayed neural networks with stochastic parameters and incomplete measurements in this paper the event triggered state estimation problem is investigated for a class of discrete time multidelayed neural networks with stochastic parameters and incomplete measurements in order to cater for more realistic transmission process of the neural signals we make the first attempt to introduce a set of stochastic variables to characterize the random fluctuations of system parameters in the addressed neural network model the delays among the interconnections are allowed to be different which are more general than those in the existing literature the incomplete information under consideration includes randomly occurring sensor saturations and quantizations for the purpose of energy saving an event triggered state estimator is constructed and a sufficient condition is given under which the estimation error dynamics is exponentially ultimately bounded in the mean square it is worth noting that the ultimate boundedness of the error dynamics is explicitly estimated the characterization of the desired estimator gain is designed in terms of the solution to a certain matrix inequality finally a numerical simulation example is presented to illustrate the effectiveness of the proposed event triggered state estimation scheme

the discriminant of a system of equations abstract we introduce and study the discriminant of a system of polynomial equations with indeterminate coefficients generalizing a number of known special cases such as the sparse resultant and the a determinant and inheriting their nice properties one such property is the fact that the discriminant is always a hypersurface in the space of systems of equations which seems unexpected when compared to the existence of dual defect toric varieties this fact reflects the combinatorics of a certain partial order relation on the set of tuples of faces of a tuple of polytopes the newton polytopes of the equations in our case generalizing the poset of faces of one polytope this combinatorics is the main challenge in our work and can be reduced to a certain fact of tropical geometry which resembles the geometry of the discriminants that we study as a sample application of our version of the multivariate discriminant we prove that atypical fibers of a generic polynomial map are distinguished by their euler characteristics and the bifurcation set of such a map is a hypersurface whose degree we explicitly compute

stability and synchronization of discrete time markovian jumping neural networks with mixed mode dependent time delays in this paper we introduce a new class of discrete time neural networks dnns with markovian jumping parameters as well as mode dependent mixed time delays both discrete and distributed time delays specifically the parameters of the dnns are subject to the switching from one to another at different times according to a markov chain and the mixed time delays consist of both discrete and distributed delays that are dependent on the markovian jumping mode we first deal with the stability analysis problem of the addressed neural networks a special inequality is developed to account for the mixed time delays in the discrete time setting and a novel lyapunov krasovskii functional is put forward to reflect the mode dependent time delays sufficient conditions are established in terms of linear matrix inequalities lmis that guarantee the stochastic stability we then turn to the synchronization problem among an array of identical coupled markovian jumping neural networks with mixed mode dependent time delays by utilizing the lyapunov stability theory and the kronecker product it is shown that the addressed synchronization problem is solvable if several lmis are feasible hence different from the commonly used matrix norm theories such as the m matrix method a unified lmi approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation where the lmis can be easily solved by using the available matlab lmi toolbox two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained

global exponential stability and global convergence in finite time of delayed neural networks with infinite gain this paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections and neuron activations belonging to the set of discontinuous monotone increasing and possibly unbounded functions the discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity while the delay accounts for the finite switching speed of the neuron amplifiers or the finite signal propagation speed it is known that the delay in combination with high gain nonlinearities is a particularly harmful source of potential instability the goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay more precisely conditions are given under which there is a unique equilibrium point of the neural network which is globally exponentially stable for the states with a known convergence rate the conditions are easily testable and independent of the delay moreover global convergence in finite time of the state and output is investigated in doing so new interesting dynamical phenomena are highlighted with respect to the case without delay which make the study of convergence in finite time significantly more difficult the obtained results extend previous work on global stability of delayed neural networks with lipschitz continuous neuron activations and neural networks with discontinuous neuron activations but without delays

estimator design for discrete time switched neural networks with asynchronous switching and time varying delay this brief deals with the estimator design problem for discrete time switched neural networks with time varying delay one main problem is the asynchronous mode switching between the neuron state and the estimator our goal is to design a mode dependent estimator for the switched neural networks under average dwell time switching such that the estimation error system is exponentially stable with a prescribed l2 gain in the h sense from the noise signal to the estimation error a new lyapunov functional is constructed that may increase during the mismatched switchings new results on the stability and l2 gain analysis are then obtained the admissible estimator gains are computed by solving a set of linear matrix inequalities the relations among the switching law the maximal delay upper bound and the optimal h disturbance attenuation level are established the effectiveness of the proposed design method is finally illustrated by a numerical example

representations on the cohomology of hypersurfaces and mirror symmetry abstract we study the representation of a finite group acting on the cohomology of a non degenerate invariant hypersurface of a projective toric variety we deduce an explicit description of the representation when the toric variety has at worst quotient singularities as an application we conjecture a representation theoretic version of batyrev and borisov s mirror symmetry between pairs of calabi yau hypersurfaces and prove it when the hypersurfaces have dimension at most 3 an interesting consequence is the existence of pairs of calabi yau orbifolds whose hodge diamonds are mirror with respect to the usual hodge structure on singular cohomology

exponential synchronization of neural networks with discrete and distributed delays under time varying sampling this paper investigates the problem of master slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals an improved method is proposed which captures the characteristic of sampled data systems some delay dependent criteria are derived to ensure the exponential stability of the error systems and thus the master systems synchronize with the slave systems the desired sampled data controller can be achieved by solving a set of linear matrix inequalitys which depend upon the maximum sampling interval and the decay rate the obtained conditions not only have less conservatism but also have less decision variables than existing results simulation results are given to show the effectiveness and benefits of the proposed methods

hypertrees projections and moduli of stable rational curves we give a conjectural description for the cone of effective divisors of the grothendieck knudsen moduli space m 0 n of stable ra tional curves with n marked points namely we introduce new combi natorial structures called hypertrees and show that they give exceptional divisors onm 0 n with many remarkable properties x1 introduction a major open problem inspired by the pioneering work of harris and mumford hm on the kodaira dimension of the moduli space of stable curves is to understand geometry of its birational models and in particular to describe its cone of effective divisors and a decomposition of this cone into mori chambers hk encoding ample divisors on birational models here we study the genus zero case the moduli spaces m 0 n parame trize stable rational curves i e nodal trees of p 1 s with n marked points and without automorphisms for any subseti of marked points m 0 n has a natural boundary divisor i whose general element parametrizes stable rational curves with two irreducible components one marked by points in i and another marked by points ini c we will introduce new combinatorial objects called hypertrees with an eye towards the following 1 1 conjecture the effective cone of m 0 n is generated by boundary divisors and by divisorsd defined below parametrized by irreducible hypertrees

global spherical tropicalization via toric embeddings the first steps in defining tropicalization for spherical varieties have been taken in the last few years there are two parts to this theory tropicalizing subvarieties of homogeneous spaces and tropicalizing their closures in spherical embeddings in this paper we obtain a new description of spherical tropicalization that is equivalent to the other theories this works by embedding in a toric variety tropicalizing there and then applying a particular piecewise projection map we use this theory to prove that taking closures commutes with the spherical tropicalization operation

new robust exponential stability results for discrete time switched fuzzy neural networks with time delays this paper provides a novel result on robust exponential stability for a class of uncertain discrete time switched fuzzy neural networks dsfnns with time varying delays and parameter uncertainties by implementing an average dwell time approach with a new lyapunov krasovskii functional we obtain some delay dependent sufficient conditions guaranteeing the robust exponential stability of the considered switched fuzzy neural networks in other words a class of switching signals specified by the average dwell time is identified to guarantee the exponential stability of the considered dsfnns the obtained conditions are formulated in terms of linear matrix inequalities lmis which can be easily verified via the lmi toolbox finally numerical examples with simulation results are provided to illustrate the applicability and usefulness of the obtained results

compactifications of subvarieties of tori we study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non archimedean amoebas these compactifications have many nice properties for example any k boundary divisors intersect in codimension k we consider some examples including m 0 n subset overline m 0 n and more generally log canonical models of complements of hyperplane arrangements and compact quotients of grassmannians by a maximal torus

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

observer based finite time robust control of nonlinear time delay systems via hamiltonian function method this paper investigates the observer based finite time robust control problem of a general class of nonlinear time delay systems via hamiltonian function method and proposes some new finite time r

fully discrete error estimation for a quasi newtonian fluid structure interaction problem we consider an incompressible quasi newtonian fluid structure interaction fsi problem formulated in a monolithic framework where the matching conditions at the moving interface are satisfied the fully discretized fsi system is discussed with detailed analysis for the stability and error estimate as well as numerical experiments that confirm the theoretical results

robust stability criteria for discrete time switched neural networks with various activation functions abstract this paper is concerned with the problem of robust stabilization and h control for a class of discrete time switched neural networks with various activation functions and mixed time delays by using the average dwell time approach together with the multiple lyapunov function technique we propose a state feedback controller to guarantee that the switched neural networks is robustly exponentially stable with the disturbance attenuation level 0 about its equilibrium point for all admissible uncertainties the obtained results are formulated in terms of linear matrix inequalities lmis which can be easily verified by the matlab lmi control toolbox finally numerical examples with simulation result are given to illustrate the effectiveness and applicability of the obtained results

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

stability and stabilization of nonlinear switched systems under average dwell time in this paper the problems of stability and stabilization of nonlinear discrete time switched systems is investigated firstly in order to implement the lower bound of minimum average dwell time adt of discrete time switched nonlinear systems the open chain and quasi cyclic switching signals are introduced secondly the problem of these underlying nonlinear discrete time switched systems are solved by using the interval type 2 it2 fuzzy modeling approach thirdly a novel delayed it2 fuzzy controller is devised to guarantee the asymptotically stable of the resulting systems finally a numerical simulation example is given to show the merit and effectiveness of the proposed approach

the interaction between quasilinear elastodynamics and the navier stokes equations the interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations coupled to one another along the moving material interface through the continuity of the velocity and traction vectors we prove the existence and uniqueness locally in time of strong solutions in sobolev spaces for quasilinear elastodynamics coupled to the incompressible navier stokes equations unlike our approach in 5 for the case of linear elastodynamics we cannot employ a fixed point argument on the nonlinear system itself and are instead forced to regularize it by a particular parabolic artificial viscosity term we proceed to show that with this specific regularization we obtain a time interval of existence which is independent of the artificial viscosity together with a priori estimates we identify the global solution in both phases as well as the interface motion as a weak limit in strong norms of our sequence of regularized problems

computing resolutions of quotient singularities abstract let g gl n be a finite group without pseudo reflections we present an algorithm to compute and verify a candidate for the cox ring of a resolution x c n g which is based just on the geometry of the singularity c n g without further knowledge of its resolutions we explain the use of our implementation of the algorithms in singular as an application we determine the cox rings of resolutions x c 3 g for all g gl 3 with the aforementioned property and of order g 12 we also provide examples in dimension 4

a generalized lmi based approach to the global asymptotic stability of delayed cellular neural networks a novel linear matrix inequality lmi based criterion for the global asymptotic stability and uniqueness of the equilibrium point of a class of delayed cellular neural networks cnns is presented the criterion turns out to be a generalization and improvement over some previous criteria

new calabi yau orbifolds with mirror hodge diamonds abstract we prove a representation theoretic version of borisov batyrev mirror symmetry and use it to construct infinitely many new pairs of orbifolds with mirror hodge diamonds with respect to the usual hodge structure on singular complex cohomology we conjecture that the corresponding orbifold hodge diamonds are also mirror when x is the fermat quintic in p 4 and x is a sym 5 equivariant toric resolution of its mirror x we deduce that for any subgroup of the alternating group a 5 the hilbert schemes hilb x and hilb x are smooth calabi yau threefolds with explicitly computed mirror hodge diamonds

kinematic splitting algorithm for fluid structure interaction in hemodynamics abstract in this paper we study a kinematic splitting algorithm for fluid structure interaction problems this algorithm belongs to the class of loosely coupled fluid structure interaction schemes we will present stability analysis for a coupled problem of non newtonian shear dependent fluids in moving domains with viscoelastic boundaries fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms for simplicity of presentation the structure is modelled by the generalized string equation but the results presented in the paper may be generalized to more complex structure models the arbitrary lagrangian eulerian approach is used in order to take into account moving computational domain numerical experiments including numerical error analysis and comparison of hemodynamic parameters for newtonian and non newtonian fluids demonstrate reliability of the proposed scheme

stability analysis of genetic regulatory networks with switching parameters and time delays this paper is concerned with the exponential stability analysis of genetic regulatory networks grns with switching parameters and time delays in this paper a new integral inequality and an improved reciprocally convex combination inequality are considered by using the average dwell time approach together with a novel lyapunov krasovskii functional we derived some conditions to ensure the switched grns with switching parameters and time delays are exponentially stable finally we give two numerical examples to clarify that our derived results are effective

tropical compactification in log regular varieties in this article we define a natural tropicalization procedure for closed subsets of log regular varieties in the case of constant coefficients and study its basic properties this framework allows us to generalize some of tevelev s results on tropical compactification as well as hacking s result on the cohomology of the link of a tropical variety to log regular varieties

analysis of a streamline diffusion finite element method for the stokes and navier stokes equations for the stokes equations with convection and the incompressible navier stokes equations the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure thus allowing the use of arbitrary pairs of velocity pressure spaces for the linear problem the authors obtain for all mesh peclet numbers optimal error estimates in natural norms including in particular the l 2 norm of the pressure the same holds for the nonlinear problem which close to a regular branch of solutions i e the linearized operator is an isomorphism of the norm of the inverse of which still depends on the reynolds number consequently the dependence of the error constants on the reynolds number is not completely resolved in this case

on the sn invariant f conjecture abstract by using classical invariant theory we reduce the s n invariant f conjecture to a feasibility problem in polyhedral geometry we show by computer that for n 19 every integral s n invariant f nef divisor on the moduli space of genus zero stable n pointed curves is semi ample over arbitrary characteristic furthermore for n 16 we show that for every integral s n invariant nef resp ample divisor d on the moduli space 2d is base point free resp very ample as applications we obtain the nef cone of the moduli space of stable curves without marked points and the semi ample cone of the moduli space of genus 0 stable maps to grassmannian for small numerical values

equivariant ehrhart theory abstract motivated by representation theory and geometry we introduce and develop an equivariant generalization of ehrhart theory the study of lattice points in dilations of lattice polytopes we prove representation theoretic analogues of numerous classical results and give applications to the ehrhart theory of rational polytopes and centrally symmetric polytopes we also recover a character formula of procesi dolgachev lunts and stembridge for the action of a weyl group on the cohomology of a toric variety associated to a root system

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory

robust synchronization of an array of coupled stochastic discrete time delayed neural networks this paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete time neural networks with time varying delay the individual neural network is subject to parameter uncertainty stochastic disturbance and time varying delay where the norm bounded parameter uncertainties exist in both the state and weight matrices the stochastic disturbance is in the form of a scalar wiener process and the time delay enters into the activation function for the array of coupled neural networks the constant coupling and delayed coupling are simultaneously considered we aim to establish easy to verify conditions under which the addressed neural networks are synchronized by using the kronecker product as an effective tool a linear matrix inequality lmi approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally robustly exponentially synchronized in the mean square the lmi based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time varying delay and can be solved efficiently via the matlab lmi toolbox two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme

chow rings of toric varieties defined by atomic lattices we study a graded algebra d d mathcal l mathcal g over defined by a finite lattice and a subset mathcal g in a so called building set this algebra is a generalization of the cohomology algebras of hyperplane arrangement compactifications found in work of de concini and procesi 2 our main result is a representation of d for an arbitrary atomic lattice as the chow ring of a smooth toric variety that we construct from and mathcal g we describe this variety both by its fan and geometrically by a series of blowups and orbit removal also we find a grobner basis of the relation ideal of d and a monomial basis of d