on the decay rates of homogeneous positive systems of any degree with time varying delays this technical note studies the stability problem of homogeneous positive systems of any degree with time varying delays delay independent conditions are derived for asymptotic and finite time stability estimates on the decay rates which reveal how the system delays affect the rates of convergence are obtained more precisely this technical note features three contributions first we derive a necessary and sufficient condition for global polynomial stability of continuous time homogeneous cooperative systems with time varying delays when the degree of homogeneity is greater than one second we characterize finite time stability of continuous time homogeneous cooperative delay free systems of degree smaller than one finally for discrete time positive systems with time varying delays a local exponential stability criterion is established when the vector fields are order preserving and homogeneous of degree greater than one an illustrative example is given to show the effectiveness of our results

exponential stability of discrete time switched linear positive systems with time delay abstract this paper addresses the exponential stability problem for a class of discrete time switched linear positive systems dslpss with time delay firstly an exponential stability criterion for a non switched delay positive system is proposed then by constructing a suitable co positive type lyapunov krasovskii functional an exponential stability criterion for switched delay positive systems is derived via the average dwell time approach and a stability criterion for switched positive systems with multiple delays is stated and its proof is sketched finally a numerical example is given to illustrate the obtained results

finite size corrections and numerical calculations for long spin 1 2 heisenberg chains in the critical region leading and next to leading order finite size corrections to the ground and first excited states are calculated for the spin 1 2 anisotropic heisenberg model in the critical region the analytic results are compared to numerical data obtained for chains up to a length of n 1024 it is found that near the isotropic point the asymptotic region where the results obtained for n to infinity are applicable sets in at very large n values and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms even at large n 100 chain lengths

k double schur functions and equivariant co homology of the affine grassmannian the schubert bases of the torus equivariant homology and cohomology rings of the affine grassmannian of sl k 1 are realized by new families of symmetric functions called k double schur functions and affine double schur functions

stability and stabilization analysis of positive polynomial fuzzy systems with time delay considering piecewise membership functions this paper is concerned with the stability analysis of positive polynomial fuzzy model based control systems with time delay each of the polynomial fuzzy model and the polynomial fuzzy controller is allowed to have its own set of premise membership functions which can improve the design and realization flexibility conditions showing the positivity of the system are first obtained then to deal with the difficulty resulting from the mismatched premise membership functions to the stability stabilization analysis approximated membership functions representing the original ones are constructed and the information of membership functions is brought into the stability conditions this way the stability conditions can be relaxed since the extra knowledge on the system is considered stability conditions are obtained by using the sum of squares approach based on the lyapunov stability theory a simulation example is provided to verify the effectiveness of this method

on the decay rate of discrete time linear delay systems with cone invariance this technical note is concerned with the decay rate constrained stability analysis for linear delay systems that possess cone invariant property in order to capture the decay rate of such systems we introduce a nondecreasing positive function whose reciprocal represents the decay rate under mild assumptions on the growth rate of this function an explicit condition is given to ensure that a cone preserving linear system with unbounded time varying delays is asymptotically stable with a given decay rate as typical cases necessary and sufficient conditions are given to characterize the decay rate when the delay is restricted by a linear sublinear or logarithmic growth rate finally some numerical examples are given to illustrate the effectiveness of the theoretical results

stability analysis for positive singular systems with distributed delays abstract this paper is concerned with the stability analysis for continuous time positive singular systems with distributed delays by introducing an auxiliary system a necessary and sufficient positivity condition is proposed for singular systems with distributed lags based on this condition we present a sufficient stability condition for positive singular systems with distributed delays and extend the result to systems with distributed delays over a bounded time varying interval in addition this stability condition is also necessary when strictly positive initial conditions are available numerical simulations are utilized to illustrate the effectiveness of our results

on the fundamental domain of affine springer fibers let g be a connected reductive algebraic group over an algebraically closed field k gamma in mathfrak g k epsilon a semisimple regular element we introduce a fundamental domain f gamma for the affine springer fibers mathscr x gamma we show that the purity conjecture of mathscr x gamma is equivalent to that of f gamma via the arthur kottwitz reduction we then concentrate on the unramified affine springer fibers for the group mathrm gl d it turns out that their fundamental domains behave nicely with respect to the root valuation of gamma we formulate a rationality conjecture about a generating series of their poincare polynomials and study them in detail for the group mathrm gl 3 in particular we pave them in affine spaces and we prove the rationality conjecture

infinite grassmannians and moduli spaces of g bundles let c be a smooth projective irreducible algebraic curve over c of any genus and g a connected simply connected simple affine algebraic group over c in this paper we elucidate the relationship between 1 the space of vacua conformal blocks defined in conformal field theory using an integrable highest weight representation of the affine kac moody algebra associated to g and 2 the space of regular sections generalised theta functions of a line bundle on the moduli space ta of semistable principal g bundles on c fix a point p in c and let p resp kp be the completion of the local ring p of c at p resp the quotient field of c p let g kp the kp rational points of the algebraic group g be the loop group of g and let g p be the standard maximal parahoric subgroup of then the generalised flag variety x n is an inductive limit of projective varieties in fact of generalised schubert varieties one has a natural r line bundle s on x cf sect 2 2 and the picard group pic x is isomorphic to z which is generated by s proposition 2 3 where f is the universal central extension of by the multiplicative group c cf sect 2 2 by an analogue of the borel weil theorem proved in the kac moody setting by kumar and also by mathieu the space h 162 s of the regular sections of the line bundle y dxo y xo for any d 0 is canonically isomorphic with the full vector space dual v dxo of the integrable highest weight irreducible module v dxo of the affine kacmoody group or of the associated affine kac moody algebra which is a certain one dimensional central extension of the loop algebra lie g with highest weight dxo cf sect 6 1

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

conformal anomaly and critical exponents of the spin 1 takhtajan babujian model the authors consider the critical behaviour of the spin 1 hamiltonian of the takhtajan babujian model the bethe ansatz equations for this antiferromagnet in a finite chain are investigated analytically and numerically the conformal anomaly and critical exponents are obtained by exploiting their relations with the eigenspectrum of the finite system the results strongly support the conjecture that the wess zumino witten non linear sigma model with topological charge k 2 is the underlying field theory for this statistical mechanics model

improved results on stability of continuous time switched positive linear systems in this paper the problems of stability for switched positive linear systems splss under arbitrary switching are investigated in a continuous time context the so called copositive polynomial lyapunov function cplf giving a generalization of copositive types of lyapunov function is first proposed which is formulated in a higher order form of the positive states of the underlying systems it is illustrated in this paper that some classical types of lyapunov functions can be seen as special cases of the proposed cplf then new stability conditions are developed by the new lyapunov function approach it is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases a numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques

brief paper unconditional stability of the foschini miljanic algorithm in this note we prove the unconditional stability of the foschini miljanic algorithm our results show that the foschini miljanic algorithm is unconditionally stable convergent even in the presence of bounded time varying communication delays and in the presence of topology changes the implication of our results may be important for the design of code division multiple access cdma based wireless networks

model based control and stability analysis of discrete time polynomial fuzzy systems with time delay and positivity constraints this paper proposes a novel lyapunov stabilization analysis of discrete time polynomial fuzzy model based control systems with time delay under positivity constraint the polynomial fuzzy model is constructed to describe the dynamics of a nonlinear discrete time system with time delay a model based polynomial fuzzy controller is designed using nonparallel distributed compensation technique to stabilize the system while driving the system states to positive using the positivity constraints the lyapunov stability and positivity conditions are formulated as sum of squares to relax the conservativeness of the obtained stability results two main methods are proposed in this paper first the piecewise linear membership functions plmfs are used to introduce the approximate error between piecewise and the original membership functions into the stability analysis and second introduce the boundary information of the premise variables into the stability analysis since the premise variables hold rich nonlinearity information a numerical example is given to demonstrate the effectiveness of the proposed approach

the fundamental lemma of jacquet and rallis we prove both the group version and the lie algebra version of the fundamental lemma appearing in a relative trace formula of jacquet and rallis in the function field case when the characteristic is greater than the rank of the relevant groups in the appendix by gordon our results are transferred to the p adic field case for sufficiently large p

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

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

exponential stabilization of switched time varying systems with delays and disturbances abstract this paper deals with exponential stabilization for a class of switched time varying systems by taking time varying delays and nonlinear disturbances into consideration time dependent switching signals have been characterized in terms of metzler matrices such that the resulting system is globally exponentially stable compared with preceding works we introduce a model transformation and an approach without involving the lyapunov krasovskii functional to derive new exponential stability criteria for switched time varying systems under the average dwell time switching numerical examples show that the obtained theoretical results can be applied to some cases not covered by some existing results

fibration de hitchin et endoscopie we propose a geometric interpretation of the theory of elliptic endoscopy due to langlands and kottwitz in terms of the hitchin fibration as applications we prove a global analog of a purity conjecture due to goresky kottwitz and macpherson for unitary groups this global purity statement has been used in a joint work with g laumon to prove the fundamental lemma over a local fields of equal characteristics

exponential stability of homogeneous positive systems of degree one with time varying delays while the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated the theory for nonlinear positive systems is considerably less well developed this technical note presents a set of conditions for establishing delay independent stability and bounding the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case specifically when the time delays have a known upper bound we derive necessary and sufficient conditions for exponential stability of a continuous time positive systems whose vector fields are homogeneous and cooperative and b discrete time positive systems whose vector fields are homogeneous and order preserving we then present explicit expressions that allow us to quantify the impact of delays on the decay rate and show that the best decay rate of positive linear systems that our bounds provide can be found via convex optimization finally we extend the results to general linear systems with time varying delays

convex polytopes for the central degeneration of the affine grassmannian abstract we study the algebraic geometry and combinatorics of the central degeneration the degeneration that shows up in local models of shimura varieties and gaitsgory s central sheaves in type a more specifically we elucidate the central degeneration of semi infinite orbits and explain its relations with levi restriction also we discuss the central degeneration of mirkovic vilonen cycles in the affine grassmannian and the corresponding transformations of mirkovic vilonen polytopes in addition we shed some light on the geometry of iwahori mv cycles in the affine grassmannian and generalized mv cycles in the affine flag variety which are closely related to demazure modules and affine deligne lusztig varieties respectively

on reachable sets for positive linear systems under constrained exogenous inputs this paper focuses on positive linear time invariant systems with constant coefficients and specific exogenous disturbance the problem of finding a hyper pyramid to bound the set of the states that are reachable from the origin in the euclidean space is addressed subject to inputs whose 1 1 norm or 1 norm is bounded by a prescribed constant the lyapunov approach is applied and a bounding hyper pyramid is obtained by solving a set of inequalities iterative procedures with an adjustable parameter for reducing the hyper volume of the bounding hyper pyramid for the reachable set are proposed

schubert polynomials and classes of hessenberg varieties abstract regular semisimple hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory numerical analysis representation theory algebraic geometry and combinatorics we give a giambelli formula expressing the classes of regular semisimple hessenberg varieties in terms of chern classes in fact we show that the cohomology class of each regular semisimple hessenberg variety is the specialization of a certain double schubert polynomial giving a natural geometric interpretation to such specializations we also decompose such classes in terms of the schubert basis for the cohomology ring of the flag variety the coefficients obtained are nonnegative and we give closed combinatorial formulas for the coefficients in many cases we introduce a closely related family of schemes called regular nilpotent hessenberg schemes and use our results to determine when such schemes are reduced

the xi stability on the affine grassmannian we introduce a notion of xi stability on the affine grassmannian sic for the classical groups this is the local version of the xi stability on the moduli space of higgs bundles on a curve introduced by chaudouard and laumon we prove that the quotient sic xi t of the stable part sic xi by the maximal torus t exists as an ind k scheme and we introduce a reduction process analogous to the harder narasimhan reduction for vector bundles over an algebraic curve for the group we calculate the poincar series of the quotient sic xi t

stability analysis and delay control for switched positive linear systems in this paper the problems of stability analysis and delay control for switched positive linear systems splss are studied by using average dwell time adt switching by developing a new class of multiple piecewise continuous linear copositive lyapunov function mplclf approach an improved stability condition for splss is obtained which can obtain a tighter bound on the adt guaranteeing the stability the obtained stability condition covers the existing results on stability analysis for splss since the multiple linear copositive lyapunov function used in the literature can be viewed as a special case of our proposed mplclf and our result can obtain a tighter bound of the adt then a more efficient controller design method over the existing ones is also established for splss with switching delay to guarantee the underlying system to be exponentially stable to illustrate the advantages of our proposed results two numerical examples are finally given

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

constrained control of positive systems with delays this technical note addresses controller design for continuous time delayed linear systems the control is under positivity constraint which means that the resulting closed loop systems are not only stable but also positive bounded control is also considered further requiring that the trajectory of the closed loop system is bounded by a prescribed boundary if the initial condition is bounded by the same boundary the contribution lies in three aspects first some necessary and sufficient conditions are presented for the existence of controllers satisfying the positivity constraint second a necessary and sufficient condition is established determining whether the trajectory of a positive system can be bounded by a prescribed boundary provided that the initial condition is bounded by the same boundary third a sufficient condition is presented for bounded control and it is shown to be also necessary if asymptotic stability is not required

stability analysis of positive polynomial fuzzy model based control systems with time delay under imperfect premise matching this paper deals with the stability and positivity analysis of polynomial fuzzy model based pfmb control systems with time delay which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop under imperfect premise matching to improve the design and realization flexibility the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions a sum of squares based stability analysis approach using the lyapunov stability theory is employed to investigate the positivity and stability of the pfmb control systems and synthesize the polynomial fuzzy controller in order to relax the stability results we propose two methods first membership functions are considered as symbolic variables in the stability analysis and second the property of the membership functions and the boundary information of the membership functions are considered in the stability analysis a simulation example is given to illustrate the effectiveness of the proposed approach

nonnegative realization of spectra having negative real parts abstract the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions for a list of complex numbers to be the spectrum of a nonnegative matrix in this paper the problem is completely solved in the case when all numbers in the given list except for one the perron eigenvalue have real parts smaller than or equal to zero

on linear copositive lyapunov functions and the stability of switched positive linear systems we consider the problem of common linear copositive lyapunov function existence for positive switched linear systems in particular we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time invariant systems several applications of this result are also given

l l gain analysis for positive linear systems with unbounded time varying delays this technical note addresses the l gain respectively l gain analysis problem for discrete time respectively continuous time positive linear systems with unbounded time varying delays for the discrete time case by virtue of the monotonicity of an auxiliary system and the corresponding delay free system it is shown that the l gain of discrete time positive systems with unbounded delays is insensitive of the magnitude of delays for the continuous time case we first construct a sampled data positive system and analyze its monotonicity and asymptotic behavior then by comparing the delayed positive system with the proposed sampled data positive system and the corresponding delay free system it is further proved that the l gain of continuous time positive systems with unbounded delays is also independent of the delays and fully determined by the system matrices the application of the results is illustrated by a sampled data system with unbounded sampling intervals

a positivity based approach to delay dependent stability of systems with large time varying delays abstract in this paper we propose new explicit tests for positivity and exponential stability of systems with large time varying delays our approach is based on nonoscillation of solutions of the corresponding diagonal scalar delay differential equations numerical examples illustrate the efficiency of the results

the geometry of fixed point varieties on affine flag manifolds let g be a semisimple simply connected algebraic group over an algebraically closed field k with lie algebra g we study the spaces of parahoric subalgebras of a given type containing a fixed nil elliptic element of gk i e fixed point varieties on affine flag manifolds we definea natural class of k actions on affine flag manifolds generalizing actions introduced by lusztig and smelt we formulate a condition on a pair n f consisting of n 2 g k and a k action f of the specified type which guarantees that f induces an action on the variety of parahoric subalgebras containing n for the special linear and symplectic groups we characterize all regular semisimple and nil elliptic conjugacy classes containing a representative whose fixed point variety admits such an action we then use these actions to find simple formulas for the euler characteristics of those varieties for which the k fixed points are finite we also obtain a combinatorial description of the euler characteristics of the spaces of parabolic subalgebras containing a given element of certain nilpotent conjugacy classes of g

positive and compartmental systems when dealing with compartmental systems an important question is given an experiment i e an input output sequence and supposing there is no error in the data is the sequence compatible with the compartmental assumption if the process under analysis is linear then the previous question is obviously equivalent to asking whether a given transfer function is that of a compartmental system in this note we provide an answer to the latter question giving necessary and sufficient conditions for a transfer function to be that of a compartmental system of some finite order i e number of compartments another problem tackled in this note originates from the observation that in many cases one wants to determine the number of compartments involved in the process in this note we report a step toward the solution of this fundamental problem by proving necessary and sufficient conditions for a given third order transfer function with real poles to be that of a compartmental system with three compartments

on the algebraic riccati inequality arising in cone preserving time delay systems abstract this paper studies the problem of riccati stability of a pair of matrices for a matrix pair a b it was recently shown that if its corresponding time delay system is internally positive meaning that a is metzler and b is nonnegative then the pair a b is diagonally riccati stable if and only if a b is hurwitz we extend this to the case when the pair a b corresponds to a time delay system with a more general cone preserving property we show that if the time delay system relating to the pair a b is invariant on a symmetric cone the corresponding algebraic riccati inequality admits positive definite solutions which can be constructed via the scaling transformation on the euclidean jordan algebra associated with the symmetric cone for the special case when the symmetric cone is the positive semi definite cone an application to a class of stochastic systems is discussed

le lemma fondamental pour les groupes unitaires let g be an unramified reductive group over a nonarchimedian local field f the so called langlands fundamental lemma is a family of conjectural identities between orbital integrals for g f and orbital integrals for endoscopic groups of g in this paper we prove the langlands fundamental lemma in the particular case where f is a finite extension of fp t g is a unitary group and p rank g waldspurger has shown that this particular case implies the langlands fundamental lemma for unitary groups of rank p when f is any finite extension of qp we follow in part a strategy initiated by goresky kottwitz and macpherson our main new tool is a deformation of orbital integrals which is constructed with the help of the hitchin fibration for unitary groups over projective curves

delay independent asymptotic stability in monotone systems monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties it is known that under the property of quasimonotonicity time delayed systems become monotone and some remarkable properties have been reported for such systems these include for example the fact that for linear systems global asymptotic stability of the undelayed system implies global asymptotic stability for the delayed system under arbitrary bounded delays nevertheless extensions to nonlinear systems have thus far relied primarily on the conditions of homogeneity and subhomogeneity and it has been conjectured that these can be relaxed our aim in this paper is to show that this is feasible for a general class of nonlinear monotone systems by deriving convergence results in which simple properties of the undelayed system lead to delay independent stability in particular one of our results shows that if the undelayed system has a convergent trajectory that is unbounded in all components as t rightarrow infty then the system is globally asymptotically stable for arbitrary bounded time varying delays this follows from a more general result derived in the paper that allows to quantify delay independent regions of attraction which can be used to prove global asymptotic stability for various classes of systems these also recover various known delay independent stability results that are discussed within the paper

exponential stability of two dimensional homogeneous monotone systems with bounded directional delays one dimensional 1 d monotone systems have received considerable attention recently due to their wide applicability and interesting mathematical properties one of these special properties is that for lti monotone systems exponential stability is insensitive to time delays some extensions to 1 d nonlinear monotone systems based on conditions of homogeneity have also been reported in this paper we study the problem of exponential stability of discrete time 2 d nonlinear monotone systems described by the roesser model with time varying delays specifically based on the monotone property and homogeneity of the associated vector fields necessary and sufficient delay independent exponential stability conditions are derived the magnitudes of delays are also taken into deriving an explicit estimation of the exponential decay rate which correlates the impact of delays on the system performance two examples are given to demonstrate the effectiveness of the obtained results

stability of discrete time positive switched linear systems with stable and marginally stable subsystems abstract in this paper we investigate the stability of discrete time positive switched linear systems the highlight of this work is that each subsystem is only assumed to be stable or marginally stable some sufficient conditions imposed on the subsystem matrices and switching signals are established to guarantee exponential stability of the considered positive switched linear systems an extension to the case of time varying and unbounded delay is also given compared with the continuous time counterparts in the literature our discrete time case is much more complicated involving the transitive connectivity between the subsystems specified by the switching signals

homology of affine springer fibers in the unramified case assuming a certain purity conjecture we derive a formula for the complex cohomology groups of the affine springer fiber corresponding to any unramified regular semisimple element we use this calculation to present a complex analog of the fundamental lemma for function fields we show that the kappa orbital integral that arises in the fundamental lemma is equal to the lefschetz trace of the frobenius acting on the etale cohomology of a related variety

robust stabilization for delayed discrete time fuzzy systems via basis dependent lyapunov krasovskii function abstract this paper deals with the robust control problem for a class of uncertain discrete time fuzzy systems with time delay the uncertainty is assumed to be of structured linear fractional form which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities by using basis dependent lyapunov krasovskii function a robust control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov krasovskii and the system matrices which make the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis the development represents an important step towards reducing the conservatism of previous design methods and the results also generalize earlier works for a more general parametric uncertainty structure numerical examples are also given to demonstrate the applicability of the proposed approach

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

stability analysis of linear delay systems with cone invariance this paper is concerned with the stability and input output gain analysis of linear delay systems with cone invariance based on the partial ordering over a cone the monotonicity of the trajectory of the cone preserving systems with constant delays is first studied then by comparing the trajectory of the constant delay systems and that of time varying delay systems we prove that a cone preserving system with interval time varying delays is asymptotically stable if and only if the corresponding delay free system is asymptotically stable this implies that the stability of a cone preserving system is insensitive to the magnitude of the delays moreover based on the cone induced norms an explicit characterization on the cone induced gain of an input output cone preserving system is given in terms of system matrices finally numerical examples are provided to illustrate the theoretical results

investigating the effects of time delays on stochastic stability and designing l1 gain controllers for positive discrete time markov jump linear systems with time delay this paper is concerned with stochastic stability l1 gain performance analysis and positivity preserving l1 gain controller design for a positive discrete time markov jump linear system with time delay first necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co positive stochastic lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time delay and the transition probability it is revealed that stochastic stability of the positive discrete time markov jump linear system with time delay is influenced by the size of time delay and it is demonstrated by an example that the effect of time delay on stochastic stability can be either positive or negative second exact computation on an l1 gain index of a stochastically stable positive discrete time markov jump linear system with time delay is presented and a necessary and sufficient condition for the l1 gain performance is derived in the form of linear programming third an iterative algorithm is proposed to design a positivity preserving l1 gain controller and in single input case an optimal controller is obtained analytically such that the closed loop system achieves the minimal l1 gain performance then a modified pest s structured population dynamic model is developed to illustrate the effectiveness of the designed method

sur l homologie des fibres de springer affines tronquees en suivant les travaux de goresky kottwitz et macpherson 12 on calcule l homologie des fibres de springer affines tronquees dans le cas non ramifie mais sous une hypothese de purete dans le cas equivalue on demontre cette hypothese de purete la troncature depend d un parametre qui est un diviseur sur une variete torique l adique dans les cas non ramifies et equivalues pour chaque fibre de springer affine tronquee on definit un faisceau coherent gradue sur cette variete torique dont l espace des sections globales s identifie a l homologie l adique de la fibre consideree pour certaines familles de groupes endoscopiques ces faisceaux apparaissent dans des suites exactes on en deduit alors le lemme fondamental pondere d arthur 5 conjecture 5 1 dans les cas equivalues et non ramifies

dynamic output feedback control for continuous time interval positive systems under l1 performance this paper is concerned with the design of l1 induced dynamic output feedback controller for continuous time positive systems with interval uncertainties a necessary and sufficient condition for stability and l1 induced performance of positive linear systems is proposed in terms of linear inequalities based on this conditions for the existence of robust dynamic output feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions one illustrative example is provided to show the effectiveness and applicability of the theoretical results

sato tate theorem for families and low lying zeros of automorphic l functions we consider certain families of automorphic representations over number fields arising from the principle of functoriality of langlands let g be a reductive group over a number field f which admits discrete series representations at infinity let l g widehat g rtimes mathrm gal bar f f be the associated l group and r l g rightarrow mathrm gl d mathbb c a continuous homomorphism which is irreducible and does not factor through mathrm gal bar f f the families under consideration consist of discrete automorphic representations of g mathbb a f of given weight and level and we let either the weight or the level grow to infinity we establish a quantitative plancherel and a quantitative sato tate equidistribution theorem for the satake parameters of these families this generalizes earlier results in the subject notably of sarnak prog math 70 321 331 1987 and serre j am math soc 10 1 75 102 1997 as an application we study the distribution of the low lying zeros of the associated family of l functions l s pi r assuming from the principle of functoriality that these l functions are automorphic we find that the distribution of the 1 level densities coincides with the distribution of the 1 level densities of eigenvalues of one of the unitary symplectic and orthogonal ensembles in accordance with the katz sarnak heuristics we provide a criterion based on the frobenius schur indicator to determine this symmetry type if r is not isomorphic to its dual r vee then the symmetry type is unitary otherwise there is a bilinear form on mathbb c d which realizes the isomorphism between r and r vee if the bilinear form is symmetric resp alternating then r is real resp quaternionic and the symmetry type is symplectic resp orthogonal

stability radii of higher order positive difference systems in this paper we study stability radii of positive polynomial matrices under affine perturbations of the coefficient matrices it is shown that the real and complex stability radii coincide moreover explicit formulas are derived for these stability radii and illustrated by some examples

affine demazure modules and t fixed point subschemes in the affine grassmannian let g be a simple algebraic group defined over c and t be a maximal torus of g for a dominant coweight of g the t fixed point subscheme formula of the schubert variety formula in the affine grassmannian grg is a finite scheme we prove that for all such if g is of type a or d and for many of them if g is of type e there is a natural isomorphism between the dual of the level one affine demazure module corresponding to and the ring of functions twisted by certain line bundle on grg of formula we use this fact to give a geometrical proof of the frenkel kac segal isomorphism between basic representations of affine algebras of a d e type and lattice vertex algebras

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

positivity and stability of coupled differential difference equations with time varying delays this paper studies the asymptotic stability of a special class of coupled delay differential difference equations with internal positive property an explicit characterization on the positivity of coupled differential difference equations is firstly given then based on the positivity of coupled differential difference equations with constant delays we investigate the entrywise monotonicity and asymptotic property of their state trajectories starting from appropriately chosen initial conditions furthermore the time varying delay system is analyzed through comparing with the corresponding constant delay system it turns out that an internally positive coupled differential difference equation with bounded time varying delays is asymptotically stable as long as the corresponding delay free system is asymptotically stable

an analytic treatment of finite size corrections in the spin 1 antiferromagnetic xxz chain it is known that the standard method for calculating finite size corrections in bethe ansatz solvable systems is not applicable to the takhtajan babujian model and its anisotropic xxz generalisation the authors develop a new analytic method explicitly avoiding root densities and associated problems nonlinear integral equations are derived whose solutions yield the correct central charges c 1 and c 3 2 for the spin 1 2 and spin 1 xxz chains respectively in the spin 1 case the authors obtain as a by product the finite size deviation of the bethe ansatz roots from the 2 string formation

on a class of positive linear differential equations with infinite delay abstract we give an explicit criterion for positivity of the solution semigroup of linear differential equations with infinite delay and a perron frobenius type theorem for positive equations furthermore a novel criterion for the exponential asymptotic stability of positive equations is presented finally we provide a sufficient condition for the exponential asymptotic stability of positive equations subjected to structured perturbations a simple example is given to illustrate the obtained results

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

finite size corrections for spin s heisenberg chains and conformal properties the author compares recent results on finite size corrections for the isotropic xxx heisenberg chain and its integrable generalisations with former numerical and analytic calculations for the ground state and its lowest excitations leading and non leading terms are considered the analysis confirms the predictions of conformal invariance and sheds some new light on the fine structure of finite size corrections

finite size effects in the integrable xxz heisenberg model with arbitrary spin the finite size effects in the spectrum of the integrable xxz heisenberg chain with arbitrary spin s are studied analytically on the basis of the string hypothesis for bound states and numerically by solving the associated bethe ansatz equations the finite size corrections to the spectrum and to the low temperature behaviour of the free energy are found to be similar to the universal predictions for conformally invariant theories although the model is in general not lorentz invariant since it can have an arbitrary number of branches for low energy excitations with different fermi velocities depending on the value of s and the anisotropy parameter gamma

stability analysis of nonlinear time delay systems using a novel piecewise positive systems method we propose a method that uses piecewise positive comparison systems to analyze the stability of nonlinear differential systems with time varying delays a new stability criterion is provided and two numerical examples are given to demonstrate the advantages of our obtained result

on the stability of positive linear switched systems under arbitrary switching laws we consider n dimensional positive linear switched systems a necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is hurwitz several researchers conjectured that for positive linear switched systems this condition is also sufficient recently gurvits shorten and mason showed that this conjecture is true for the case n 2 but is not true in general their results imply that there exists some minimal integer np such that the conjecture is true for all n np but is not true for n np we show that np 3

le lemme fondamental pondere ii enonces cohomologiques dans cet article on etudie la cohomologie de la fibration de hitchin tronquee introduite dans un article precedent on etend les principaux theoremes de ngo sur la cohomologie de la partie elliptique de la fibration de hitchin comme consequence on obtient une demonstration du lemme fondamental pondere d arthur in this paper we study the cohomology of the truncated hitchin fibration which was introduced in a previous paper we extend ngo s main theorems on the cohomology of the elliptic part of the hitchin fibration as a consequence we get a proof of arthur s weighted fundamental lemma