traveling waves for a diffusive sir model with delay abstract in this paper we study traveling waves connecting the infection free equilibrium state and the endemic equilibrium state for a diffusive sir model with delay and saturated incidence rate since this system does not enjoy the comparison principle we will use an iteration process to construct a pair of upper and lower solutions with the aid of the pair of upper and lower solutions we can apply the schauder fixed point theorem to construct a family of solutions of the truncated problems which via the limiting argument can generate the traveling wave indeed we show that there exists c 0 such that this system admits a traveling wave solution with speed c iff c c

spatial dynamics of a nonlocal and time delayed reaction diffusion system in this paper we investigate the spatial dynamics of a nonlocal and time delayed reaction diffusion system which is motivated by an age structured population model with distributed maturation delay the spreading speed c the existence of traveling waves with the wave speed c c and the nonexistence of traveling waves with c c are obtained it turns out that the spreading speed coincides with the minimal wave speed for monotone traveling waves

a poincare inequality on loop spaces we show that the laplacian on the loop space over a class of riemannian manifolds has a spectral gap the laplacian is defined using the levi civita connection the brownian bridge measure and the standard bismut tangent spaces

on ensembles of low density parity check codes asymptotic distance distributions we derive expressions for the average distance distributions in several ensembles of regular low density parity check codes ldpc among these ensembles are the standard one defined by matrices having given column and row sums ensembles defined by matrices with given column sums or given row sums and an ensemble defined by bipartite graphs

stability and traveling waves of a vaccination model with nonlinear incidence abstract in this paper we propose a spatial vaccination model with nonlinear incidence first we consider the well posedness of solutions of the model second in the case of the bounded spatial habitat r n we investigate the global stability of the model more precisely it is shown that if the threshold value r 0 1 then the disease free equilibrium e 0 is globally asymptotically stable if r 0 1 then there exists a unique disease equilibrium e which is globally asymptotically stable third in the case of the unbounded spatial habitat r n we study the existence of traveling wave solutions of the model here we show that when the threshold value r 0 1 then there exists c 0 such that there exist positive traveling wave solutions of the model connecting the two equilibria e 0 and e with speed c c and when r 0 1 there is not such a traveling wave solution with speed c c numerical simulations are performed to illustrate our analytic results our results indicate that the global dynamics of the model are completely determined by the threshold value r 0

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

small time gaussian behavior of symmetric diffusion semi groups this work is involved with the short time asymptotics of diffusion semigroups in a general setting a generalization of fang s version of varadhan s formula is proven for general dirichlet spaces that are local and conservative the intrinsic metric appearing in the formula is characterized by pointwise distance for canonical dirichlet spaces on loop groups

numerical study of an influenza epidemic model with diffusion abstract a diffusive epidemic model is investigated with a view to describe the transmission of influenza as an epidemic the equations are solved numerically using the splitting method under different initial distribution of population density it is shown that the initial population distribution and diffusion play an important role for spread of disease it is also shown that interventions medical and nonmedical significantly slow down the spread of disease stability of equilibria of the numerical solutions are also established

logarithmic sobolev inequalities on loop groups let g be a compact lie group denote by m the brownian bridge measure on the loop group y g c 0 1 g g 0 g 1 e the finite energy subgroup of y determines in a natural way a gradient operation for functions on y the following logarithmic sobolev inequality is proven f2 log f dm gradf y 2 v y f y 2 dm f 2log f wherein f denotes the l2 m norm and v is a potential which is quadratic in the associated lie algebra valued brownian motion the inequality is derived by a method of inheritance from the known inequality for the g valued brownian motion

a cameron martin type quasi invariance theorem for pinned brownian motion on a compact riemannian manifold the results in driver 13 for quasi invariance of wiener measure on the path space of a compact riemannian manifold m are extended to the case of pinned wiener measure to be more explicit let h 0 1 tom be a c1 function where m is a compact riemannian manifold o e m is a base point and tom is the tangent space to m at o e m let w m be the space of continuous paths from 0 1 into m v be wiener measure on w m concentrated on paths starting at o e m and hs w denote the stochastic parallel translation operator along a path to e w m up to time s note hs w is only well defined up to v equivalence for c e w m let xh w denote the vector field along a given by xsh c hs cw h s for each s e 0 1 one should interpret xh as a vector field on w m the vector field xh induces a flow sh t w m w m which leaves wiener measure v quasi invariant see driver 13 it is shown in this paper that the same result is valid if h l 0 and the wiener measure v is replaced by a pinned wiener measure ive the measure ve is proportional to the measure v conditioned on the set of paths which start at 0 e m and end at a fixed end point e e m also as in 13 one gets an integration by parts formula for the vector fields xh defined above

distance distributions in ensembles of irregular low density parity check codes we derive asymptotic expressions for the average distance distributions in ensembles of irregular low density parity check ldpc codes the ensembles are defined by matrices with given profiles of column and row sums

on coset leader graphs of ldpc codes our main technical result is that in the coset leader graph of a linear binary code of block length n the metric balls spanned by constant weight vectors grow exponentially slower than those in 0 1 n following the approach of friedman and tillich we use this fact to improve on the first linear programming bound on the rate of low density parity check ldpc codes as the function of their minimal relative distance this improvement combined with the techniques of ben haim and litsyn improves the rate versus distance bounds for ldpc codes in a significant subrange of relative distances

traveling waves for a nonlocal dispersal sir model with delay and external supplies this paper is concerned with the existence nonexistence and minimal wave speed of traveling waves of a nonlocal dispersal delayed sir model with constant external supplies and holling ii incidence rate we find that the existence and nonexistence of traveling waves of the system are not only determined by the minimal wave speed c but also by the so called basic reproduction number r 0 of the corresponding reaction system that is we establish the existence of traveling waves for r 0 1 and each wave speed c c and the nonexistence for r 0 1 and any 0 c c or r 0 1 we also discuss how the latency of infection and the spatial movement of the infective individuals affect the minimal wave speed biologically speaking the longer the latency of infection in a vector is the slower the disease spreads

asymptotic enumeration methods for analyzing ldpc codes we show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low density parity check ldpc codes in particular we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular ldpc code ensembles we then consider the binary erasure channel bec using these estimates we derive lower bounds on the error exponent under iterative decoding of ldpc codes used over the bec both regular and irregular code structures are considered these bounds are compared to the corresponding bounds when optimal maximum likelihood ml decoding is applied

global attractivity spreading speeds and traveling waves of delayed nonlocal reaction diffusion systems abstract the purpose of this work is to study the spatial dynamics of some delayed nonlocal reaction diffusion systems in whole space we first establish a series of comparison theorems to investigate the global attractivity of the equilibria for a delayed nonlocal reaction diffusion system with and without quasi monotonicity then we show that the spreading speed of a general system without quasi monotone conditions is coincident with the minimal wave speed applying a fluctuation method we further provide some sufficient conditions to ensure the upward convergence of the spreading speed and traveling wave solutions finally we point out the effects of the delay and nonlocality on the spreading speed of the non quasi monotone systems

travelling wave solutions for a nonlocal dispersal hiv infection dynamical model abstract this paper is devoted to developing a nonlocal dispersal hiv infection dynamical model the existence of travelling wave solutions is investigated by employing schauder s fixed point theorem that is we study the existence of travelling wave solutions for r 0 1 and each wave speed c c in addition the boundary asymptotic behaviour of travelling wave solutions at is obtained by constructing suitable lyapunov functions and employing lebesgue dominated convergence theorem by employing a limiting argument we investigate the existence of travelling wave solutions for r 0 1 and c c the main difficulties are that the semiflow generated by the model does not have the order preserving property and the solutions lack of regularity

minimal wave speed for a class of non cooperative diffusion reaction system abstract in this paper we consider a class of non cooperative diffusion reaction systems which include prey predator models and disease transmission models the concept of weak traveling wave solutions is proposed the necessary and sufficient conditions for the existence of such solutions are obtained by the schauder s fixed point theorem and persistence theory the introduction of persistence theory is very technical and crucial the lasalle s invariance principle is applied to show that traveling wave solutions connect two equilibria the nonexistence of traveling wave solutions is proved by introducing a negative one sided laplace transform the results are applied to a prey predator model and a disease transmission model with specific interaction functions we find that the profile of traveling wave solutions may depend on different eigenvalues according to the corresponding condition which is a new phenomenon

dynamics of a diffusive vaccination model with nonlinear incidence abstract a recent paper xu et al 2018 studied the global stability and traveling wave solution of a vaccination model with nonlinear incidence furthermore in this paper we first study the local stability of this model and then establish the uniform persistence result our results are a supplement to above paper

traveling waves in a delayed sir model with nonlocal dispersal and nonlinear incidence this paper is concerned with traveling waves of a delayed sir model with nonlocal dispersal and a general nonlinear incidence the existence and nonexistence of traveling waves of the system are established respectively by schauder s fixed point theorem and two sided laplace transform it is also shown that the spread speed c is influenced by the dispersal rate of the infected individuals and the delay

global stability for reaction diffusion equations in biology the aim of this work is to study the global stability for some diffusion equations in biology by constructing lyapunov functionals these lyapunov functionals are obtained from those for ordinary differential equations several examples from virology and epidemiology are given to illustrate our method

traveling waves in a delayed sir epidemic model with nonlinear incidence we study the traveling waves of a diffusive sir epidemic model with a general nonlinear incidence we obtain the threshold dynamics for spatial spread of the disease we show that c is the minimum wave speed for the existence of traveling wave solutions we establish the existence and non existence of traveling wave solutions for a diffusive sir model with a general nonlinear incidence the existence proof is shown by introducing an auxiliary system applying schauder s fixed point theorem and then a limiting argument the nonexistence proof is obtained by two sided laplace transform when the speed is less than the critical velocity numerical simulations support the theoretical results we also point out the effects of the delay and the diffusion rate of the infective individuals on the spreading speed

wave propagation in an infectious disease model abstract this paper is devoted to the study of the wave propagation in a reaction convection infectious disease model with a spatio temporal delay previous numerical studies have demonstrated the existence of traveling wave fronts for the system and obtained a critical value c which is the minimal wave speed of the traveling waves in the present paper we provide a complete and rigorous proof to overcome the difficulty due to the lack of monotonicity for the system we construct a pair of upper and lower solutions and then apply the schauder fixed point theorem to establish the existence of a nonnegative solution for the wave equation on a bounded interval moreover we use a limiting argument and in turn generate the solution on the unbounded interval r in particular by constructing a suitable lyapunov functional we further show that the traveling wave solution converges to the epidemic equilibrium point as t

a tight rate bound and matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures this paper considers the natural extension of locally recoverable codes lrc to the case of t 1 erased symbols while several approaches have been proposed for the handling of multiple erasures in the approach considered here the t erased symbols are recovered in succession each time contacting at most r other symbols for assistance under the local recovery constraint this sequential approach is the most general and hence offers the maximum possible code rate we characterize the rate of an lrc with sequential recovery for any r geq 3 and any t by first deriving an upper bound on the code rate and then constructing a binary code achieving this optimal rate the upper bound derived here proves an earlier conjecture our approach permits us to deduce the structure of the parity check matrix of a rate optimal lrc with sequential recovery the derived structure of parity check matrix leads to a graphical description of the code used in code construction a subclass of binary codes that are both rate and block length optimal are shown to correspond to certain regular graphs known as moore graphs that have the smallest number of vertices for a given girth a connection with tornado codes is also made

spectral bound and reproduction number for infinite dimensional population structure and time heterogeneity spectral bounds of quasi positive matrices are crucial mathematical threshold parameters in population models that are formulated as systems of ordinary differential equations the sign of the spectral bound of the variational matrix at 0 decides whether at low density the population becomes extinct or grows another important threshold parameter is the reproduction number mathcal r which is the spectral radius of a related positive matrix as is well known the spectral bound and mathcal r 1 have the same sign provided that the matrices have a particular form the relation between spectral bound and reproduction number extends to models with infinite dimensional state space and then holds between the spectral bound of a resolvent positive closed linear operator and the spectral radius of a positive bounded linear operator we also extend an analogous relation between the spectral radii of two positive linear operators which is relevant for discrete time models we illustrate the general theory

upper bounds on the rate of ldpc codes as a function of minimum distance new upper bounds on the rate of low density parity check ldpc codes as a function of the minimum distance of the code are derived the bounds apply to regular ldpc codes and sometimes also to right regular ldpc codes their derivation is based on combinatorial arguments and linear programming the new bounds improve upon the previous bounds due to burshtein et al it is proved that at least for high rates regular ldpc codes with full rank parity check matrices have worse relative minimum distance than the one guaranteed by the gilbert varshamov bound

the taylor map on complex path groups let w g denote the path group of an arbitrary complex connected lie group the existence of a heat kernel measure t on w g has been shown in m cecil b k driver heat kernel measure on loop and path groups preprint http www math uconn edu cecil papers p2 pdf infin dimens anal quantum probab relat top submitted for publication the present work establishes an isometric map the taylor map from the space of l2 t holomorphic functions on w g to a subspace of the dual of the universal enveloping algebra of lie h g where h g is the lie subgroup of finite energy paths this map is shown to be surjective in the case where g is a simply connected graded lie group

minimal wave speed for a class of non cooperative reaction diffusion systems of three equations abstract in this paper we study the traveling wave solutions and minimal wave speed for a class of non cooperative reaction diffusion systems consisting of three equations based on the eigenvalues a pair of upper lower solutions connecting only the invasion free equilibrium are constructed and the schauder s fixed point theorem is applied to show the existence of traveling semi fronts for an auxiliary system then the existence of traveling semi fronts of original system is obtained by limit arguments the traveling semi fronts are proved to connect another equilibrium if natural birth and death rates are not considered and to be persistent if these rates are incorporated then non existence of bounded traveling semi fronts is obtained by two sided laplace transform then the above results are applied to some disease transmission models and a predator prey model

hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic ising models abstract we describe some results relating the spectral gap and logarithmic sobolev constants we work initially in the context of symmetric diffusions on a finite dimensional manifold and later apply our results to the analysis of certain infinite systems of mildly interacting diffusions

endemic models with arbitrarily distributed periods of infection i fundamental properties of the model this paper is dedicated to frank hoppensteadt on the occasion of his 60th birthday abstract a model is developed for the spread of anin fectious disease ina populationwith constant recruitment of new susceptibles and the fundamental properties of its solutions are analyzed the model allows for arbitrarily many stages of infection all of which have general length distributions and disease mortalities existence and uniqueness of solutions to the model equations are established a basic reproduction ratio is derived and related to the existence of an endemic equilibrium to the stability of the disease free equilibrium and to weak and strong endemicity persistence of the disease a characteristic equation is found the zeros of which determine the local stability of the endemic equilibrium and sufficient stability conditions are given for the case that infected individuals do not return into the susceptible class in a subsequent paper explicit sufficient and necessary stability conditions will be derived for the case that the disease dynamics are much faster than the demographics

mixed types of waves in a discrete diffusive epidemic model with nonlinear incidence and time delay abstract in this paper we investigate the traveling wave solutions of a discrete diffusive epidemic model with nonlinear incidence and time delay employing the method of upper and lower solutions schauder s fixed point theorem and a limiting approach we prove the existence of bounded super critical and critical traveling wave solutions moreover we obtain the positiveness and asymptotic boundary of the traveling wave solutions which guarantee that the traveling wave solutions are non trivial the existence results show that the traveling waves are mixed of front type and pulse type by way of contradiction and two sided laplace transform we derive the non existence of non trivial positive and bounded traveling wave solutions it is the first time to apply the method of upper and lower solutions together with schauder s fixed point theorem and two sided laplace transform to investigate the existence and non existence of traveling wave solutions for discrete diffusive epidemic models respectively

a cameron martin type quasi invariance theorem for brownian motion on a compact riemannian manifold abstract let m be a compact manifold without boundary o be a fixed base point in m g be a riemannian metric on m and be a g compatible covariant derivative on tm the tangent space to m assume the torsion t of satisfies the skew symmetry condition g t x y y 0 for all vector fields x and y on m for example take to be the levi civita covariant derivative on m g also let denote the wiener measure on w0 m c 0 1 m 0 o and let h s denote stochastic parallel translation relative to along the path w0 m up to time s 0 1 given a c1 function h 0 1 t0m it is shown that the differential equation t h t h with initial condition 0 id w m w m has a solution r maps w m w m the measurable maps from w m to w m this function is a flow on w m i e for all t r t t furthermore t has the quasi invariance property the law t of t with respect to the wiener measure is equivalent to for all t r this result is used to prove an integration by parts formula for the h derivative hf defined by h f d dt 0 f t where f is a c2 cylinder function on w m

the need for structure in quantum ldpc codes the existence of quantum ldpc codes with minimal distance scaling linearly in the number of qubits is a central open problem in quantum information despite years of research good quantum ldpc codes are not known to exist but at the very least it is known they cannot be defined on very regular topologies like low dimensional grids in this work we establish a complementary result showing that good quantum css codes which are sparsely generated require structure in the local terms that constrain the code space so as not to be too random in a well defined sense to show this we prove a weak converse to a theorem of krasikov and litsyn on weight distributions of classical codes due to which may be of independent interest subspaces for which the distribution of weights in the dual space is approximately binomial have very few codewords of low weight tantamount to having a non negligible approximate minimal distance while they may not have a large minimal non zero weight they still have very few words of low hamming weight

quickest sequence phase detection a phase detection sequence is a length n cyclic sequence such that the location of any length k contiguous subsequence can be determined from a noisy observation of that subsequence in this paper we derive bounds on the minimal possible k in the limit of n to infty and describe some sequence constructions we further consider multiple phase detection sequences where the location of any length k contiguous subsequence of each sequence can be determined simultaneously from a noisy mixture of those subsequences we study the optimal trade offs between the lengths of the sequences and describe some sequence constructions we compare these phase detection problems to their natural channel coding counterparts and show a strict separation between the fundamental limits in the multiple sequence case both adversarial and probabilistic noise models are addressed

spreading speed and traveling waves for a multi type sis epidemic model abstract the theory of asymptotic speeds of spread and monotone traveling waves for monotone semiflows is applied to a multi type sis epidemic model to obtain the spreading speed c and the nonexistence of traveling waves with wave speed c c then the method of upper and lower solutions is used to establish the existence of monotone traveling waves connecting the disease free and endemic equilibria for c c this shows that the spreading speed coincides with the minimum wave speed for monotone traveling waves we also give an affirmative answer to an open problem presented by rass and radcliffe l rass j radcliffe spatial deterministic epidemics math surveys monogr 102 amer math soc providence ri 2003

yang mills theory and the segal bargmann transform we use a variant of the segal bargmann transform to study canonically quantized yang mills theory on a space time cylinder with a compact structure group k the non existent lebesgue measure on the space of connections is approximated by a gaussian measure with large variance the segal bargmann transform is then a unitary map from the l 2 space over the space of connections to a holomorphicl 2 space over the space of complexified connections with a certain gaussian measure this transform is given roughly bye t1a 2 followed by analytic continuation here 1a is the laplacian on the space of connections and is the hamiltonian for the quantized theory on the gauge trivial subspace consisting of functions of the holonomy around the spatial circle the segal bargmann transform becomes e t1 k 2 followed by analytic continuation where 1k is the laplacian for the structure group k this result gives a rigorous meaning to the idea that 1a reduces to 1k on functions of the holonomy by letting the variance of the gaussian measure tend to infinity we recover the standard realization of the quantized yang mills theory on a space time cylinder namely 1 1k is the hamiltonian and l 2 k is the hilbert space as a byproduct of these considera tions we find a new one parameter family of unitary transforms from l 2 k to certain holomorphicl 2 spaces over the complexification of k this family of transformations interpolates between the two previously known unitary transformations our work is motivated by results of landsman and wren and uses probabilistic techniques similar to those of gross and malliavin

bounds on the parameters of locally recoverable codes a locally recoverable code lrc code is a code over a finite alphabet such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set in this paper we derive new finite length and asymptotic bounds on the parameters of lrc codes for lrc codes with a single recovering set for every coordinate we derive an asymptotic gilbert varshamov type bound for lrc codes and find the maximum attainable relative distance of asymptotically good lrc codes similar results are established for lrc codes with two disjoint recovering sets for every coordinate for the case of multiple recovering sets the availability problem we derive a lower bound on the parameters using expander graph arguments finally we also derive finite length upper bounds on the rate and the distance of lrc codes with multiple recovering sets

logarithmic sobolev inequalities for pinned loop groups abstract letgbe a connected compact type lie group equipped with anadg invariant inner product on the lie algebra g ofg given this data there is a well known left invariant h1 riemannian structure on l l g the infinite dimensional group of continuous based loops ing using this riemannian structure we define and construct a heat kernel t g0 associated to the laplace beltrami operator on l g heret 0 g0 l g and t g0 is a certain probability measure on l g for fixedg0 l g andt 0 we use the measure t g0 and the riemannian structure on l g to construct a classical pre dirichlet form the main theorem of this paper asserts that this pre dirichlet form admits a logarithmic sobolev inequality

on the equivalence of measures on loop space let k be a simply connected compact lie group equipped with an ad k invariant inner product on the lie algebra of k given this data there is a well known left invariant h 1 riemannian structure on l k the infinite dimensional group of continuous based loops in k as well as a heat kernel t k 0 associated with the laplace beltrami operator on l k here t 0 k 0 l k and t k 0 is a certain probability measure on l k in this paper we show that 1 e is equivalent to pinned wiener measure on k on s0 x t t 0 s 0 the algebra generated by truncated loops up to time s 0

poincare inequality for weighted first order sobolev spaces on loop spaces abstract let e be the loop space over a compact connected riemannian manifold with a torsion skew symmetric connection let l d be the ornstein uhlenbeck operator on a nonempty connected component d of the loop space e and let v d r be the restriction on d of the potential in the logarithmic sobolev inequality found by l gross on the loop group by s aida and by f z gong and z m ma on the loop space respectively we prove that the schrodinger operator l v l d v always has a spectral gap at the bottom 0 v of its spectrum and thus has its ground state transformed operator 1 l v 0 v where is the unique ground state of l v in particular our result proves l gross s conjecture about the existence of a spectral gap for the ground state transform of the schrodinger operator studied by him on the loop group in addition in all the above cases we identify the domain of the dirichlet forms associated with the ground state transforms as weighted first order sobolev spaces with weight given by 2 thus establishing a poincare inequality for them all these results are consequences from some new results in this paper on dirichlet forms characterizing certain classes with spectral gaps and from results by s aida and m hino

super critical and critical traveling waves in a three component delayed disease system with mixed diffusion abstract this paper deals with traveling waves of a three component delayed disease system with mixed diffusion when the basic reproduction number of the corresponding spatial homogenous delayed differential system r 0 1 and the wave velocity c c c is critical velocity we obtain that the system admits a positive traveling wave solution when r 0 1 and c r or r 0 1 and c c we prove that the system has no positive traveling wave solutions our theoretical results may be conducive to disease prevention and control

a delayed diffusive influenza model with two strain and two vaccinations abstract this paper deals with the global stability of a delayed diffusive influenza model with two strain and two vaccinations first we consider the well posedness of solutions of the model and show that the model admits four constant equilibria a disease free equilibrium two single strain infection equilibria and a double strain infection equilibrium which are determined by three threshold parameters r 1 r 2 and r 3 or r 4 second constructing four suitable lyapunov functionals and using the lasalle s invariant principle we establish the global stability of these equilibria finally we give several numerical simulations to illustrates the analytic results

traveling waves in a kermack mckendrick epidemic model with diffusion and latent period abstract this paper is devoted to the study of a kermack mckendrick epidemic model with diffusion and latent period we first consider the well posedness of solutions of the model furthermore using the schauder fixed point theorem and laplace transform we show that if the threshold value r 0 1 then there exists c 0 such that for every c c the model admits a traveling wave solution and if r 0 1 and c 0 or r 0 1 and c 0 c then the model admits no traveling wave solutions hence the existence and non existence of traveling wave solutions is determined completely by r 0 and the constant c is the minimum speed for the existence of traveling wave solutions of the model

travelling waves of a diffusive kermack mckendrick epidemic model with non local delayed transmission we obtain full information about the existence and non existence of travelling wave solutions for a general class of diffusive kermack mckendrick sir models with non local and delayed disease transmission we show that this information is determined by the basic reproduction number of the corresponding ordinary differential model and the minimal wave speed is explicitly determined by the delay such as the latent period and non locality in disease transmission and the spatial movement pattern of the infected individuals the difficulty is the lack of order preserving property of the general system and we obtain the threshold dynamics for spatial spread of the disease by constructing an invariant cone and applying schauder s fixed point theorem

absolute continuity of heat kernel measure with pinned wiener measure on loop groups let t 0 k be a connected compact lie group equipped with an ad k invariant inner product on the lie algebra of k associated to this data are two measures 0 t and t 0 on l k the space of continuous loops based at e e k the measure 0 t is pinned wiener measure with variance t while the measure 0 t is a heat kernel measure on l k the measure 0 t is constructed using a k valued brownian motion while the measure 0 t is constructed using a l k valued brownian motion in this paper we show that 0 t is absolutely continuous with respect to 0 t and the radon nikodym derivative d 0 t d 0 t is bounded

integration by parts and quasi invariance for heat kernel measures on loop groups abstract integration by parts formulas are established both for wiener measure on the path space of a loop group and for the heat kernel measures on the loop group the wiener measure is defined to be the law of a certain loop group valued brownian motion and the heat kernel measures are time t t 0 distributions of this brownian motion a corollary of either of these integrations by parts formulas is the closability of the pre dirichlet form considered by b k driver and t lohrenz 1996 j functional anal 140 381 448 we also show that the heat kernel measures are quasi invariant under right under right and left translations by finite energy loops

on relations between covering radius and dual distance the covering radius of a code tells us how far in the sense of hamming distance an arbitrary word of the ambient space can be from the code for a few decades this parameter has been widely studied we estimate the covering ratios of a code when the dual distance is known we derive a new bound on covering radii of linear codes it improves essentially on the previously known estimates in a certain wide range we also study asymptotic bounds on the cardinality of constant weight codes

on traveling wave solutions in general reaction diffusion systems with time delays abstract we study the existence of traveling wave solutions in a general class of mixed quasi monotone reaction diffusion systems with time delays first by applying the schauder fixed point theorem we prove the existence of a traveling wave solution between classically defined upper and lower solutions for better applications of the upper lower solution method on various real life models the existence result is further extended under weak form or piecewise smooth upper lower solutions in several reaction diffusion systems with time delays single species logistic growth n species competition and ratio dependent predator prey with gompertz growth we apply our main result to establish the existence of traveling wave solutions flowing towards the positive or coexistent states under reasonable conditions on ecological parameters

global dynamics of a general class of multistage models for infectious diseases we propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages the models can describe disease progression through multiple latent or infectious stages as in the case of hiv and tuberculosis amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment the models also incorporate general nonlinear incidences and general nonlinear forms of population transfer among stages under biologically motivated assumptions we derive the basic reproduction number r 0 and show that the global dynamics are completely determined by r 0 if r 0 leq 1 the disease free equilibrium is globally asymptotically stable and the disease dies out if r 0 1 then the disease persists in all stages and a unique endemic equilibrium is globally asymptotically stable

critical traveling waves in a diffusive disease model abstract in this paper the existence of a non trivial positive and bounded critical traveling wave solution of a diffusive disease model whose reaction system has infinitely many equilibria is obtained for the first time this gives an affirmative answer to an open problem left in wang et al 2012 19 our result shows that the critical traveling wave in this model is a mix of front s component and pulse i component type

a nonlocal and time delayed reaction diffusion model of dengue transmission a nonlocal and time delayed reaction diffusion model of dengue fever is first proposed that incorporates the aquatic stage the winged stage and the incubation periods of the dengue virus within mosquitos and hosts then the basic reproduction number r 0 is established for the model system and an explicit formula of r 0 is obtained in the case of spatially homogeneous infections it is shown that this r 0 gives the threshold dynamics in the sense that the disease free equilibrium is asymptotically stable if r 0 1 the influences of diffusion coefficients time delays and infection heterogeneity on the spread of the disease are also studied via numerical simulations it turns out that the infection risk may be underestimated if the spatially averaged parameters are used to compute the basic reproduction number for spatially heterogeneous infections

existence of traveling wave solutions for influenza model with treatment abstract to investigate the spreading speed of influenza and the influence of treatment on the spreading speed a reaction diffusion influenza model with treatment is established the existence of traveling wave solutions is shown by introducing an auxiliary system and applying the schauder fixed point theorem the non existence of traveling wave solutions is proved by a two sided laplace transform which needs a new approach for the prior estimate of exponential decay of traveling wave solutions

a qualitative study of a vaccination model with non linear incidence we propose a new deterministic model for the dynamics of an infectious disease in the presence of a preventive prophylactic vaccine and an effective therapeutic treatment the three dimensional model which assumes a non linear incidence rate is analysed qualitatively to determine the stability of its equilibria the optimal vaccine coverage threshold needed for disease control and eradication is determined analytically and verified using numerical simulations the case where no vaccination is given vaccination free model is also investigated using a dulac function it is shown that the vaccination free model has no limit cycles

convergence of finite dimensional distributions of heat kernel measures on loop groups abstract in this paper we consider heat kernel measure on loop groups associated to the h 1 2 metric unlike h s case s 1 2 there is a difficulty that h 1 2 is not contained in the space of continuous loops so we take limits there are two limiting methods one is to use delta functions and to let s go down to 1 2 the other is to fix s at 1 2 and to approximate the delta functions for the second approach a generalization of heat kernel measures is needed then the first approach can be obtained as a special case of the second one the limit in the sense of finite dimensional distribution is the fictitious infinite dimensional haar measure

an estimate of the gap of spectrum of schrodinger operators which generate hyperbounded semigroups abstract logarithmic sobolev inequalities with potential functions on loop spaces were proved by l gross 1991 j funct anal 102 265 313 s aida 1996 in proceedings of the fifth gregynog symposium stochastic analysis and applications pp 1 19 world scientific singapore and f z gong and z m ma 1998 j funct anal 599 623 the generators of the dirichlet forms are schrodinger operators on loop spaces and they generate hyperbounded semigroups recently f z gong m rockner and l m wu 2000 poincare inequality for weighted first order sobolev spaces on loop spaces submitted proved the existence of the gap of spectrum at the lowest eigenvalue of the schrodinger operators by using m hino s exponential decay estimates of the semigroup 2000 osaka j math 37 603 624 and the author s strong ergodicity property of the semi group s aida 1998 j funct anal 158 152 185 in this paper we will give a lower bound on the gap by using a weak poincare inequality which was introduced by m rockner and f y wang 2000 weak poincare inequalities and l 2 convergence rates of markov semigroups preprint also we will give estimates on the distribution function of ground states using the weak poincare inequality