the dynamics of traveling waves for a nonlinear belousov zhabotinskii system abstract in this paper we consider the existence of traveling wave fronts in a belousov zhabotinskii system with delay by traveling wave transformation and time scale transformation we change the belousov zhabotinskii system with delay into a singularly perturbed differential system by applying geometric singular perturbation theory we construct a locally invariant manifold for the associated traveling wave equation and obtain the traveling wave fronts for the equation by using the fredholm orthogonality finally we discuss the asymptotic behaviors of traveling wave solutions by applying the asymptotic theory

traveling wave solutions in a diffusive system with two preys and one predator abstract this paper is concerned with the traveling wave solutions in a diffusive system with two preys and one predator by constructing upper and lower solutions the existence of nontrivial traveling wave solutions is established the asymptotic behavior of traveling wave solutions is also confirmed by combining the asymptotic spreading with the contracting rectangles applying the theory of asymptotic spreading the nonexistence of traveling wave solutions is proved

cluster expansion for abstract polymer models a new direct proof of convergence of cluster expansions for polymer contour models is given in an abstract setting it does not rely on kirkwood salsburg type equations or combinatorics of trees a distinctive feature is that at all steps the considered clusters contain every polymer at most once

convolutionally coded transmission over markov gaussian channels analysis and decoding metrics it has been widely acknowledged that the aggregate interference at the receiver for various practical communication channels can often deviate markedly from the classical additive white gaussian noise awgn assumption due to various ambient phenomena moreover the physical nature of the underlying interference generating process in such cases can lead to a bursty behaviour of the interfering signal implying that it is highly likely that consecutive symbols are affected by similar noise levels in this paper we devise and analyze detection techniques in conjunction with a convolution code for such interference channels that possess non negligible memory by considering optimum and sub optimum decoding metrics in particular the inherent memory in the noise process is modeled as a first order markov chain whose state selects the variance of the instantaneous gaussian noise leading to a markov gaussian channel model analytical expressions are obtained for the cut off rate which is an ensemble code parameter and the bit error rate for a convolutionally coded system that are subsequently employed for an extensive evaluation of the various metrics considered furthermore the interleaving depth is considered as a design parameter and its effect on performance is analyzed over a range of noise scenarios

pilot assisted and blind joint data detection and channel estimation in partial time jamming we consider a communication scenario in which a message is received in the presence of partial time gaussian jamming and additive white gaussian noise we consider a quasi static channel in which the amplitude and phase are constant over each packet transmission the receiver does not know the amplitude and phase of the incoming signal which symbols are jammed or even the statistics of the jammer such as the jamming power and jamming probability in this scenario the receiver must accurately estimate the parameters of the channel and the jamming to achieve good performance we apply the expectation maximization em algorithm to iteratively approximate the maximum likelihood ml estimator for all of the parameters we find that the overall performance of the em algorithm is very sensitive to the initial estimates so we propose a new initial estimator that offers good performance the em algorithm approach requires pilot symbols to resolve a phase ambiguity thus we also present a blind estimation algorithm to avoid the reduction in overall code rate from the use of pilot symbols

a geometric approach in the study of traveling waves for some classes of non monotone reaction diffusion systems abstract in this paper we further extend a recently developed method to investigate the existence of traveling waves solutions and their minimum wave speed for non monotone reaction diffusion systems our approach consists of two steps first we develop a geometrical shooting argument with the aid of the theorem of homotopy invariance on the fundamental group to obtain the positive semi traveling wave solutions for a large class of reaction diffusion systems including the models of predator prey interaction for both predator independent dependent functional responses the models of combustion belousov zhabotinskii reaction si type of disease transmission and the model of biological flow reactor in chemostat next we apply the results obtained from the first step to some models such as the beddinton deangelis model and the model of biolocal flow reactor to show the convergence of these semi traveling wave solutions to an interior equilibrium point by the construction of a lyapunov type function or the convergence of semi traveling waves to another boundary equilibrium point by the further analysis of the asymptotical behavior of semi traveling wave solutions

wetting of heterogeneous surfaces at the mesoscopic scale we consider the problem of wetting on a heterogeneous wall with mesoscopic defects i e defects of order l e 0 e 1 where l is some typical length scale of the system in this framework we extend several former rigorous results which were shown for walls with microscopic defects 10 11 namely using statistical techniques applied to a suitably defined semi infinite ising model we derive a generalization of young s law for rough and heterogeneous surfaces which is known as the generalized cassie wenzel s equation in the homogeneous case we also show that for a particular geometry of the wall the model can exhibit a surface phase transition between two regimes which are either governed by wenzel s or by cassie s law

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

performance analysis for bicm transmission over gaussian mixture noise fading channels bit interleaved coded modulation bicm has been adopted in many systems and standards for spectrally efficient coded transmission the analytical evaluation of bicm performance parameters in particular bit error rate ber has received considerable attention in the recent past in this paper we derive ber approximations for bicm transmission over general fading channels impaired by gaussian mixture noise gmn to this end we build upon the saddlepoint approximation of the pairwise error probability pep and a recently established approximation for the probability density function pdf of bit wise reliability metrics for nonfading additive white gaussian noise awgn channels we extend this pdf approximation to the case of gmn and obtain closed form expressions for its laplace transform for fading gmn channels the latter allows us to express the pep and thus ber via the saddlepoint approximation for the special case of fading awgn channels the presented approximations are closed form since the saddlepoint is well approximated by 1 2 for bicm decoding furthermore we derive closed form pep expressions also for gmn channels in the high signal to noise ratio regime and establish the diversity and coding gain for bicm transmission over fading gmn channels selected numerical results for the ber of convolutional coded bicm highlight the usefulness of the proposed approximations and the differences between awgn and gmn channels

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

traveling waves in diffusive predator prey equations periodic orbits and point to periodic heteroclinic orbits we demonstrate the existence of periodic traveling wave train and traveling front solutions for a diffusive predator prey system the analysis is in the three dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator prey system in the traveling wave variable the analysis shows the existence of periodic orbits heteroclinic orbits and a heteroclinic connection of a point and a periodic orbit the proof uses shooting techniques invariant manifold theory and the qualitative theory of ordinary differential equations

on the microscopic validity of the wulff construction and of the generalized young equation for a large class of 1 1 dimensional interfaces of the solid on solid type we prove on a microscopic basis the validity of the wulff construction and of the generalized young equation which gives the contact angle of a sessile drop on a wall our proof relies on a new method to treat random walks with a finite number of global constraints

em based recursive estimation of channel parameters recursive online expectation maximization em algorithm along with stochastic approximation is employed in this paper to estimate unknown time invariant variant parameters the impulse response of a linear system channel is modeled as an unknown deterministic vector process and as a gaussian vector process with unknown stochastic characteristics using these models which are embedded in white or colored gaussian noise different types of recursive least squares rls kalman filtering and smoothing and combined rls and kalman type algorithms are derived directly from the recursive em algorithm the estimation of unknown parameters also generates new recursive algorithms for situations such as additive colored noise modeled by an autoregressive process the recursive em algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods

generalized traveling waves for time dependent reaction diffusion systems traveling wave solutions in general time dependent including time periodic reaction diffusion equations and systems of equations have attracted great attention in the last two decades the aim of this paper is to study the propagation phenomenon in a general time heterogeneous environment more specifically we investigate generalized traveling wave solutions for a two component time dependent non cooperative reaction diffusion system which has applications in epidemiology and ecology sufficient conditions on the existence and nonexistence of generalized traveling wave solutions are established in the susceptible infectious epidemic model setting generalized traveling waves describe the spatio temporal invasion of a disease into a totally susceptible population in the context of predator prey systems the generalized traveling waves describe the spatial invasion of predators introduced into a new environment where the prey population is at its carrying capacity

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

on the convergence of cluster expansions abstract a new simple proof of the convergence of cluster expansions in statistical mechanics is presented in the case of an abstract polymer system

invasion traveling wave solutions of a predator prey system abstract this paper is concerned with the traveling wave solutions of a predator prey system in which intra specific conflictions are involved by using the comparison principle and the asymptotic speed of spreading the existence nonexistence and minimal wave speed of non negative traveling wave solutions are established such a traveling wave solution can model the spatial temporal process where the predator invades the territory of the prey and they eventually coexist

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

traveling wave solutions of diffusive lotka volterra equations a heteroclinic connection in we establish the existence of traveling wave solutions for a reaction dif fusion system based on the lotka volterra differential equation model of a predator and prey interaction the waves are of transition front type analogous to the solutions discussed by fisher and kolmogorov et al for a scalar reaction diffusion equation the waves discussed here are not necessarily monotone there is a speed c 0 such that for c c there is a traveling wave moving with speed c the proof uses a shooting argument based on the nonequivalence of a simply connected region and a nonsimply connected region together with a liapunov function to guarantee the existence of the traveling wave solution the traveling wave solution is equivalent to a heteroclinic orbit in 4 dimensional phase space

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

the existence and stability of travelling waves with transition layers for some singular cross diffusion systems abstract this paper is concerned with the existence and the stability of travelling waves for a class of quasilinear cross diffusion systems describing two competing or predator prey species firstly by geometric singular perturbation method the existence of travelling waves with transition layers is proved which extends the results of hosono and mimura y hosono m mimura singular perturbation approach to travelling waves in competing and diffusion species models j math kyoto univ 22 1982 435 461 and gardner r a gardner topological methods arising in the study of travelling waves reaction diffusion equations clarendon press oxford 1990 pp 173 198 for non cross diffusion systems and wu y wu the existence of travelling waves for a cross diffusion system with small parameter beijing math 3 1997 74 85 to more general cross diffusion systems applying the stability index method introduced in alexsander et al j alexsander r a gardner c k r t jones a topological invariant arising in the stability analysis of travelling waves j die reine angewandte math 410 1990 167 212 and gardner and jones r a gardner c r k t jones stability of travelling wave solutions of diffusive predator prey systems trans am soc 327 1991 465 524 to the more general eigenvalue problem induced by the quasilinear cross diffusion systems by detailed spectral and topological analysis the travelling waves with transition layers for the cross diffusion systems are proved to be stable which also extends the results of gardner and jones r a gardner c r k t jones stability of travelling wave solutions of diffusive predator prey systems trans am soc 327 1991 465 524 to the more general systems

low complexity erasure insertion in rs coded sfh spread spectrum communications with partial band interference and nakagami m fading we propose two novel low complexity low delay erasure insertion schemes namely the output threshold test ott and joint maximum output and ratio threshold test mo rtt the employment of the ott and mo rtt is beneficial in the context of the errors and erasures reed solomon rs decoding in a slow frequency hopping spread spectrum sfh ss system using m ary frequency shift keying mfsk the statistics of the erasure insertion related decision variables associated with the ott mo rtt as well as with the ratio threshold test rtt are investigated when the channel of each frequency hopping fh slot is modeled as flat nakagami m fading the transmitted signals also experience both additive white gaussian noise awgn as well as partial band gaussian interference pbgi the properties of these erasure insertion schemes are investigated with the aid of their statistics the performance of the proposed erasure insertion schemes and that of the erasure insertion scheme using the rtt is investigated and compared in the context of rs coded sfh ss systems using mfsk furthermore the performance of the rs coded sfh ss systems is also compared both with and without side information concerning the pbgi

rigorous generalization of young s law for heterogeneous and rough substrates we consider a sos type model of interfaces on a substrate which is both heterogeneous and rough we first show that for appropriate values of the parameters the differential wall tension that governs wetting on such a substrate satisfies a generalized law which combines both cassie and wenzel laws then in the case of an homogeneous substrate we show that this differential wall tension satisfies either the wenzel s law or the cassie s law according to the values of the parameters

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

joint parameter estimation and symbol detection for linear or nonlinear unknown channels we present an iterative method for joint channel parameter estimation and symbol selection via the baum welch algorithm or equivalently the expectation maximization em algorithm channel parameters including noise variance are estimated using a maximum likelihood criterion the markovian properties of the channel state sequence enable us to calculate the required likelihood using a forward backward algorithm the calculated likelihood functions can easily give optimum decisions on information symbols which minimize the symbol error probability the proposed receiver can be used for both linear and nonlinear channels it improves the system throughput by making saving in the transmission of known symbols usually employed for channel identification simulation results which show fast convergence are presented

partial to complete wetting a microscopic derivation of the young relation this paper is devoted to the study of the young equation which gives a connection between surface tensions and contact angle we derive the generalized form of this equation for anisotropic models using thermodynamic considerations in two dimensions with sos like approximations of the interface we prove that the surface tension may be computed explicitly as a simple integral which of course depends upon the orientation of the interface this allows a complete study of the wetting transition when a constant wall attraction is taken into account within the sos and gaussian models we therefore give a complete analysis of the variation of the contact angle with the temperature for those models it is found that for certain values of the parameters two wetting transitions may successively appear one at low temperature and one at high temperature giving the following states film droplet film this study rests upon the generalized young equation the validity of which is proved for the gaussian model with a constant wall attraction using microscopic considerations

performance of reed solomon coded frequency hop spread spectrum communications in partial band interference this paper is concerned with the performance of a communications system which utilizes frequency hop spread spectrum diversity transmission reed solomon coding and parallel error correction and erasure correction decoding both binary signaling and m ary orthogonal signaling are considered the goals are twofold first it is desirable to provide good performance in partial band gaussian noise interference by use of coding and diversity with an efficient error correction algorithm second it is necessary to totally neutralize narrow band interference regardless of the power level or statistical distribution of the interference in order to have an effective spread spectrum system through an analysis of the effects of partial band interference on a frequency hop spread spectrum system with diversity it is shown that the use of reedsolomon coding with a parallel errors and erasures decoding algorithm accomplishes these goals the paper also investigates the accuracy of the chernoff bound as an approximation to the true performance of a frequency hop spreadspectrum communication system with diversity side information m ary orthogonal signaling and reed solomon coding the performance results presented in the paper are based on analysis and computer evaluation approximate results based on the chernoff bound are also given it is shown that the chernoff bound for m ary orthogonal signaling gives a very poor approximation for many cases of interest this is largely due to the looseness of the union bound

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

the existence of periodic travelling waves for singularly perturbed predator prey equations via the conley index this paper is concerned with the existence of periodic travelling wave solutions of reactiondiffusion equations which arise as models of predator prey interactions in mathematical ecology the relevant equations are somewhat similar to the fitz hugh nagumo equations and our results apply to this latter system as well in studying the fitz hugh nagumo equations conley 3 i initiated a new topological approach to this problem his method depends on the construction of an isolating neighborhood cf section 2a about a singular periodic solution associated with such a neighborhood is a topological invariant the conley index which when nontrivial implies the existence of a smooth solution near the singular one the new aspects of the present discussion are in the method used to construct the isolating neighborhood in ifi4 and in the computation of the index with regard to the isolating neighborhood our construction is global in that a parameter taken to be small in conley s equations is now allowed to assume large values in order to compute the index we continue our equations to those studied by conley actually we go one step further and continue conley s equations to the van der pol equations crossed with a pair of linear equations admitting a repelling critical point the index for this latter system is easily computed and turns out to be non trivial it follows from the invariance of the index under continuation 21 that the desired

spectral stability of small shock waves this paper is the first in a series of articles that study the eigenvalue problem for small amplitude shock waves in systems of conservation laws with viscosity or relaxation the papers show in various contexts that in the zero amplitude limit appropriately scaled versions of the associated evans bundles converge to suspensions of evans bundles for fixed shock waves in related reduced systems with lower dimensional state space in this article the new geometric framework establishing this connection is introduced in the simplest context that of shock waves associated with a simple genuinely nonlinear mode in systems with identity viscosity in one space dimension

traveling waves for a generalized holling tanner predator prey model abstract we study traveling wave solutions for holling tanner type predator prey models where the predator equation has a singularity at zero prey population the traveling wave solutions here connect the prey only equilibrium 1 0 with the unique constant coexistence equilibrium u v first we give a sharp existence result on weak traveling wave solutions for a rather general class of predator prey systems with minimal speed explicitly determined such a weak traveling wave u v connects 1 0 at but needs not connect u v at next we modify the holling tanner model to remove its singularity and apply the general result to obtain a weak traveling wave solution for the modified model and show that the prey component in this weak traveling wave solution has a positive lower bound and thus is a weak traveling wave solution of the original model these results for weak traveling wave solutions hold under rather general conditions then we use two methods a squeeze method and a lyapunov function method to prove that under additional conditions the weak traveling wave solutions are actually traveling wave solutions namely they converge to the coexistence equilibrium as

cassie s law and concavity of wall tension with respect to disorder for the semiinfinite ising model with quenched boundary disorder we prove concavity inequalities for the difference of wall tensions associated with the minus and plus phases these inequalities generalize phenomenological equalitiesknown as cassie s law

dynamic behavior of a beddington deangelis type stage structured predator prey model abstract this paper deals with a robust stage structured predator prey model with beddington deangelis type functional response the proposed mathematical model consists of a system of three nonlinear ordinary differential equations to stimulate the interactions between prey population juvenile predators and adult predator population the positivity boundedness and the conditions for uniform persistence have been derived the dynamical behavior of the system both analytically and numerically investigated from the point of view of local stability persistence and global stability the global stability of the system has been derived by using the theory of competitive systems stability of periodic orbits and compound matrices for the interior equilibrium point depending on the conversion rate of the prey population to juvenile predator the model exhibits hopf bifurcation the model admit periodic solutions which is produced from the stage structure of the predator populations numerical simulations have been accomplished to validate our analytical findings

travelling wave solutions to monostable reaction diffusion systems of mixed monotone type theorems concerning the existence and stability of travelling wave solutions to mono stable reaction diffusion systems of mixed monotone type are established these results are applied to an autocatalytic system which is a particular case in the class of monostable systems of mixed monotone type a series of numerical experiments is conducted to simulate formation and propagation of waves

stability of travelling wave solutions of diffusive predator prey systems the stability of travelling wave solutions of singularly perturbed diffusive predator prey systems is proved by showing that the linearized operator about such a solution has no unstable spectrum and that the translation eigenvalue at a 0 is simple the proof illustrates the application of some recently developed geometric and topological methods for counting eigenvalues

travelling waves for delayed reaction diffusion equations with global response we develop a new approach to obtain the existence of travelling wave solutions for reaction diffusion equations with delayed non local response the approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain banach space coupled with an index formula of the associated fredholm operator and some careful estimation of the nonlinear perturbation the general result relates the existence of travelling wave solutions to the existence of heteroclinic connecting orbits of a corresponding functional differential equation and this result is illustrated by an application to a model describing the population growth when the species has two age classes and the diffusion of the individual during the maturation process leads to an interesting non local and delayed response for the matured population

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

on perron frobenius property of matrices having some negative entries we extend the theory of nonnegative matrices to the matrices that have some negative entries we present and prove some properties which give us information when a matrix possesses a perron frobenius eigenpair we apply also this theory by proposing the perron frobenius splitting for the solution of the linear system ax b by classical iterative methods perron frobenius splittings constitute an extension of the well known regular splittings weak regular splittings and nonnegative splittings convergence and comparison properties are given and proved

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

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

traveling waves connecting equilibrium and periodic orbit for reaction diffusion equations with time delay and nonlocal response abstract a class of reaction diffusion equations with time delay and nonlocal response is considered assuming that the corresponding reaction equations have heteroclinic orbits connecting an equilibrium point and a periodic solution we show the existence of traveling wave solutions of large wave speed joining an equilibrium point and a periodic solution for reaction diffusion equations our approach is based on a transformation of the differential equations to integral equations in a banach space and the rigorous analysis of the property for a corresponding linear operator our approach eventually reduces a singular perturbation problem to a regular perturbation problem the existence of traveling wave solution therefore is obtained by the application of liapunov schmidt method and the implicit function theorem

em based joint data detection and channel estimation of ds cdma signals we present two efficient iterative receiver structures of tractable complexity for joint multiuser detection and multichannel estimation jde of direct sequence code division multiple access signals the schemes result from an application of the expectation maximization em and the space alternating generalized expectation maximization sage algorithms respectively the em jde receiver updates the data bit sequences in parallel while the sage jde receiver reestimates them successively the channel parameters are updated in parallel in both schemes the em algorithm provides a set of free parameters called weight coefficients which can be selected to optimize its performance two optimality criteria are defined and analytical expressions for the corresponding optimized weight coefficients are given monte carlo simulations of a synchronous scenario show that the proposed jde receivers have excellent multiuser efficiency and are robust against errors in the estimation of the channel parameters moreover very short training sequences are required for the jde schemes to converge simulation results further demonstrate that the sage jde receiver exhibits a better performance when the users bit sequences are updated in the order of increasing signal strength i e the bit sequence of the user with the weakest signal strength is updated first at each stage

stability of the travelling wave solution of the fitzhugh nagumo system on demontre la stabilite relative au systeme complet d equations aux derivees partielles de ces ondes de propagation

existence of travelling wave solutions of predator prey systems via the connection index we consider a reaction diffusion system which arises as a model of predator prey interactions in mathematical ecology the system admits four constant equilibria two of which are stable the main result is an existence theorem for travelling wave solutions which connect the two stable equilibria most previous efforts with regard to travelling waves for systems employ singular perturbations to locate the connecting orbit the new aspect of the present discussion lies in devising some novel methods for locating the connecting solution in phase space which do not require that the equations be singularly perturbed in certain cases the main result holds for an arbitrary choice of diffusion coefficients

influence of the geometry of a rough substrate on wetting the wall tension of a rough wall is considered within a semi infinite planar ising model using monte carlo simulation techniques we have studied the influence of the geometry of a rough surface on the wall tension different geometries are examined in detail ranging from elementary deformation of the flat surface including pores to more realistic substrates generated randomly with a given roughness we give evidence that complex geometries lead to wall tensions that are bounded by those associated with two simple well characterized substrates protrusion and pits

capacity achieving input distributions of additive quadrature gaussian mixture noise channels this paper studies the characterization of the optimal input and the computation of the capacity of additive quadrature gaussian mixture gm noise channels under an average power constraint the considered model can be used to represent a wide variety of channels with impulsive interference such as the well known bernoulli gaussian and middleton class a impulsive noise channels as well as multiple access interference channels and cognitive radio channels under imperfect sensing at first we demonstrate that there exists a unique input distribution that achieves the channel capacity and the capacity achieving input distribution has a uniformly distributed phase by examining the kuhn tucker alignment conditions ktcs we further show that if the optimal input amplitude distribution contains an infinite number of mass points on a bounded interval the channel output must be gaussian distributed however by using bernstein s theorem to examine the completely monotonic condition it is shown that the assumption of a gaussian distributed output is not valid as a result there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution in addition by applying a novel bounding technique on the ktc and using the envelop theorem we demonstrate that the optimal amplitude distribution cannot have an infinite number of mass points this gives us the unique solution of the optimal input having discrete amplitude with a finite number of mass points given this discrete nature of the optimal input we then develop a simple method to compute the discrete optimal input and the corresponding capacity our numerical examples show that in many cases the capacity achieving distribution consists of only one or two mass points

monostable waves in a class of non local convolution differential equation abstract the current paper is devoted to the study of wave propagation dynamics for a class of convolution equation with monostable structure it is shown that this equation admits traveling wave solution connecting the zero steady state even when the nonlinear term of this equation is without monotonicity a sufficient condition for the traveling wave solution that converges to the positive steady state is also established

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

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

existence of traveling wave solutions for diffusive predator prey type systems abstract in this work we investigate the existence of traveling wave solutions for a class of diffusive predator prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions the profile equations for the above system can be reduced as a four dimensional ode system and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system applying the methods of wazewski theorem lasalle s invariance principle and hopf bifurcation theory we obtain the existence results our results can apply to various kinds of ecological models

sequence estimation in the presence of random parameters via the em algorithm the expectation maximization em algorithm was first introduced in the statistics literature as an iterative procedure that under some conditions produces maximum likelihood hit parameter estimates in this paper we investigate the application of the em algorithm to sequence estimation in the presence of random disturbances and additive white gaussian noise as examples of the use of the em algorithm we look at the random phase and fading channels and show that a formulation of the sequence estimation problem based on the em algorithm can provide a means of obtaining ml sequence estimates a task that has been previously too complex to perform