convergence of relaxed multisplitting usaor methods for h matrices linear systems relaxed technique is one of the techniques for improving convergence rate of splitting iterative methods in this paper based on the methods in frommer and mayer a frommer f mayer convergene of relaxed parallel multisplitting methods linear algebra and its applications 119 1989 141 152 and zhang et al l t zhang t z huang t x gu global relaxed non stationary multisplitting multi parameters methods international journal of computer mathematics 85 2 2008 211 224 we present local relaxed parallel multisplitting method global relaxed parallel multisplitting method local relaxed non stationary parallel multisplitting multi parameters method and global relaxed non stationary parallel multisplitting multi parameters method and study the convergence of our methods associated with usaor multisplitting for solving a large sparse linear system whose coefficient matrix is an h matrix when choosing the approximately optimal relaxed parameters our methods have faster convergence rate which is showed through numerical examples c 2008 elsevier inc all rights reserved

spreading dynamics of forget remember mechanism we study extensively the forget remember mechanism frm for message spreading originally introduced in eur phys j b 62 247 2008 epjbfy1434 602810 1140 epjb e2008 00139 4 the freedom of specifying forget remember functions governing the frm can enrich the spreading dynamics to a very large extent the master equation is derived for describing the frm dynamics by applying the mean field techniques we have shown how the steady states can be reached under certain conditions which agrees well with the monte carlo simulations the distributions of forget and remember times can be explicitly given when the forget remember functions take linear or exponential forms which might shed some light on understanding the temporal nature of diseases like flu for time dependent frm there is an epidemic threshold related to the frm parameters we have proven that the mean field critical transmissibility for the sis model and the critical transmissibility for the sir model are the lower and the the upper bounds of the critical transmissibility for the frm model respectively

discrete time deterministic and stochastic models for the spread of rabies discrete spatial and temporal models for the spread and control of rabies are developed analyzed and simulated first a deterministic model is formulated then an analogous stochastic model the models are structured with respect to space m patches age juveniles and adults and disease state for each patch there are six state variables corresponding to either juveniles or adults and their disease state susceptible infected or vaccinated the models have seven stages which repeat every year the impact of different vaccination strategies on the dynamics of the deterministic and stochastic models are compared in particular the relationships among the vaccination proportion the width of the vaccination barrier the initial number infected and the transmissibility of the disease are examined an estimate for the probability of disease elimination is given for the stochastic model it is shown that in some cases where the deterministic model predicts disease persistence the stochastic model predicts a high probability of disease elimination

convergence of parallel multisplitting iterative methods for m matrices abstract despite the major recent activity in parallel processing few effective new algorithms designed exclusively for multiprocessors have been put forth one such is the multisplitting iterative algorithm suggested by o leary and white although they have given some sufficient conditions for convergence a general convergence theory has not been developed even for the classical situation where the coefficient matrix a is an m matrix or is symmetric positive definite in this paper we study the m matrix case in detail the multisplitting process for a rn n is recast as an ordinary iterative process for a certain block matrix a r kn kn where k is the number of processors and standard convergence results are used to develop a convergence theory for multisplitting iterative methods where a is an m matrix comparison results between multisplitting methods are established in terms of monotonic norms and for the case where a is irreducible in terms of the asymptotic convergence rate a key observation here is that in certain cases the rate of global convergence of these parallel iterative methods is inherent in the splitting of a and is independent of the manner in which the work is distributed among the processors thus in general one can distribute the work for load balancing purposes without affecting the convergence rate

asymptotically autonomous semiflows chain recurrence and lyapunov functions from the work of c conley it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set here we improve a result of l markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow in the special case that there is a lyapunov function for the limiting semiflow sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the lyapunov function

stability of bounded subsets of metzler sparse matrix cones abstract we study the existence of hurwitz matrices in a class of metzler sparse matrix cones where the non zero entries are constrained to be in a bounded set in particular we provide necessary and sufficient conditions for the existence of one or more hurwitz matrices in this class of sparse matrix spaces for scenarios with uniform and non uniform bounds several examples illustrate our results

a non markovian sir network model with fixed infectious period and preventive rewiring abstract in the face of disease occurrence susceptible individuals tend to protect themselves by rewiring their links i e cutting off connection with infected person and switching to contact with healthy ones therefore the adaptive rewiring mechanism is considered in the network epidemic model moreover the infection periods for different diseases do not always follow exponential distributions in the process of disease transmission which may be of fixed length using the idea of age structure we establish the susceptible infected recovered epidemic model for each node and each link resulting in a delayed non markovian sir pairwise model with fixed infectious period and preventive rewiring then give the pairwise reproduction number r 0 p and provide the formula for the final epidemic size by rigorous analysis and tedious computation the simulation results show that adaptive rewiring inhibits the spread of disease and decreases the size of disease outbreak while the extension of the infectious period promotes disease transmission in addition the numerical simulation results are in good agreement with the stochastic simulation to our best knowledge the approach in building our model is novel the results may provide new insights into the study of the network disease transmission

comparison theorems of preconditioned gauss seidel methods for m matrices in this paper a new preconditioner for the gauss seidel method is proposed for solving linear systems whose coefficient matrix is an m matrix several comparison theorems are shown for the proposed method with several preconditioners it follows from the comparison results that our preconditioner is one of the best preconditioners in the sense of convergence rate finally numerical examples are given to illustrate our theoretical results two conjectures are proposed as well based on our numerical tests

new approximations and policy implications from a delayed dynamic model of a fast pandemic abstract we study an seiqr susceptible exposed infectious quarantined recovered model due to young et al 2019 for an infectious disease with time delays for latency and an asymptomatic phase for fast pandemics where nobody has prior immunity and everyone has immunity after recovery the seiqr model decouples into two nonlinear delay differential equations ddes with five parameters one parameter is set to unity by scaling time the simple subcase of perfect quarantining and zero self recovery before quarantine with two free parameters is examined first the method of multiple scales yields a hyperbolic tangent solution and a long wave short delay approximation yields a first order ordinary differential equation ode with imperfect quarantining and nonzero self recovery the long wave approximation is a second order ode these three approximations each capture the full outbreak from infinitesimal initiation to final saturation low dimensional dynamics in the ddes is demonstrated using a six state non delayed reduced order model obtained by galerkin projection numerical solutions from the reduced order model match the dde over a range of parameter choices and initial conditions finally stability analysis and numerics show how a well executed temporary phase of social distancing can reduce the total number of people affected the reduction can be by as much as half for a weak pandemic and is smaller but still substantial for stronger pandemics an explicit formula for the greatest possible reduction is given

distributed averaging with linear objective maps a distributed averaging system is a linear multi agent system in which agents communicate to reach an agreement or a consensus state defined as the average of the initial states of the agents consider a more generalized situation in which each agent is given a nonnegative weight and the agreement state is defined as the weighted average of the initial conditions we characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph specifically we introduce a linear function called the objective map that defines the desired final state as a function of the initial states of the agents we then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map in particular we characterize not only the set of objective maps that are feasible for a given digraph but also the consensus dynamics that implements the objective map in addition we present a decentralized algorithm to design the consensus dynamics

finiteness conditions co frobenius hopf algebras and quantum groups abstract some finiteness conditions for infinite dimensional coalgebras particularly right or left semiperfect coalgebras or co frobenius hopf algebras are studied as well examples of co frobenius hopf algebras are constructed via a hopf algebra structure on an ore extension of a group algebra and it is shown that bicrossproducts of co frobenius hopf algebras are themselves co frobenius

an approach to quasi hopf algebras via frobenius coordinates abstract we study quasi hopf algebras and their subobjects over certain commutative rings from the point of view of frobenius algebras we introduce a type of radford formula involving an anti automorphism and the nakayama automorphism of a frobenius algebra then view several results in quantum algebras from this vantage point in addition separability and strong separability of quasi hopf algebras are studied as frobenius algebras

the reproductive number for an hiv model with differential infectivity and staged progression we formulate an hiv epidemic model with differential infectivity and staged disease progression to account for variations in viral loads and in the rate of disease progression in infected individuals the stability of the infection free equilibrium determines the threshold conditions under which the modeled disease either dies out or persists in the population this stability expressed in terms of the epidemic reproductive number can be determined by the spectral radius of the next generation operator or from the eigenvalues of the jacobian matrix for the model system linearized about the infection free equilibrium we derive an explicit formula for the reproductive number employing both of these techniques by investigating the spectral radius of the next generation operator and by directly applying m matrix theory with recursive forward and backward inductions to characterize the eigenvalues of the jacobian matrix in terms of the reproductive number

galois extensions for co frobenius hopf algebras abstract forhan infinite dimensional co frobenius hopf algebra over a fieldk andaanh comodule algebra the smash producta h ratis linked to the ring of coinvariantsacohby a morita context we use the morita setting to show that for co frobeniush equivalent conditions fora acohto be galois parallel the case ofhfinite dimensional

on the structure of weak hopf algebras we study the group of group like elements of a weak hopf algebra and derive an analogue of radford s formula for the fourth power of the antipode s which implies that the antipode has a finite order modulo a trivial automorphism we find a sufficient condition in terms of tr s2 for a weak hopf algebra to be semisimple discuss relation between semisimplicity and cosemisimplicity and apply our results to show that a dynamical twisting deformation of a semisimple hopf algebra is cosemisimple

stability analysis of delayed sir epidemic models with a class of nonlinear incidence rates we analyze stability of equilibria for a delayed sir epidemic model in which population growth is subject to logistic growth in absence of disease with a nonlinear incidence rate satisfying suitable monotonicity conditions the model admits a unique endemic equilibrium if and only if the basic reproduction number r0 exceeds one while the trivial equilibrium and the disease free equilibrium always exist first we show that the disease free equilibrium is globally asymptotically stable if and only if r0 1 second we show that the model is permanent if and only if r0 1 moreover using a threshold parameter r0 characterized by the nonlinear incidence function we establish that the endemic equilibrium is locally asymptotically stable for 1 r0 r0 and it loses stability as the length of the delay increases past a critical value for 1 r0 r0 our result is an extension of the stability results in j j wang j z zhang z jin analysis of an sir model with bilinear incidence rate nonl anal rwa 11 2009 2390 2402

existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods given a nonsingular matrix a and a matrix t of the same order under certain very mild conditions there is a unique splitting a b c such that t b 1 c moreover all properties of the splitting are derived directly from the iteration matrix t these results do not hold when the matrix a is singular in this case given a matrix t and a splitting a b c such that t b 1 c there are infinitely many other splittings corresponding to the same matrices a and t and different splittings can have different properties for instance when t is nonnegative some of these splittings can be regular splittings while others can be only weak splittings analogous results hold in the symmetric positive semidefinite case given a singular matrix a not for all iteration matrices t there is a splitting corresponding to them necessary and sufficient conditions for the existence of such splittings are examined as an illustration of the theory developed the convergence of certain alternating iterations is analyzed different cases where the matrix is monotone singular and positive semi definite are studied

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

a characterization of convex problems in decentralized control ast we consider the problem of constructing optimal decentralized controllers we formulate this problem as one of minimizing the closed loop norm of a feedback system subject to constraints on the controller structure we define the notion of quadratic invariance of a constraint set with respect to a system and show that if the constraint set has this property then the constrained minimum norm problem may be solved via convex programming we also show that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback these results are developed in a very general framework and are shown to hold in both continuous and discrete time for both stable and unstable systems and for any norm this notion unifies many previous results identifying specific tractable decentralized control problems and delineates the largest known class of convex problems in decentralized control as an example we show that optimal stabilizing controllers may be efficiently computed in the case where distributed controllers can communicate faster than their dynamics propagate we also show that symmetric synthesis is included in this classification and provide a test for sparsity constraints to be quadratically invariant and thus amenable to convex synthesis

preconditioned parallel multisplitting usaor method for h matrices linear systems in this paper the preconditioned multisplitting usaor method is established for solving the system of linear equations the convergence and comparison results of the method are given when the coefficient matrices of the linear systems are h matrices the method for h matrices is proved to be more efficient than the multisplitting usaor method for m matrices finally a numerical example is given to illustrate the efficiency of our method

sparse stable systems abstract in the design of decentralized networked systems it is important to know whether a given network topology can sustain stable dynamics we consider a basic version of this problem here given a vector space of sparse real matrices does it contain a stable hurwitz matrix said differently is a feedback channel corresponding to a non zero entry necessary for stabilization or can it be done without we provide in this paper a set of necessary conditions and a set of sufficient conditions for the existence of stable matrices in a vector space of sparse matrices we further prove some properties of the set of sparse matrix spaces that contain hurwitz matrices the conditions we exhibit are most easily stated in the language of graph theory which we thus adopt in this paper

convergence of relaxed parallel multisplitting methods with different weighting schemes1supported by the state major key project for basic researches and the doctorial point foundation of china 1 multisplitting methods are parallel methods for the solution of a linear system ax b it has been observed that the convergence of multisplitting methods is often improved if some kind of relaxation and some different weighting other than the traditional postweighting are used in this paper by using a result on extrapolation method cf lemma 6 below and the comparison theorem of elsner l elsner numer math 56 1989 283 289 we study the convergence of two different variants of relaxed multisplitting methods with different weighting schemes the results obtained considerably improve and generalize the previous ones moreover some comparison theorems are also presented when a is a monotone matrix or an m matrix

convergence of relaxed parallel multisplitting methods abstract multisplitting methods are parallel methods for the solution of a linear system ax b it has been observed that the convergence of multisplitting methods is often improved if some kind of relaxation is used we investigate two different variants of relaxed multisplitting methods if a is an h matrix these methods converge if the relaxation parameter is from an interval 0 0 with 0 1

self organized segregation on the grid we consider an agent based model with exponentially distributed waiting times in which two types of agents interact locally over a graph and based on this interaction and on the value of a common intolerance threshold tau decide whether to change their types this is equivalent to a zero temperature ising model with glauber dynamics an asynchronous cellular automaton with extended moore neighborhoods or a schelling model of self organized segregation in an open system and has applications in the analysis of social and biological networks and spin glasses systems some rigorous results were recently obtained in the theoretical computer science literature and this work provides several extensions we enlarge the intolerance interval leading to the expected formation of large segregated regions of agents of a single type from the known size epsilon 0 to size approx 0 134 namely we show that for 0 433 tau 1 2 and by symmetry 1 2 tau 0 567 the expected size of the largest segregated region containing an arbitrary agent is exponential in the size of the neighborhood we further extend the interval leading to expected large segregated regions to size approx 0 312 considering almost segregated regions namely regions where the ratio of the number of agents of one type and the number of agents of the other type vanishes quickly as the size of the neighborhood grows in this case we show that for 0 344 tau le 0 433 and by symmetry for 0 567 le tau 0 656 the expected size of the largest almost segregated region containing an arbitrary agent is exponential in the size of the neighborhood this behavior is reminiscent of supercritical percolation where small clusters of empty sites can be observed within any sufficiently large region of the occupied percolation cluster the exponential bounds that we provide also imply that complete segregation where agents of a single type cover the whole grid does not occur with high probability for p 1 2 and the range of intolerance considered

sign properties of metzler matrices with applications abstract several results about sign properties of metzler matrices are obtained it is first established that checking the sign stability of a metzler sign matrix can be either characterized in terms of the hurwitz stability of the unit sign matrix in the corresponding qualitative class or in terms the negativity of the diagonal elements of the metzler sign matrix and the acyclicity of the associated directed graph similar results are obtained for the case of metzler block matrices and metzler mixed matrices the latter being a class of metzler matrices containing both sign and real type entries the problem of assessing the sign stability of the convex hull of a finite and summable family of metzler matrices is also solved and a necessary and sufficient condition for the existence of common lyapunov functions for all the matrices in the convex hull is obtained the concept of sign stability is then generalized to the concept of ker b sign stability a problem that arises in the analysis of certain jump markov processes a sufficient condition for the ker b sign stability of metzler sign matrices is obtained and formulated using inverses of sign matrices and the concept of l matrices several applications of the results are discussed in the last section

control of minimally persistent formations in the plane this paper studies the problem of controlling the shape of a formation of point agents in the plane a model is considered where the distance between certain agent pairs is maintained by one of the agents making up the pair if enough appropriately chosen distances are maintained with the number growing linearly with the number of agents then the shape of the formation will be maintained the detailed question examined in the paper is how one may construct decentralized nonlinear control laws to be operated at each agent that will restore the shape of the formation in the presence of small distortions from the nominal shape using the theory of rigid and persistent graphs the question is answered as it turns out a certain submatrix of a matrix known as the rigidity matrix can be proved to have nonzero leading principal minors which allows the determination of a stabilizing control law

stability and bifurcation analysis of a delayed predator prey model of prey dispersal in two patch environments abstract in this paper a class of delayed predator prey model of prey dispersal in two patch environments is considered by analyzing the associated characteristic transcendental equation its linear stability is investigated and hopf bifurcation is demonstrated some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulation for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

stochastic spatial models in the models we will consider space is represented by a grid of sites that can be in one of a finite number of states and that change at rates that depend on the states of a finite number of sites our main aim here is to explain an idea of durrett and levin 1994 the behavior of these models can be predicted from the properties of the mean field ode i e the equations for the densities of the various types that result from pretending that all sites are always independent we will illustrate this picture through a discussion of eight families of examples from statistical mechanics genetics population biology epidemiology and ecology some of our findings are only conjectures based on simulation but in a number of cases we are able to prove results for systems with fast stirring by exploiting connections between the spatial model and an associated reaction diffusion equation

two sided bounds for the inverse of an h matrix abstract the paper presents a simple characterization of a real h matrix and two sided componentwise bounds for its inverse in terms of the comparison matrix and the so called z and positive parts these bounds improving the well known ostrowsky result are also extended to a larger class of matrices

a fractional order infectivity sir model fractional order sir models have become increasingly popular in the literature in recent years however unlike the standard sir model they often lack a derivation from an underlying stochastic process here we derive a fractional order infectivity sir model from a stochastic process that incorporates a time since infection dependence on the infectivity of individuals the fractional derivative appears in the generalised master equations of a continuous time random walk through sir compartments with a power law function in the infectivity we show that this model can also be formulated as an infection age structured kermack mckendrick integro differential sir model under the appropriate limit the fractional infectivity model reduces to the standard ordinary differential equation sir model

endemic thresholds and stability in a class of age structured epidemics an age structured epidemic model is analyzed when the fertility mortality and removal rates depend on age for certain general forms of the force of infection terms endemic threshold criteria are derived and the stability of steady state solutions is determined the relation between age structured models of this type and catalytic curve models of epidemics is derived the possibility of identifying vertically transmitted diseases from the catalytic curve is demonstrated

analysis of a nonautonomous dynamical model of diseases through droplet infection and direct contact in this paper we have considered a nonautonomous dynamical model of diseases that spread by droplet infection and also through direct contact with a lower risk with varying total population size and distributed time delay to become infectious it is assumed that there is a time lag due to incubation period of pathogens i e the development of an infection from the time the pathogen enters the body until signs or symptoms first appear here we have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique we have obtained the explicit formula of the eventual lower bounds of infected persons we have introduced some new threshold values by lyapunov functional method we have also obtained some sufficient conditions for global asymptotic stability of this model computer simulations are carried out to explain the analytical findings the aim of the analysis of this model is to trace the parameters of interest for further study with a view to informing and assisting policy maker in targeting prevention and treatment resources for maximum effectiveness

reproduction numbers and the stability of equilibria of si models for heterogeneous populations a major project in deterministic epidemiological modeling of heterogeneous populations is to find conditions for the local and global stability of the equilibria and to work out the relations among these stability conditions the thresholds for epidemic take off and endemicity and the basic reproduction number s most of the work to date has been on models of homogeneous populations of constant size motivated by their analysis of models of the dynamics of human immunodeficiency virus acquired immunodeficiency syndrome hiv aids the authors carry out this project for si models of diseases that have multiple stages which can lead to death and which infect heterogeneous populations with intricate mixing patterns and varying sizes in such models it is even difficult to find the analytical expression for the stability threshold and the reproduction number the authors show how the number of disease transmitting contacts by infectives can be used as a lyapunov function to carry out a systematic stabili

the susceptible infected recovered model on a euclidean network we consider a susceptible infected recovered sir epidemic model on a euclidean network in one dimension in which nodes at a distance l are connected with probability p l l in addition to nearest neighbors the topology of the network changes as is varied and its effect on the sir model is studied r t the recovered fraction of population up to time t and the total duration of the epidemic are calculated for different values of the infection probabilities q and a threshold behavior is observed for all up to 2 0 above the threshold value q qc the saturation value rsat attains a finite value both rsat and show scaling behavior in a finite system of size n and qc is constant for 0 qc the results are compared to static percolation phenomena and also to mean field results for finite systems discussions on the properties of the euclidean network are made in the light of the present results

comparisons of weak regular splittings and multisplitting methods comparison results for weak regular splittings of monotone matrices are derived as an application we get upper and lower bounds for the convergence rate of iterative procedures based on multisplittings this yields a very simple proof of results of neumann plemmons on upper bounds and establishes lower bounds which has in special cases been conjectured by these authors

inverse problem for coefficient identification in sir epidemic models abstract this work deals with the development of a numerical method for solving an inverse problem for identifying coefficients from over posed data in an sir mathematical model of infectious diseases spread through a population the parameters are identified using a generalized least squares method which is similar to the technique called method of variational imbedding where the original inverse problem is replaced by a minimization problem a difference scheme and a numerical algorithm for solving the parameter identification problem are developed the correctness of the embedded problem is discussed numerical results of the parameters representing the solution to the inverse problem are presented

stabilization of bilinear sparse matrix control systems using periodic inputs abstract in this brief paper using results from the theory of averaging of bilinear systems we provide a graph theoretic characterization for the existence of periodic control inputs that stabilize a sparse matrix system to the origin in particular we introduce a class of extensions to the directed graph corresponding to a given sparse matrix system which when contains a stable sparse matrix system implies that the original system is stabilizable using periodic inputs when this condition holds we provide a systematic procedure for designing such controllers our technical approach combines ideas from the theory of bilinear control systems and averaging theory with graph theoretic results

allee effect with time varying migration on heterogeneous graphs abstract the behavior of animals during day and night can be demonstrated as time varying migration we study the effect of the temporal migration in a diffusively coupled allee model on heterogeneous graphs we present the metapopulation dynamic model for temporally heterogeneous graphs using the allee effect of mobile individuals we consider the small graphs with three and four nodes and the star graphs with n nodes a subpopulation patch is represented by a node on a graph a link represents a temporal migration path between subpopulations mobile individuals move temporally by random walk through a link between nodes individuals grow or die out according to the allee population dynamics within each subpopulation the population dynamics in the metapopulation model are presented by reaction diffusion equations with time dependent diffusion coefficients to evaluate the population size of each subpopulation node we obtain the solutions of the reaction diffusion equations numerically for the small graphs and star graphs the temporal migration path induces complex behavior for the allee dynamics the period the inverse of frequency of this temporal path has an important effect on the allee dynamics

radford s s 4 formula for co frobenius hopf algebras abstract this note extends radford s formula for the fourth power of the antipode of a finite dimensional hopf algebra to co frobenius hopf algebras and studies equivalent conditions to a hopf algebra being involutory for finite dimensional and co frobenius hopf algebras

a unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations abstract a unified framework for the construction of various synchronous and asynchronous parallel matrix multisplitting iterative methods suitable to the simd and mimd multiprocessor systems respectively is presented and its convergence theory is established under rather weak conditions these afford general method models and systematical convergence criterions for studying the parallel iterations in the sense of matrix multisplitting in addition how the known parallel matrix multisplitting iterative methods can be classified into this new framework and what novel ones can be generated by it are shown in detail

analysis of nonlinear integro differential equations arising in age dependent epidemic models basically there are two modes for directly transmitting an infectious disease within a single population vertical transmission and horizontal transmission vertical transmission is defined as the direct transfer of infection from a parent organism to its offsprings horizontal transmission is any transfer of infection except that which is vertically transmitted for example aids is both vertically and horizontally transmitted while malaria is horizontally transmitted vertically transmitted diseases have seldom been considered in mathematical models of epidemics examples of previous such models are found in anderson and may i cooke and busenberg 7 busenberg and cooke 3 busenberg cooke and pozio 4 fine lo and re gniere 171 likewise age dependent diseases has been presented by cooke and busenberg 7 and dietz 8 age dependence introduces a coupling of age structure and vertical transmission which can produce novel dynamic behavior in this paper a system of nonlinear integro differential equations which model an agedependent epidemic of a disease with vertical transmission is investigated this model treats the simple s i type of epidemic in this new setting existence and uniqueness are proved under suitable hypotheses and the asymptotic behavior of the system is determined a renewal theorem is used to study the behavior of the model equations in various pertinent parameter ranges a numerical method for integrating this system of equations is developed and is used to obtain approximations of its solutions for some special cases which illustrate the results obtained via analytical means moreover numerical integrations of the equations are used to study some phenomena that were not treated analytically

analysis of a bacteria immunity model with delay quorum sensing a bacteria immunity model with bacterial quorum sensing is formulated which describes the competition between bacteria and immune cells a distributed delay is introduced to characterize the time in which bacteria receive signal molecules and then combat with immune cells in this paper we focus on a subsystem of the bacteria immunity model analyze the stability of the equilibrium points discuss the existence and stability of periodic solutions bifurcated from the positive equilibrium point and finally investigate the stability of the nonhyperbolic equilibrium point by the center manifold theorem

the ergodicity and extinction of stochastically perturbed sir and seir epidemic models with saturated incidence abstract in this paper we include stochastic perturbations into sir and seir epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number r 0 the long time behavior of the two stochastic systems is studied mainly we utilize stochastic lyapunov functions to show under some conditions the solution has the ergodic property as r 0 1 while exponential stability as r 0 1 at last we make simulations to conform our analytical results

on the antipode of a quasitriangular hopf algebra let a r be a quasitriangular hopf algebra with antipode s in the category of vector spaces over a field k in this paper we show that s2 is inner which means s is bijective and when a is finite dimensional there is a grouplike element h e a such that s4 a h r for all a e a suppose that a is any hopf algebra with antipode s over the field k proposition 1 of section 1 gives a sufficient condition for 3 to be inner which we apply to quasitriangular hopf algebras in section 2 its statement and proof are based on calculations found in 2 pp 66671 generally s2 need not be inner suppose that a is finite dimensional if s2 were inner then all ideals of a would be invariant under s2 and hence all subcoalgebras of the dual hopf algebra a would be invariant under s where s s is the antipode of a there are examples 5 over algebraically closed lields in which the latter is not the case section 2 begins with a discussion of properties of quasit angular hopf algebras a r over the held k used in this paper write r cr c r ea a and set u cs r r the main result of section 2 is that u is invertible and s2 a uau for all a e a this result was established in z exercise 7 3 61 under the hypothesis that s is bijective if a is any finite dimensional hopf algebra with antipode s over the field k there are distinguished grouplike elements g e a and tl e a which relate left and right integrals and which together describe s4 in section 3 we consider s4 when a r is a unite dimensional quasit angular hopf algebra let h iiu where u c s r r l is defined as above and u s u i by relating h to g and 1 we are able to show that h is a grouplike element and that s4 a hah for all a e a when a is unimodular we prove that h g thus the product vu does not depend on r in the unimodular case we assume that the reader has some familiarity with the elementary aspects of the theory of hopf algebras a recommended reference is 6

an epidemic model for cholera with optimal control treatment we propose a mathematical model for cholera with treatment through quarantine the model is shown to be both epidemiologically and mathematically well posed in particular we prove that all solutions of the model are positive and bounded and that every solution with initial conditions in a certain meaningful set remains in that set for all time the existence of unique disease free and endemic equilibrium points is proved and the basic reproduction number is computed then we study the local asymptotic stability of these equilibrium points an optimal control problem is proposed and analyzed whose goal is to obtain a successful treatment through quarantine we provide the optimal quarantine strategy for the minimization of the number of infectious individuals and bacteria concentration as well as the costs associated with the quarantine finally a numerical simulation of the cholera outbreak in the department of artibonite haiti in 2010 is carried out illustrating the usefulness of the model and its analysis

finite dimensional cosemisimple hopf algebras in characteristic 0 are semisimple finite dimensional cosemisimple hopf algebras are a natural generalization of group algebras much of the representation theory of finite groups can be extended to such hopf algebras however there are still many unanswered basic questions for such hopf algebras one such question is a conjecture mentioned by kaplansky i the square of the antipode of a finite dimensional cosemisimple hopf algebra is the identity in this paper we prove that the fourth power of the antipode is the identity in a finite dimensional cosemisimple hopf algebra over a field of characteristic 0 in the course of proving this we investigate two elements of the hopf algebra which are roughly analogous to the sum of the group elements in a group algebra we show that kaplansky s conjecture is equivalent to these two elements being equal for a finite dimensional hopf algebra a with antipode s over a field let l p q pq for p q e a denote the left module action of a on itself in this paper we study two elements of a defined by the trace function the element i defined by p a tr l p s for all pe a and the element x defined by p x tr l p for all p e a we show that 2 is a left integral and use it to prove theorem 3 3 the main result of this paper a finite dimensional cosemisimple hopf algebra over a field of characteristic 0 is also semisimple hence its antipode has order 1 2 or 4 we extend the first corollary to 3 proposition 91 in theorems 4 3 and 4 4 by finding necessary and sufficient conditions for s to be a non zero left integral in which case x a and also study how x relates to the structure of a in particular when dim a 1 0 the right ideal xa may be thought of as a measure of the extent to which s i the elements ji and k are two examples of elements of a associated with an endomorphism of a in general for f end a we define a e a by p a tr l p cf for all pea thus i as2 and x a in section 2 267 0021 8693 88 33 00

global stability in a viral infection model with lytic and nonlytic immune responses this paper investigates the global stability of a viral infection model with lytic and nonlytic immune responses if the basic reproductive ratio of the virus is less than or equal to one by the lasalle s invariance principle and center manifold theorem the disease free steady state is globally asymptotically stable if the basic reproductive ratio of the virus is greater than one then the virus persists in the host and the disease steady state is locally asymptotically stable furthermore by the method of lyapunov function the global stability of the disease steady state is established at the same time if we neglect the efficacy of the lytic component using a geometrical approach we obtain a different type of conditions for the global stability of the disease steady state

traveling waves for a two group epidemic model with latent period in a patchy environment abstract in this paper we derive a two group sir epidemic model with latent period in a patchy environment by applying discrete fourier transform it is assumed that the infectious disease spreads between two groups and it has a fixed latent period when the basic reproduction number r 0 1 we prove that the system admits a nontrivial traveling wave solution for each admissible speed c namely c c where c is the minimal wave speed we also show that there is no positive traveling wave solution 1 2 1 2 satisfying i 0 i s i 0 and i s i when r 0 1 and c 0 or r 0 1 and c 0 c where i 1 2