parasite population delay model of malaria type with stochastic perturbation and environmental criterion for limitation of disease we present a stochastic delay model of an infectious disease malaria transmitted by a vectors mosquitoes after an incubation time a criterion for limitation of disease is found

global dynamics for a new high dimensional sir model with distributed delay abstract in this paper a new high dimensional sir epidemic model with double epidemic hypothesis and delays is proposed which is a high dimensional system of impulsive functional differential equations with time delays the linear chain trick technique is employed to prove the upper boundedness of solutions of the impulsive delay differential equations and scaling method techniques for inequalities and classification method are used to study the permanence of the high dimensional system we also prove that the infection free periodic solution of the system is globally attractive when r 1 1 and the system is permanent under r 2 1 moreover numerical simulation for impulsive and delayed system is presented to illustrate our main conclusions which shows that time delays and pulse vaccination have significant effects on the dynamics behaviors of the model the feature of the present paper is that the double epidemic hypothesis have different forms of delays to more realistically describe the spread of epidemic though which makes the high dimensional system more complex

dynamic behavior for a nonautonomous sirs epidemic model with distributed delays a nonautonomous sirs epidemic model with distributed delay is investigated two new threshold values r and r are derived the model is permanent as r 1 and r 1 implies the extinction of the disease using the liapunov functional method global behavior of the model is studied

some groups generated by transvection subgroups in the 1960 s j e mclaughlin lo 111 determined all irreducible finite dimensional linear groups generated by transvection subgroups a trans section of a k vector space v is linear map t cp x v t given by vt cp x 2 vqj y for all t e v where xe vand pe v are non zero and xcp 0 v is the dual space of v a k transvection subgroup t cp x consists of the identity and all r cp x where q and x range over the l dimensional subspaces spanned by cp and x respectively it is isomorphic to the additive group of k mclaughlin showed that the only such groups are the special linear and symplectic groups and in the case when k is f the field with two elements the orthogonal and symmetric groups it is our purpose to give a new proof of a result which includes mclaughlin s we discard the assumptions of finiteness of the dimension of v over k and also to some extent the irreducibility of the group while still obtaining a result which is recognizably like mclaughlin s our result for irreducible groups is the following unexplained terminol ogy will be defined after the statement of the theorem the more com plicated result under a weaker hypothesis is stated near the end of the introduction

multibunch solutions of the differential difference equation for traffic flow the newell whitham type of car following model with a hyperbolic tangent as the optimal velocity function has a finite number of exact steady traveling wave solutions that can be expressed in terms of elliptic theta functions each such solution describes a density wave with a definite number of car bunches on a circuit in our numerical simulations we observe a transition process from uniform flow to congested flow described by a one bunch analytic solution which appears to be an attractor of the system in this process the system exhibits a series of transitions through which it comes to assume configurations closely approximating multibunch solutions with successively fewer bunches

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

an equivariant analogue of glauberman s zj theorem we will prove an analogue of glauberman s zj theorem 4 and 6 theorem 8 2 1 p 279 that can be used to study finite groups that admit a coprime group of automorphisms this analogue is unusual in that no hypothesis of p stability is required used in conjunction with the bender method it may make it possible to prove very general results about finite groups that admit a coprime group of automorphisms the reader is referred to 7 and 8 for a fuller discussion of the bender method glauberman s zj theorem and p stability before stating the main result of this paper we introduce some notation if r and g are groups then we say that r acts coprimely on g if r acts as a group of automorphisms on g if r and g have coprime orders and if at least one of r or g is soluble suppose that r acts coprimely on g and that p is a prime define

global stability of a delayed sir epidemic model with density dependent birth and death rates an sir epidemic model with density dependent birth and death rates is formulated in our model it is assumed that the total number of the population is governed by logistic equation the transmission of infection is assumed to be of the standard form namely proportional to i t h n t h where n t is the total variable population size i t is the size of the infective population and a time delay h is a fixed time during which the infectious agents develop in the vector we consider transmission dynamics for the model stability of an endemic equilibrium is investigated the stability result is stated in terms of a threshold parameter that is a basic reproduction number r 0

practical criterion for delay estimation using random perturbations many systems contain an internal time delay which significantly influences their dynamical properties methods to estimate this delay from times series in the presence of dynamical noise are not systematically studied addressing this problem we demonstrate that it is sufficient to analyze the system s response to short correlated external disturbances or internal noise following this idea it is shown for linear and nonlinear systems as well as for periodic dynamics that the delay can be estimated by analyzing the correlation function this method covers the case of strong noise and multiple delays

baumann components of finite groups of characteristic p general theory abstract in this paper we introduce a new conjugacy class bau p g of p subgroups of finite groups g of characteristic p we then prove some factorization and decomposition theorems related to this conjugacy class in particular these results show that the only obstructions for b bau p g being normal in g are the baumann components of g a class of subnormal subgroups e with e o p e quasisimple or sl 2 p for p 3

quasiprimitive linear groups with quadratic elements abstract a semisimple complex linear transformation with exactly two distinct eigenvalues is called a quadratic element in this paper the finite irreducible linear groups generated by quadratic elements of order 3 for which the multiplicities of the eigenvalues are distinct are determined this is used to obtain bounds on the degree of an irreducible primitive linear group containing such elements there are no irreducible primitive linear groups containing quadratic elements of order 4 with eigenvalues 1 i with distinct multiplicities where i is a primitive fourth root of 1

quadratic pairs without commuting root subgroups abstract suppose g is a subgroup of gl k m a finite dimensional vectorspace over the field k with char k 2 generated by quadratic elements satisfying c g for all c k then one can define root subgroups of g intrinsically i e just in terms of the quadratic elements in this paper we determine such groups g generated by three root subgroups which do not contain a pair of commuting root subgroups this is a further step of the determination of groups g when g m is a quadratic pair

threshold and stability results for an age structured seir epidemic model abstract in this paper an age structured seir epidemic model is considered the existence and uniqueness of a positive solution for this model is proved threshold results for the existence of endemic states are established under certain conditions the local stability for the steady states is also examined

complete global analysis of a two scale network sirs epidemic dynamic model with distributed delay and random perturbations the model validation results are established the basic reproduction numbers at three human vector contact levels are computed the stochastic stability of equilibria is proven interplay between stability and human mobility are exhibited in real life scenarios a stochastic sirs epidemic dynamic model with distributed time delay for vector borne diseases in two scale network structured populations is presented the distributed delay accounts for the varying incubation period of the disease furthermore the disease dynamics is influenced by random environmental perturbations in the disease transmission process as well as the two scale human mobility process the basic reproduction numbers at three human vector contact levels in the two scale population are computed and the results for the stochastic asymptotic stability of the equilibria are presented moreover the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented numerical simulation results are presented

a collocation method for the gurtin maccamy equation with finite life span a collocation method along the characteristics for a stiff problem arising from population dynamics is proposed and analyzed it is a fourth order implicit runge kutta method of two stage to the integration of the ode along the characteristics whose collocation points are zeros of the linearly transformed legendre monic polynomial nonnegativity of the numerical solutions is shown the stability of the method is discussed it is proven that the scheme is convergent at a fourth order rate in the maximum norm several numerical examples are presented

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

linear transvection groups and embedded polar spaces most classical groups arising from anti hermitian forms or pseudo quadratic forms contain so called isotropic transvections the isotropic transvection subgroups of these classical groups i e the subgroups generated by all isotropic transvections with a fixed axis form a class of abelian subgroups which is a class of abstract transvection groups in the sense of timmesfeld 24 in this paper we give a common characterization of all these classical groups with isotropic transvections as linear groups generated by a class of abstract transvection groups such that the elements of a are transvections

cross characteristic representations of odd characteristic symplectic groups and unitary groups in ls landazuri and seitz gave lower bounds for irreducible representations of chevalley groups in non defining characteristic when referring to irreducible representations for quasisimple groups g we will assume that the modules are nontrivial on f g see also sz gpps ho for some improvements on these bounds these results have proved to be useful in many applications in particular they have been used to classify the maximal subgroups of classical groups containing an element of prime order acting irreducibly on a subspace of large dimension cf gpps and to show that low dimensional modules in characteristic p for groups with no normal p subgroup are semisimple see gu it is also important to identify the modules which have dimension close to the smallest possible dimension and to prove that there are no irreducible modules with dimension in a certain range above it this was done in gpps and gt for sln q further improvements were obtained by brundan and kleshchev brk hiss and malle hm have obtained results similar to gt for unitary groups in this paper we consider the groups g sp2n q with n 2 and q p odd and g sun q with n 3 landazuri and seitz ls had already shown that the minimal dimension d of any irreducible module in the nondefining characteristic has dimension exactly q 1 2 for the symplectic case and q 1 q 1 for the unitary case it was proved in gpps that aside from some small exceptions every irreducible kg module in a nondefining characteristic has dimension d d 1 or at least dimension 2d in characteristic 0 tiep and zalesskii tz1 using deligne lusztig

some characterizations of the weil representations of the symplectic and unitary groups abstract let g be a finite symplectic or unitary group we characterize the weil representations of g via their restriction to a standard subgroup then we complete the determination of complex representations of g with specific minimal polynomials of certain elements by showing that they coincide with the weil representations

algebraic structures related to universal covers of special rank one groups abstract in this note we give a presentation of special rank one groups with abelian unipotent subgroups abbreviated aus depending on some algebraic structure k and then show that each special rank one group with aus is a center factor group of a so presented group as shown in t de medts r weiss moufang sets and jordan division algebras math ann 335 2006 415 433 one example of such an algebraic structure is unital quadratic jordan division algebras in subsequent work my student sebastian weis studied these structures called r structures systematically and showed among other things that the problem of classifying such special rank one groups with aus is equivalent to the classification of these r structures up to isotopy

global stability of a delayed sirs epidemic model with saturation incidence and temporary immunity in this paper a delayed sirs epidemic model with saturation incidence and temporary immunity is investigated the immunity gained by experiencing a disease is temporary whenever infected the diseased individuals will return to the susceptible class after a fixed period by analyzing the corresponding characteristic equations the local stability of an endemic equilibrium and a disease free equilibrium is discussed by comparison arguments it is proved that if the basic reproduction number is less than unity the disease free equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity by means of an iteration technique sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium numerical simulations are carried out to illustrate the main theoretical results

complete reducibility of quadratic modules for finite lie type groups let g be a finite lie type group in char p 3 different from sl2 3 and v a zpg module on which the root groups of g act quadratically i e v ar ar 0 for all roots of the root system of g then we show that v is completely reducible

the geometry of k transvection groups abstract let k be a commutative field and g a group then a conjugacy class of abelian subgroups of g is called a class of k transvection subgroups in g if and only if it generates g and any two elements of the class either commute or are full unipotent subgroups of the group they generate and which is isomorphic to p sl 2 k in this paper we study the geometry of k transvection groups given a class of k transvection groups we consider a partial linear space whose points are the elements of and whose lines correspond to the groups generated by two noncommuting elements from we derive several properties of this partial linear space these properties are used to give a characterization of the geometries of k transvection groups and provide a classification of groups generated by k transvection subgroups

classification of 2f modules i abstract we classify the 2f modules for nearly simple groups excluding the case of modules for groups of lie type in their defining characteristic we also show that for all such modules there exists an offender with cubic action these modules play a crucial role in the current revisions of the classification of the finite simple groups

groups of lie type generated by long root elements in f4 k abstract let k be a field and g a quasi simple subgroup of the chevalley group f4 k we assume that g is generated by a class of abstract root subgroups such that there are a c with a c and any a is contained in a long root subgroup of f4 k we determine the possibilities for g and describe the embedding of g in f4 k

permanence of an sir epidemic model with density dependent birth rate and distributed time delay abstract in this paper we investigate the permanence of an sir epidemic model with a density dependent birth rate and a distributed time delay we first consider the attractivity of the disease free equilibrium and then show that for any time delay the delayed sir epidemic model is permanent if and only if an endemic equilibrium exists numerical examples are given to illustrate the theoretical analysis the results obtained are also compared with those from the analog system with a discrete time delay

global stability of an sir epidemic model with constant infectious period in this paper we derive and study an sir epidemic model with constant infectious period which is incorporated as a time delay both trivial and endemic equilibrium are found and their stability is investigated using lyapunov functional approach sufficient conditions for global stability of endemic equilibrium is obtained

dynamics of a discretized sir epidemic model with pulse vaccination and time delay we derive a discretized sir epidemic model with pulse vaccination and time delay from the original continuous model the sufficient conditions for global attractivity of an infection free periodic solution and permanence of our model are obtained improving discretization our results are corresponding to those in the original continuous model

hybrid stabilization and synchronization of nonlinear systems with unbounded delays the stabilization of nonlinear systems with bounded and unbounded time delays via hybrid control is studied we investigate and identify switching rules for which stabilization can be verified a priori when this approach is inadequate stabilizing state dependent switching rules are constructed this method is based on partitioning the state space into switching regions unwanted physical behavior such as chattering and zeno behavior is avoided sufficient conditions are established using razumikhin like theorems the theoretical results provide insight into how hybrid control strategies can be constructed to synchronize a class of nonlinear systems with unbounded delay the findings are illustrated through numerical simulations

splitting methods for the numerical approximation of some models of age structured population dynamics and epidemiology splitting methods for nonlinear models arising from population dynamics and epidemiology are described and analyzed a backward finite differencing along the characteristic is used for the approximation it is shown that the schemes are convergent at first order rate in the maximum norm the stability of the methods is discussed several numerical examples are presented

an epidemic model of a vector borne disease with direct transmission and time delay abstract this paper considers an epidemic model of a vector borne disease which has direct mode of transmission in addition to the vector mediated transmission the incidence term is assumed to be of the bilinear mass action form we include both a baseline ode version of the model and a differential delay model with a discrete time delay the ode model shows that the dynamics is completely determined by the basic reproduction number r 0 if r 0 1 the disease free equilibrium is globally stable and the disease dies out if r 0 1 a unique endemic equilibrium exists and is locally asymptotically stable in the interior of the feasible region the delay in the differential delay model accounts for the incubation time the vectors need to become infectious we study the effect of that delay on the stability of the equilibria we show that the introduction of a time delay in the host to vector transmission term can destabilize the system and periodic solutions can arise through hopf bifurcation

backward bifurcation of an epidemic model with saturated treatment function an epidemic model with saturated incidence rate and saturated treatment function is studied here the treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals is getting larger and the medical condition is limited the global dynamics of the model indicate that the basic reproduction number being the unity is a strict threshold for disease eradication when such effect is weak however it is shown that a backward bifurcation will take place when this delayed effect for treatment is strong therefore driving the basic reproduction number below the unity is not enough to eradicate the disease and a critical value at the turning point is deduced as a new threshold some sufficient conditions for the disease free equilibrium and the endemic equilibrium being globally asymptotically stable are also obtained mathematical results in this paper suggest that giving the patients timely treatment improving the cure efficiency and decreasing the infective coefficient are all valid methods for the control of disease

lie algebras generated by extremal elements abstract we study lie algebras generated by extremal elements i e elements spanning inner ideals over a field of characteristic distinct from 2 there is an associative bilinear form on such a lie algebra we study its connections with the killing form any lie algebra generated by a finite number of extremal elements is finite dimensional the minimal numbers of extremal generators for the lie algebras of type a n n 1 b n n 3 c n n 2 d n n 4 e n n 6 7 8 f 4 and g 2 are shown to be n 1 n 1 2 n n 5 5 and 4 in the respective cases these results are related to group theoretic ones for the corresponding chevalley groups

nonlinear analysis of a differential difference equation with next nearest neighbour interaction for traffic flow we analyse the newell whitham type car following model described by a differential difference equation with a generalized optimal velocity function which depends not only on the headway of each car but also on the headway of the immediately preceding one linear stability analysis shows that the model is stabilized for larger delay time by taking into account the headway of the immediately preceding car from the nonlinear analysis the propagating kink solution for traffic jams is obtained the fundamental diagram and the relation between the headway and the delay time are examined by numerical simulation we find that the result from the nonlinear analysis is in good agreement with that obtained from the numerical simulation

global analysis of an infection age model with a class of nonlinear incidence rates abstract sir infection age models with a very general class of nonlinear incidence rates f s j are investigated we give a necessary and sufficient condition for global asymptotic stability of the free equilibrium related to the basic reproduction number furthermore additional conditions allow us to prove an exponential stability of this disease free equilibrium finally by using a lyapunov functional we show the global asymptotic stability of the endemic equilibrium whenever it exists

endemic threshold results for an age structured sis epidemic model with periodic parameters abstract the main contribution of this paper is to obtain a threshold value for the existence and uniqueness of a nontrivial endemic periodic solution of an age structured sis epidemic model with periodic parameters under the assumption of the weak ergodicity of a non autonomous lotka mckendrick system we formulate a normalized system for an infected population as an initial boundary value problem of a partial differential equation the existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on a banach space of locally integrable periodic l 1 valued functions we prove that the spectral radius of the frechet derivative of the integral operator at zero plays the role of a threshold for the existence and uniqueness of a nontrivial fixed point of the operator corresponding to a nontrivial periodic solution of the original differential equation in a weak sense if the malthusian parameter of the host population is equal to zero our threshold value is equal to the well known epidemiological threshold value the basic reproduction number r 0 however if it is not the case then two threshold values are different from each other and we have to pay attention on their actual biological implications

analysis of an improved epidemic model with stochastic disease transmission abstract this paper proposes an improved logistic epidemic model and carries out the complete parameters analysis of asymptotic behavior of infectious diseases some interesting details such as the threshold value of outbreak of epidemics and critical states of disease spread are derived the mean and variance of proportion of infected population are given explicitly the results show that our model is more reasonable and applicable to describe the real situation especially p 1 2 might be considered as the alarm for relate institutions to make effective policies to prevent and control some epidemics