the daily computed weighted averaging basic reproduction number r0 k ωn for mers cov in south korea abstract in this paper we propose the daily computed weighted averaging basic reproduction number r 0 k n for middle east respiratory syndrome coronavirus mers cov outbreak in south korea may to july 2015 we use an sir model with piecewise constant parameters contact rate and removed rate we use the explicit euler s method for the solution of the sir model and a nonlinear least square fitting procedure for finding the best parameters in r 0 k n the parameters n k and w denote days from a reference date the number of days in averaging and a weighting factor respectively we perform a series of numerical experiments and compare the results with the real world data in particular using the predicted reproduction number based on the previous two consecutive reproduction numbers we can predict the future behavior of the reproduction number

on pro p analogues of limit groups via extensions of centralizers we begin a study of a pro p analogue of limit groups via extensions of centralizers and call mathcal l this new class of pro p groups we show that the pro p groups of mathcal l have finite cohomological dimension type fp and non positive euler characteristic among the group theoretic properties it is proved that they are free by torsion free nilpotent and if non abelian do not have a finitely generated non trivial normal subgroup of infinite index furthermore it is shown that every 2 generated pro p group in the class mathcal l is either free pro p or abelian

the hanna neumann conjecture for demushkin groups abstract we confirm the hanna neumann conjecture for topologically finitely generated closed subgroups u and w of a nonsolvable demushkin group g namely we show that g u g w d u g w g 1 d u d w where d k max d k 1 0 and d k is the least cardinality of a topological generating set for the group k

global threshold dynamics of a stochastic differential equation sis model abstract in this paper we further investigate the global dynamics of a stochastic differential equation sis susceptible infected susceptible epidemic model recently proposed in gray et al 2011 8 we present a stochastic threshold theorem in term of a stochastic basic reproduction number r 0 s the disease dies out with probability one if r 0 s 1 and the disease is recurrent if r 0 s 1 we prove the existence and global asymptotic stability of a unique invariant density for the fokker planck equation associated with the sde sis model when r 0 s 1 in term of the profile of the invariant density we define a persistence basic reproduction number r 0 p and give a persistence threshold theorem the disease dies out with large probability if r 0 p 1 while persists with large probability if r 0 p 1 comparing the stochastic disease prevalence with the deterministic disease prevalence we discover that the stochastic prevalence is bigger than the deterministic prevalence if the deterministic basic reproduction number r 0 d 2 this shows that noise may increase severity of disease finally we study the asymptotic dynamics of the stochastic sis model as the noise vanishes and establish a sharp connection with the threshold dynamics of the deterministic sis model in term of a limit stochastic threshold theorem

extinction and persistence of a stochastic nonlinear sis epidemic model with jumps abstract in this paper brownian motion and l e vy jumps are introduced to a sis type epidemic model with nonlinear incidence rate the dynamical behavior of the considered model is investigated in order to reveal the extinction and permanence of the disease two threshold values r 0 r 0 are showed we find that if r 0 1 the disease may die out and when r 0 1 the disease may be persistent finally the numerical simulations are presented to illustrate our mathematical results

universal coalgebra a theory of systems in the semantics of programming finite data types such as finite lists have traditionally been modelled by initial algebras later final coalgebras were used in order to deal with infinite data types coalgebras which are the dual of algebras turned out to be suited moreover as models for certain types of automata and more generally for transition and dynamical systems an important property of initial algebras is that they satisfy the familiar principle of induction such a principle was missing for coalgebras until the work of aczel 1988 on a theory of non wellfounded sets in which he introduced a proof principle nowadays called coinduction it was formulated in terms of bisimulation a notion originally stemming from the world of concurrent programming languages milner 1980 park 1981 using the notion of coalgebra homomorphism the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras aczel and mendler 1989 thus the three basic notions of universal algebra algebra homomorphism of algebras and congruence turn out to correspond to coalgebra homomorphism of coalgebras and bisimulation respectively in this paper the latter are taken as the basic ingredients of a theory called universal coalgebra some standard results from universal algebra are reformulated using the afore mentioned correspondence and proved for a large class of coalgebras leading to a series of results on e g the lattices of subcoalgebras and bisimulations simple coalgebras and coinduction and a covariety theorem for coalgebras similar to birkhoff s variety theorem

on subdirect products of free pro p groups and demushkin groups of infinite depth abstract we study subdirect products of free and demushkin pro p groups of depth developing theory similar to the abstract case see bridson et al 2002 4 furthermore we classify when a subdirect product has homological type fp m for some m 2 a problem still open for abstract groups for m 3

stability of a stochastic sir system abstract we propose a stochastic sir model with or without distributed time delay and we study the stability of disease free equilibrium the numerical simulation of the stochastic sir model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found

stationary distribution and threshold dynamics of a stochastic sirs model with a general incidence abstract in this paper we consider a stochastic epidemic model with relapse cure and a non linear incidence rate function firstly we show the existence and uniqueness of a global positive solution then in terms of a stochastic threshold r s 0 we prove the extinction of the disease when r s 0 1 we also establish the persistence in mean of the epidemic in the case of r s 0 1 furthermore we prove the existence of a stationary distribution and its asymptotic stability finally we present numerical simulations for the stochastic model to support the theoretical results

on the finite presentation of subdirect products and the nature of residually free groups we establish it virtual surjection to pairs vsp as a general criterion for the finite presentability of subdirect products of groups if gamma 1 ldots gamma n are finitely presented and s we use the vsp criterion to characterize the finitely presented residually free groups we prove that the class of such groups is recursively enumerable we describe an algorithm that given a finite presentation of a residually free group constructs a canonical embedding into a direct product of finitely many limit groups we solve the multiple conjugacy problem and membership problem for finitely presentable subgroups of residually free groups we also prove that there is an algorithm that given a finite generating set for such a subgroup will construct a finite presentation new families of subdirect products of free groups are constructed including the first examples of finitely presented subgroups that are neither rm fp infty nor of stallings bieri type

dynamics of a stochastic siqr epidemic model with standard incidence abstract in this paper a stochastic siqr epidemic model with quarantine and standard incidence is investigated we first consider the existence and uniqueness of the global positive solution to the stochastic system further we obtain conclusions that the large noise can make the disease die out exponentially and the stationary distribution will exist under certain conditions

krull dimension of iwasawa algebras for example because of their connections with number theory and arithmetic geometry see the paper by coates schneider and sujatha 4 for more details when g is a uniform pro p group g is a concrete example of a complete local noetherian ring noncommutative in general with good homological properties it is known that g has finite global dimension and is an auslander regular ring thus g falls into the class of rings studied by brown hajarnavis and maceacharn in 1 there they consider various properties of noetherian rings r of finite global dimension including the krull gabriel rentschler dimension k r a module theoretic dimension which measures how far r is from being artinian they also posed the following question

basic observables for a calculus for global computing we develop the semantic theory of a foundational language for modelling applications over global computers whose interconnection structure can be explicitly manipulated together with process distribution process mobility and remote asynchronous communication through distributed data repositories the language has primitives for explicitly modelling inter node connections and for dynamically activating and deactivating them for the proposed language we define natural notions of extensional observations and study their closure under operational reductions and or language contexts to obtain barbed congruence and may testing equivalence we then focus on barbed congruence and provide an alternative characterisation in terms of a labelled bisimulation to test practical usability of the semantic theory we model a system of communicating mobile devices and use the introduced proof techniques to verify one of its key properties

structure and finiteness properties of subdirect products of groups we investigate the structure of subdirect products of groups particularly their finiteness properties we pay special attention to the subdirect products of free groups surface groups and hnn extensions we prove that a finitely presented subdirect product of free and surface groups virtually contains a term of the lower central series of the direct product or else fails to intersect one of the direct summands this leads to a characterization of the finitely presented subgroups of the direct product of 3 free or surface groups and to a solution to the conjugacy problem for arbitrary finitely presented subgroups of direct products of surface groups we obtain a formula for the first homology of a subdirect product of two free groups and use it to show there is no algorithm to determine the first homology of a finitely generated subgroup a useful structure theory for subgroups of finite direct products of groups has yet to be developed to begin to study such subgroups it is natural to assume one knows about the subgroups of the direct factors and to concentrate on subdirect products recall that g is termed a subdirect product of the groups a1 an if g a1 an is a subgroup that projects surjectively to each factor work by various authors has exposed the surprisingly rich structure to be found amongst the subdirect products of superficially tame groups for example in contrast to the fact that subdirect products of abelian or nilpotent groups are again in the specified class nonabelian free groups harbour a great diversity of subdirect products including some with unsolvable decision problems 21 this diversity has long been known but it is only as a result of more recent work by baumslag roseblade 5 and bridson howie miller short 9 that it has been understood as a phenomenon that is intimately tied to the failure of various homological finiteness conditions from this background we pick out the three strains of thought to be developed in this article the subtlety of subdirect products in general 1991 mathematics subject classification 20f05 20e07 20f67 20j05 20f10

a network conscious π calculus and its coalgebraic semantics traditional process calculi usually abstract away from network details modeling only communication over shared channels they however seem inadequate to describe new network architectures such as software defined networks where programs are allowed to manipulate the infrastructure in this paper we present the network conscious p calculus ncpi a proper extension of the p calculus with an explicit notion of network network links and nodes are represented as names in full analogy with ordinary p calculus names and observations are routing paths through which data is transported however restricted links do not appear in the observations which thus can possibly be as abstract as in the p calculus then we construct a presheaf based coalgebraic semantics for ncpi along the lines of turi plotkin s approach by indexing processes with the network resources they use we give a model for observational equivalence in this context and we prove that it admits an equivalent nominal automaton hd automaton suitable for verification finally we give a concurrent semantics for ncpi where observations are multisets of routing paths we show that bisimilarity for this semantics is a congruence and this property holds also for the concurrent version of the p calculus

subgroups of direct products of limit groups if ti tn are limit groups and s c t x x tn is of type fp q then s contains a subgroup of finite index that is itself a direct product of at most n limit groups this answers a question of sela

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

reactive systems semi saturated semantics and coalgebras on presheaves the semantics of process calculi has traditionally been specified by labelled transition systems ltss but with the development of name calculi it turned out that reaction rules i e unlabelled transition rules are often more natural this leads to the question of how behavioral equivalences bisimilarity trace equivalence etc defined for lts can be transferred to unlabelled transition systems recently in order to answer this question several proposals have been made with the aim of automatically deriving an lts from reaction rules in such a way that the resulting equivalences are congruences furthermore these equivalences should agree with the standard semantics whenever one exists in this paper we propose saturated semantics based on a weaker notion of observation and orthogonal to all the previous proposals and we demonstrate the appropriateness of our semantics by means of two examples logic programming and open petri nets we also show that saturated semantics can be efficiently characterized through the so called semi saturated games finally we provide coalgebraic models relying on presheaves

threshold behavior in a stochastic sir epidemic model with logistic birth abstract in this paper we consider a stochastic sir epidemic model with logistic birth by using the stochastic lyapunov function method we show that the stochastic basic reproduction number r 0 s can be used to determine the threshold dynamics of the stochastic system if r 0 s 1 we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model while if r 0 s 1 under some extra conditions we obtain sufficient conditions for extinction of the disease finally some examples and numerical simulations are provided to illustrate the theoretical results

structured coalgebras and minimal hd automata for the π calculus the coalgebraic framework developed for the classical process algebras and in particular its advantages concerning minimal realizations does not fully apply to the calculus due to the constraints on the freshly generated names that appear in the bisimulation in this paper we propose to model the transition system of the calculus as a coalgebra on a category of name permutation algebras and to define its abstract semantics as the final coalgebra of such a category we show that permutations are sufficient to represent in an explicit way fresh name generation thus allowing for the definition of minimal realizations we also link the coalgebraic semantics with a slightly improved version of history dependent hd automata a model developed for verification purposes where states have local names and transitions are decorated with names and name relations hd automata associated with agents with a bounded number of threads in their derivatives are finite and can be actually minimized we show that the bisimulation relation in the coalgebraic context corresponds to the minimal hd antomaton

dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth abstract in this paper we investigate the dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth firstly by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the solutions to the model then we obtain sufficient conditions for extinction of the disease in two cases that is the first case is that the susceptible population survival and infected and exposed populations extinction the second case is that all the populations extinction

stability of sirs system with random perturbations epidemiological models with bilinear incidence rate si usually have an asymptotically stable trivial equilibrium corresponding to the disease free state or an asymptotically stable non trivial equilibrium i e interior equilibrium corresponding to the endemic state in this paper we consider an epidemiological model which is an sirs model with or without distributed time delay influenced by random perturbations we present the stability conditions of the disease free equilibrium of the associated stochastic sirs system

stationary distribution and extinction of a stochastic sirs epidemic model with standard incidence abstract in this paper we consider a stochastic sirs epidemic model with standard incidence by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of ergodic stationary distribution of the model moreover we also establish sufficient conditions for extinction of the disease

threshold behavior of a stochastic sis model with levy jumps in this paper the dynamics of a stochastic sis model with levy jumps are investigated we first prove that this model has a unique global positive solution starting from the positive initial value then taking the accumulated jump size into account we find a threshold of the model denoted by r 0 which completely determines the extinction and prevalence of the disease if r 0 1 the disease dies out exponentially with probability one if r 0 1 the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease from the view of epidemiology the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics moreover we find that levy noise can suppress disease outbreak finally we introduce some numerical simulations to support the main results obtained