duals of compact lie groups realized in the cuntz algebras and their actions on c algebras abstract as a first step towards a new duality theorem for compact groups we consider a representation category t g of a compact lie group g u d c whose objects are the tensor powers of the defining representation and whose arrows are the intertwiners we associate to t g in a natural way a c algebra og which can be identified with the fixed points of the cuntz algebra od under the natural action of g og carries a canonical endomorphism g and t g can be reconstructed from og g if g su d then og is simple we give conditions for an endomorphism of a unital c algebra a to determine an action of t su d on a such actions correspond to monomorphisms of osu d into a with natural intertwining properties

categorical formulation of finite dimensional quantum algebras we describe how frobenius monoids give the correct categorical description of certain kinds of finite dimensional quantum algebras we develop the concept of an involution monoid and use it to construct a correspondence between finite dimensional c algebras and certain types of frobenius monoids in the category of hilbert spaces using this technology we recast the spectral theorems for commutative c algebras and for normal operators into an explicitly categorical language and we examine the case that the results of measurements do not form finite sets but rather objects in a finite boolean topos we describe the relevance of these results for topological quantum field theory

superselection in the presence of constraints superselection and constraints occur together in many gauge theories and here we begin a study of such systems our main focus will be to analyze compatibility questions between constraining and superselection and we will develop an example modelled on qed in which our framework is realized we proceed from a generalization of doplicher roberts superselection theory to the case of the nontrivial center and a set of dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form this involves an analysis of the restriction and factorization of superselection structures

extensions of automorphisms and gauge symmetries we characterize the automorphisms of ac algebra open image in new window which extend to automorphisms of the crossed product open image in new window by a compact group dual the case where the inclusion open image in new window is equipped with a group of automorphisms commuting with the dual action is also treated these results are applied to the analysis of broken gauge symmetries in quantum field theory to draw conclusions on the structure of the degenerate vacua on the field algebra

renormalizing curvature integrals on poincare einstein manifolds abstract after analyzing renormalization schemes on a poincare einstein manifold we study the renormalized integrals of scalar riemannian invariants the behavior of the renormalized volume is well known and we show any scalar riemannian invariant renormalizes similarly we consider characteristic forms and their behavior under a variation of the poincare einstein structure and obtain from the renormalized integral of the pfaffian an extension of the gauss bonnet theorem

quantum charges and spacetime topology the emergence of new superselection sectors a new form of superselection sectors of topological origin is developed by that it is meant a new investigation that includes several extensions of the traditional framework of doplicher haag and roberts in local quantum theories at first we generalize the notion of representations of nets of c algebras then we provide a brand new view on selection criteria by adopting one with a strong topological flavour we prove that it is coherent with the older point of view hence a clue to a genuine extension in this light we extend roberts cohomological analysis to the case where 1 cocycles bear non trivial unitary representations of the fundamental group of the spacetime equivalently of its cauchy surface in the case of global hyperbolicity a crucial tool is a notion of group von neumann algebras generated by the 1 cocycles evaluated on loops over fixed regions one proves that these group von neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type i all that amounts to a new invariant in a topological sense which can be defined as the dimension of the factor we prove that any 1 cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored this second part much resembles what in literature is known as geometric phases indeed by the very geometrical origin of the 1 cocycles that we discuss in the paper they are essential tools in the theory of net bundles and the topological part is related to their holonomy content at the end we prove the existence of net representations

amenable groups and generalized cuntz algebras withha hilbert space ohthe generalized cuntz algebra overhendowed with the canonical action ofu h we consider a natural family s0of product representations of the zero grade part o0h and the family s obtained from s0by inducing to ohvia the natural conditional expectationp oh o0h each element of s0 and hence of s is labelled by a sequence of unit vectors inh letgbe a non compact locally compact group its regular representation onh l2 g and ohendowed with the action ofg we prove thatgis amenable iff there are ireducible covariant representations in s

boundary regularity of conformally compact einstein metrics we show that c conformally compact riemannian einstein metrics have conformal compactifications that are smooth up to the boundary in dimension 3 and all even dimensions and polyhomogeneous in odd dimensions greater than 3

degree theory on oriented infinite dimensional varieties and the morse number of minimal surfaces spanning a curve in ℝn the algebraic number of disc minimal surfaces spanning a wire in 3 is defined and shown to be equal to one

bifurcation analysis of a predator prey system involving group defence a class of odes of generalized gause type modeling predator prey interaction is considered the prey are assumed to exhibit a phenomenon called group defence that is predation is decreased or even eliminated due to the ability of the prey to defend or disguise themselves as their numbers increase using the carrying capacity of the environment as the bifurcation parameter it is shown that the model undergoes a sequence of bifurcations that includes a homoclinic bifurcation as well as a hopf bifurcation conditions that hold even in the case of no group defence that ensure a subcritical hopf bifurcation and also the spontaneous appearance of a semistable periodic orbit that splits into a pair one stable and one unstable of periodic orbits are given ecological ramifications are considered unlike the classical model sufficient enrichment of the environment combined with group defence leads to extinction of the predator deterministically for almost all initial conditions providing strong support fo

nica toeplitz algebras associated with product systems over right lcm semigroups abstract we prove uniqueness of representations of nica toeplitz algebras associated to product systems of c correspondences over right lcm semigroups by applying our previous abstract uniqueness results developed for c precategories our results provide an interpretation of conditions identified in work of fowler and fowler raeburn and apply also to their crossed product twisted by a product system in the new context of right lcm semigroups as well as to a new doplicher roberts type c algebra associated to the nica toeplitz algebra as a derived construction we develop nica toeplitz crossed products by actions with completely positive maps this provides a unified framework for nica toeplitz semigroup crossed products by endomorphisms and by transfer operators we illustrate these two classes of examples with semigroup c algebras of right and left semidirect products

the c algebra of a vector bundle and fields of cuntz algebras abstract we study the cuntz pimsner algebra associated with the module of continuous sections of a hilbert bundle and prove that it is a continuous bundle of cuntz algebras furthermore we assign to bundles of cuntz algebras carrying a global circle action a class in the representable kk group of the zero grade bundle we explicitly compute such class for the cuntz pimsner algebra of a vector bundle

non constant positive steady states of a predator prey system with non monotonic functional response and diffusion this paper deals with non constant positive steady state solutions of a predator prey system with non monotonic functional response also called holling type iv interaction terms and diffusion under the homogeneous neumann boundary condition we first establish positive upper and lower bounds for such solutions and then study their non existence global existence and bifurcation

relative positions of limit cycles in a kolmogorov type system to estimate the relative position of limit cycles for a system is always useful in the qualitative analysis of the system if the system has only one limit cycle determining the position of the limit cycle is more important the author constructs an annular region containing all the limit cycles for a kolmogorov type system since the system contains the lotka volterra gausse kuang and freedman and huang models as special cases the results obtained are also valid for those models furthermore the approach to the location of limit cycles is very applicable because the region is easy to compute

on the renormalized volume of hyperbolic 3 manifolds the renormalized volume of hyperbolic manifolds is a quantity motivated by the ads cft correspondence of string theory and computed via a certain regularization procedure the main aim of the present paper is to elucidate its geometrical meaning we use another regularization procedure based on surfaces equidistant to a given convex surface n the renormalized volume computed via this procedure is equal to what we call the w volume of the convex region n given by the usual volume of n minus the quarter of the integral of the mean curvature over n the w volume satisfies some remarkable properties first this quantity is self dual in the sense explained in the paper second it verifies some simple variational formulas analogous to the classical geometrical schlafli identities these variational formulas are invariant under a certain transformation that replaces the data at n by those at infinity of m we use the variational formulas in terms of the data at infinity to give a simple geometrical proof of results of takhtajan et al on the kahler potential on various moduli spaces

on the location and period of limit cycles in gause type predator prey systems in this paper an attempt is made to estimate the location and period of the limit cycles of gause type predator prey systems in the case when there is a unique unstable positive equilibrium an annular region which contains all the limit cycles is determined and an upper bound for the period of the limit cycles is given both the annular region and the upper bound of the period are explicitly computable

on unitary representation theories of compact quantum groups categorical structure of unitary representation of compact quantum groups is studied with relation to a metrical structure encountered in the monoidal category of bimodules of finite jones index

hopf bifurcation for a predator prey model with age structure abstract this paper deals with a prey predator model with age structure where the prey population is infected with pathogenic bacteria we formulate the model as an abstract non densely defined cauchy problem and derive the conditions for the existence of all the feasible equilibrium points of the system the criteria for global stability of two boundary equilibria are obtained the criteria for local stability and instability of positive equilibrium is also discussed bifurcation analysis indicates that the predator prey system with age structure exhibits bifurcation which is the main result of this paper finally some numerical examples are provided to illustrate our obtained results

total curvature of complete surfaces in hyperbolic space we present a gauss bonnet type formula for complete surfaces in n dimensional hyperbolic space mathbb h n under some assumptions on their asymptotic behaviour as in recent results for euclidean submanifolds see dillen kuhnel 4 and dutertre 5 the formula involves an ideal defect i e a term involving the geometry of the set of points at infinity

endomorphisms of c algebras cross products and duality for compact groups on definit une nouvelle sorte de produit croise d une c algebre par des semigroupes d endomorphismes avec des proprietes reliees a la symetrie de permutation et a l existence de conjugues un groupe compact est alors defini intrinsequement par son action duale sur le produit croise cette construction donne une caracterisation des duaux de groupes compacts abstraits qui est hors d atteinte de la theorie de dualite de taunaka kein et est independante de cette theorie ceci resout le probleme de demontrer l existence d un groupe de jauge global compact en physique des particules etant seulement donnees les observables locales

tensor categories with fusion rules of self duality for finite abelian groups abstract semisimple tensor categories with fusion rules of self duality for finite abelian groups are classified as an application we prove that the tannaka duals of the dihedral and the quaternion groups of order 8 and the eight dimensional hopf algebra of kac and paljutkin are not isomorphic as abstract tensor categories whereas they have the same fusion rule

on the continuability of periodic orbits of parametrized three dimensional differential equations on considere un systeme autonome a n dimensions d equations differentielles ordinaires a 1 parametre x f x on suppose que f est definie et continue sur un sous ensemble ouvert o de r r n et que f x 0 sur o on etudie les orbites periodiques du systeme contenues dans o

compact lie groups associated with endomorphisms of c algebras on donne des conditions sur un endomorphisme d une c algebre 7b a avec unite et centre trivial en termes d operateurs d entrelacements pour des puissances de cet endomorphisme qui suffisent a determiner un groupe de lie compact g et une action d un g dual sur 7b a

superselection sectors and general covariance i this paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories we shall analyze sharply localizable charges and use net cohomology of j e roberts as a main tool we show that to any 4 dimensional globally hyperbolic spacetime a unique up to equivalence symmetric tensor mathrm c category with conjugates in case of finite statistics is attached to any embedding between different spacetimes the corresponding categories can be embedded contravariantly in such a way that all the charged quantum numbers of sectors are preserved this entails that to any spacetime is associated a unique gauge group up to isomorphisms and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups this form of covariance between sectors also brings to light the issue whether local and global sectors are the same we conjecture this holds that at least on simply connected spacetimes it is argued that the possible failure might be related to the presence of topological charges our analysis seems to describe theories which have a well defined short distance asymptotic behaviour

a local existence result for poincare einstein metrics abstract given a closed riemannian manifold m g m of dimension n 3 we prove the existence of a conformally compact einstein metric g defined on a collar neighborhood m 0 1 whose conformal infinity is g m

global analysis of a system of predator prey equations we study a class of ode s modelling the interaction of one predator and one prey the prey is assumed to be asocial in the sense that there is a threshold below which it will die even in the absence of predators knowledge of the separatrices of the flow and the local nature of the equilibrium points yields an analogue of the kolmogorov theorem a more detailed study of the direction of hopf bifurcation and uniqueness of limit cycles together with recent work on their continuation allows us to exhibit a very rich dynamics for both this system as well as for the more classical case of a prey without threshold we briefly discuss the implications of this work for ecology

bundles of c categories we introduce the notions of multiplier c category and continuous bundle of c categories as the categorical analogues of the corresponding c algebraic notions every symmetric tensor c category with conjugates is a continuous bundle of c categories with base space the spectrum of the c algebra associated with the identity object we classify tensor c categories with fibre the dual of a compact lie group in terms of suitable principal bundles this also provides a classification for certain c algebra bundles with fibres fixed point algebras of od

the c0 x algebra of a net and index theory abstract given a connected and locally compact hausdorff space x with a good base k we assign in a functorial way a c 0 x algebra to any precosheaf of c algebras a defined over k afterwards we consider the representation theory and the kasparov k homology of a and interpret them in terms respectively of the representation theory and the k homology of the associated c 0 x algebra when a is an observable net over the spacetime x in the sense of algebraic quantum field theory this yields a geometric description of the recently discovered representations affected by the topology of x

morita homotopy theory of c categories abstract in this article we establish the foundations of the morita homotopy theory of c categories concretely we construct a cofibrantly generated simplicial symmetric monoidal quillen model structure denoted by m mor on the category c 1 cat of small unital c categories the weak equivalences are the morita equivalences and the cofibrations are the functors which are injective on objects as an application we obtain an elegant description of brown green rieffel s picard group in the associated homotopy category ho m mor we then prove that ho m mor is semi additive by group completing the induced abelian monoid structure at each hom set we obtain an additive category ho m mor 1 and a composite functor c 1 cat ho m mor ho m mor 1 which is characterized by two simple properties inversion of morita equivalences and preservation of all finite products finally we prove that the classical grothendieck group functor becomes co represented in ho m mor 1 by the tensor unit object

non constant positive steady state of one resource and two consumers model with diffusion abstract in this paper a predator prey reaction diffusion system with one resource and two consumers is considered assume that one consumer species exhibits holling ii functional response while the other consumer species exhibits beddington deangelis functional response and they compete for the common resource first it is proved that the unique positive constant steady state is stable for the ode system and the reaction diffusion system second a prior estimates of positive steady state is given finally the non existence of non constant positive steady state the existence and bifurcation of non constant positive steady state are studied

presheaves of superselection structures in curved spacetimes we show that superselection structures on curved spacetimes that are expected to describe quantum charges affected by the underlying geometry are categories of sections of presheaves of symmetric tensor categories when an embedding functor is given the superselection structure is a tannaka type dual of a locally constant group bundle which hence becomes a natural candidate for the role of the gauge group indeed we show that any locally constant group bundle with suitable structure group acts on a net of c algebras fulfilling normal commutation relations on an arbitrary spacetime we also give examples of gerbes of c algebras defined by wightman fields and constructed using projective representations of the fundamental group of the spacetime which we propose as solutions for the problem that existence and uniqueness of the embedding functor are not guaranteed

uniqueness of limit cycles in a lienard type system abstract in this paper conditions that guarantee the uniqueness of limit cycles in the lienard type system dx dt h y f x dy dt g x have been discussed the conditions obtained here are different from those of zhang and others several examples such as q x 0 are given to illustrate that our results may easily be employed in practical applications

from path representations to global morphisms for a class of minimal models we construct global observable algebras and global dhr morphisms for the virasoro minimal models with central charge c 2 q q odd to this end we pass from the irreducible highest weight modules to path representations which involve fusion graphs of the c 2 q models the paths have an interpretation in terms of quasi particles which capture some structure of non conformal perturbations of the c 2 q models the path algebras associated to the path spaces serve as algebras of bounded observables global morphisms which implement the superselection sectors are constructed using quantum symmetries we argue that there is a canonical semi simple quantum symmetry algebra for each quasi rational cft in particular for the c 2 q models these symmetry algebras act naturally on the path spaces which allows to define a global field algebra and covariant multiplets therein

uniqueness of limit cycles of generalised lienard systems and predator prey systems another interesting example of how mathematical methods in physics can be applied to the area of ecology is presented by using a theorem which first appeared in a russian paper in 1958 for a generalised lienard system a uniqueness theorem of limit cycles of a predator prey system which includes lotka volterra gause and other systems as special cases is obtained several examples show that the theorem is very useful in dealing with the uniqueness problem of limit cycles for certain ecological systems

on the dirichlet problem for minimal graphs in hyperbolic space soit r n n 2 un domaine borne on etudie le probleme de dirichlet suivant f f i f j f ij 1 df 2 n f 0 dans f 0 dans f 0 sur on considere le comportement a la frontiere de la solution

dynamics of age structured predator prey population models a predator prey model is investigated in which the prey population is assumed to have age structure and is governed by the mckendrick von foerster partial differential equation and the predator population is described by the classical volterra lotka ordinary differential equation quite general hypotheses are assumed for the mortality function the fertility function and the functional responses of predation existence and stability of three biologically meaningful equilibria corresponding to extinction of both species persistence of one species prey and coexistence of two species are studied a particular example and some numerical results are given

galois theory for braided tensor categories and the modular closure abstract given a braided tensor category c with conjugate dual objects and irreducible unit together with a full symmetric subcategory s we define a crossed product c s this construction yields a tensor category with conjugates and an irreducible unit a category is a category enriched over vect c with positive operation a galois correspondence is established between intermediate categories sitting between c and c s and closed subgroups of the galois group gal c s c aut c c s of c the latter being isomorphic to the compact group associated with s by the duality theorem of doplicher and roberts denoting by d c the full subcategory of degenerate objects i e objects which have trivial monodromy with all objects of c the braiding of c extends to a braiding of c s iff s d under this condition c s has no non trivial degenerate objects iff s d if the original category c is rational i e has only finitely many isomorphism classes of irreducible objects then the same holds for the new one the category c c d is called the modular closure of c since in the rational case it is modular i e gives rise to a unitary representation of the modular group sl 2 z if all simple objects of s have dimension one the structure of the category c s can be clarified quite explicitly in terms of group cohomology

the relationships between equilibria and positive solutions of certain nonlinear elliptic systems abstract letm u v 0 n u v 0 define two distinct phase curves 1 2in the u v phase plane this paper presents results on the relationships among the positive equilibria the phase curves and the existence of positive solutions to the pde system u um u v 0 v vn u v 0 in r n under dirichlet boundary conditions where is a bounded domain andm nare monotone functions

snakes oriented families of periodic orbits their sources sinks and continuation abstract poincare observed that for a differential equation x x depending on a parameter each periodic orbit generally lies in a connected family of orbits in x space in order to investigate certain large connected sets denoted q of orbits containing a given orbit we introduce two indices an orbit index and a center index defined at certain stationary points we show that genetically there are two types of hopf bifurcation those we call sources 1 and sinks 1 generically if the set q is bounded in x space and if there is an upper bound for periods of the orbits in q then q must have as many source hopf bifurcations as sink hopf bifurcations and each source is connected to a sink by an oriented one parameter snake of orbits a snake is a maximal path of orbits that contains no orbits whose orbit index is 0 see fig 1 1

higher dimensional algebra ii 2 hilbert spaces abstract a 2 hilbert space is a category with structures and properties analogous to those of a hilbert space more precisely we define a 2 hilbert space to be an abelian category enriched over hilb with a structure conjugate linear on the hom sets satisfying fg h g f h f hg we also define monoidal braided monoidal and symmetric monoidal versions of 2 hilbert spaces which we call 2 h algbebras braided 2 h algebras and symmetric 2 h algbebras and we describe the relation between these and tangles in two three and four dimensions respectively we prove a generalized doplicher roberts theorem starting that every symmetric 2 h algebra is equivalent to the category rep g of continuous unitary finite dimensional representations of some compact supergroupoid g the equivalence is given by a categorified version of the gelfand transform we also construct a categorified version of the fourier transform when g is a compact abelian group finally we characterize rep g by its universal properties when g is a compact classical group for example rep u n is the free connected symmetric 2 h algebra on one even object of dimension n

diagram projection rules for recoupling diagrams in the racah wigner category this paper gives three important techniques for recoupling coefficients of an arbitrary number or irreducible representations factorization as a product of smaller degree recoupling coefficients diagram projection projecting a recoupling diagram to obtain constraints on recoupling coefficients and primitive expansion expressing a recoupling coefficient in terms of primitive recoupling coefficients the first technique reduces a recoupling coefficient to its essential and simplest form the second is many faceted allowing one to work at the recoupling level importantly recoupling diagrams can be used to construct a complete set of constraints on the recoupling coefficients the third allows large degree recoupling coefficients to be expressed in terms of primitive recoupling coefficients an example of this is the fact that the 9j symbol is defined by the 3j and 6j symbols

liberation of orthogonal lie groups abstract we show that under suitable assumptions we have a one to one correspondence between classical groups and free quantum groups in the compact orthogonal case we classify the groups under correspondence with the result that there are exactly 6 of them o n s n h n b n s n b n we investigate the representation theory aspects of the correspondence with the result that for o n s n h n b n this is compatible with the bercovici pata bijection finally we discuss some more general classification problems in the compact orthogonal case notably with the construction of a new quantum group

renormalized area and properly embedded minimal surfaces in hyperbolic 3 manifolds we study the renormalized area functional mathcal a in the ads cft correspondence specifically for properly embedded minimal surfaces in convex cocompact hyperbolic 3 manifolds and somewhat more broadly poincare einstein spaces our main results include an explicit formula for the renormalized area of such a minimal surface y as an integral of local geometric quantities as well as formulae for the first and second variations of mathcal a which are given by integrals of global quantities over the asymptotic boundary loop of y all of these formulae are also obtained for a broader class of nonminimal surfaces the proper setting for the study of this functional when the ambient space is hyperbolic requires an understanding of the moduli space of all properly embedded minimal surfaces with smoothly embedded asymptotic boundary we show that this moduli space is a smooth banach manifold and develop a mathbb z valued degree theory for the natural map taking a minimal surface to its boundary curve we characterize the nondegenerate critical points of mathcal a for minimal surfaces in mathbb h 3 and finally discuss the relationship of mathcal a to the willmore functional

the fusion rules of some free wreath product quantum groups and applications abstract in this article we find the fusion rules of the free wreath product quantum groups s n for any discrete group to do this we describe the spaces of intertwiners between basic corepresentations which allows us to identify the irreducible corepresentations we then apply the knowledge of the fusion rules to prove in most cases several operator algebraic properties of the associated reduced c algebras such as simplicity and uniqueness of the trace we also prove that the associated von neumann algebra is a full type ii 1 factor and that the dual of s n has the haagerup approximation property for all finite groups

superselection theory for subsystems an inclusion of observable nets satisfying duality induces an inclusion of canonical field nets any bose net intermediate between the observable net and the field net and satisfying duality is the fixed point net of the field net under a compact group this compact group is its canonical gauge group if the occurrence of sectors with infinite statistics can be ruled out for the observable net and its vacuum hilbert space is separable

canonical actions on o we show that the group of automorphisms of the cuntz algebra o canonically associated to a group g of unitaries on the generating hilbert space is ergodic if and only if g has no non zero finite dimensional stable subspace it is prime if g is strongly compact and more generally we give necessary and sufficient conditions if the defining representation of g is the direct sum of finite dimensional representations with determinant one the fixed point subalgebra og of o is a simple c algebra these results extend in part to o results previously known for on n

consequences of double allee effect on the number of limit cycles in a predator prey model the main goal of this work is to show a comparative analysis of simple continuous time predator prey models considering the allee effect affecting the prey population also known as depensation in fisheries sciences this phenomenon may be expressed by different mathematical forms yielding a distinct number of limit cycles surrounding a positive equilibrium point when two of these different formalizations are considered in the same system it is known that the volterra predation model using the most usual form to express the allee effect has a unique limit cycle in this work considering a more complex mathematical expression the existence of two limit cycles is proved by means of the lyapunov quantities we argue that the second equation explains the existence of two allee effects affecting the same population which could justify the difference observed between the models these results imply that the election of mathematical formulation can have consequences on the fit of the observed data thus leading to mistakes for ecologists we conclude that the oscillatory behaviors and overall dynamics depend strongly on the algebraic expression of the allee effect making difficult the proposition of general results nevertheless the techniques reviewed in this paper emerge as key tools to analyze the existence of limit cycles in the presence of multiple allee effects

limit cycles in a general kolmogorov model abstract the problem of limit cycles is interesting and significant both in theory and applications in mathematical ecology finding models that display a stable limit cycle an attracting stable self sustained oscillation is a primary work in this paper a general kolmogorov system which includes the gause type model math biosci 88 1988 67 the general predator prey model j phys a math gen 21 1988 l685 math biosci 96 1989 47 and many other models j biomath 15 3 2001 266 j biomath 16 2 2001 156 j math 21 22 2001 145 is studied the conditions for the existence and uniqueness of limit cycles in this model are proved some known results are easily derived as an illustration of our work

limit cycles in a general two stroke oscillation abstract conditions of the existence of limit cycles in a general two stroke oscillation system are obtained the general oscillation is a special kind of lienard type system with isoclines approaching both positive infinites or negative infinites as t the conditions for the uniqueness of the two stroke oscillation are also proved some examples are used to illustrate our results

a duality theorem for ergodic actions of compact quantum groups on c algebras the spectral functor of an ergodic action of a compact quantum group g on a unital c algebra is quasitensor in the sense that the tensor product of two spectral subspaces is isometrically contained in the spectral subspace of the tensor product representation and the inclusion maps satisfy natural properties we show that any quasitensor functor from rep g to the category of hilbert spaces is the spectral functor of an ergodic action of g on a unital c algebra

a michaelis menten type food chain model with strong allee effect on the prey dynamical behaviours of a tritrophic food chain model with strong allee effect in the prey are studied in this paper positivity and boundedness of the system are discussed some global results on extinction of the species are derived stability analysis of the equilibrium points is presented the effect of discrete time delay is studied where the delay may be regarded as the gestation period of the superpredator numerical simulations are carried out to validate our analytical findings implications of our analytical and numerical findings are discussed critically

topological aperiodicity for product systems over semigroups of ore type we prove a version of uniqueness theorem for cuntz pimsner algebras of discrete product systems over semigroups of ore type to this end we introduce doplicher roberts picture of cuntz pimsner algebras and the semigroup dual to a product system of regular c correspondences under a certain aperiodicity condition on the latter we obtain the uniqueness theorem and a simplicity criterion for the algebras in question these results generalize the corresponding ones for crossed products by discrete groups due to archbold and spielberg and for exel s crossed products due to exel and vershik they also give interesting conditions for topological higher rank graphs and p graphs and apply to the new cuntz c algebra qn arising from the ax b semigroup over n

coexistence region and global dynamics of a harvested predator prey system the study of populational dynamics with harvesting is related to the optimal man agement of renewable resources in this paper we consider a predator prey model in which two ecologically interacting species are harvested independently with constant rates the main purpose of the present work is to offer a complete mathematical analysis for the model and to describe some of the significant qualitative results that may be expected to arise from the interplay of biological forces our study shows that the maximum safe harvest may be far less than what would be assumed from a local analysis for the equilibria it is also proved that the harvested predator prey system may exhibit very complicated dynamics such as a spontaneous appearance of a homoclinic orbit and multiple limit cycles

a new duality theory for compact groups the tannaka krein duality theory characterizes the category g of finite dimensional continuous unitary representations of a compact group as a subcategory of the category of hilbert spaces we prove a more powerful result characterizing g as an abstract category every strict symmetric monoidalc category with conjugates which has subobjects and direct sums and for which thec algebra of endomorphisms of the monoidal unit reduces to the complex numbers is isomorphic to a category g for a compact groupg unique up to isomorphism

the limit cycles of a general kolmogorov system abstract in this paper the general kolmogorov system d x d t x f x y d y d t y g x y is studied by using the theory of generalized rotated vector fields and the poincare bendixson annular region theorem we prove the sufficient conditions for the existence and uniqueness of limit cycles in this system and our results extend almost all the related existing studies on the kolmogorov and predator prey systems

completely positive maps of the cuntz algebras we construct a covariant functor from the category whose objects are the complex infinite dimensional separable hilbert spaces and whose morphisms are the contractions into the category whose objects are the unitalc algebras and whose morphisms are the completely positive identity preserving maps thec algebras involved are isomorphic to the cuntz algebra o and our functor extends the canonical action of the group of unitaries on the generating hilbert space our result cannot apply to on n

continuous fields of c algebras arising from extensions of tensor c categories abstract the notion of extension of a given c category c by a c algebra a is introduced in the commutative case a c the objects of the extension category are interpreted as fiber bundles over of objects belonging to the initial category it is shown that the doplicher roberts algebra dr algebra in the following associated to an object in the extension of a strict tensor c category is a continuous field of dr algebras coming from the initial one in the case of the category of the hermitian vector bundles over the general result implies that the dr algebra of a vector bundle is a continuous field of cuntz algebras some applications to pimsner c algebras are given

bundles of c categories ii c dynamical systems and dixmier douady invariants we introduce a cohomological invariant arising from a class in nonabelian cohomology this invariant generalises the dixmier douady class and encodes the obstruction to a c algebra bundle being the fixed point algebra of a gauge action as an application the duality breaking for group bundles vs tensor c categories with nonsimple unit is discussed in the setting of nistor troitsky gauge equivariant k theory there is a map assigning a nonabelian gerbe to a tensor category and triviality of the gerbe is equivalent to the existence of a dual group bundle at the c algebraic level this corresponds to studying c algebra bundles with fibre a fixed point algebra of the cuntz algebra and in this case our invariant describes the obstruction to finding an embedding into the cuntz pimsner algebra of a vector bundle

investigating the interactions between allee effect and harvesting behaviour of a single species model an evolutionary dynamics approach abstract in this study we propose an ecological model which is based on the smith growth model and subject to multiplicative allee effect we then investigate the equilibrium bifurcation induced by the harvesting behaviour and the allee effect and pitch fork bifurcation and saddle node bifurcation may occur assuming that the carrying capacity and harvesting rate obey a gaussian distribution we then consider the evolutionary dynamics by using continuous strategy evolutionary game theory our study shows that strong allee effect and low harvesting rate can induce bistability it also suggests that evolution prevents extinction even if population has strong allee effect numerical analysis shows that the evolutionary model can admit up to nine equilibrium points including up to four evolutionary stable strategy equilibria

existence of more limit cycles in general predator prey models determining the number of limit cycles for a system is normally very difficult the author presents some sufficient conditions which guarantee that the general predator prey model of huang 1988 has at least three limit cycles around the equilibrium point the author s approach can be generalised to discuss the existence of 2n 1 limit cycles in the model

regularity at infinity for area minimizing hypersurfaces in hyperbolic space equipped with the hyperbolic metric y z dxz dy2 a standard compactification of ih involves adding the boundary r 0 w so that i i is simply the one point compactification of the euclidean closed half space r 0 suppose 0 7 any interior singularities of m must remain in a bounded region of hyperbolic space near points of f in the euclidean topology m w f may thus be described as the graph of a function this function is the solution of an interesting partial differential equation that becomes degenerate along the part of the boundary corresponding to f the second author has recently established l a boundary higher regularity result for this equation which implies in particular that m w f is r if f is cgk for k 2 3 finally in case f bounds a star

conjugation in representation categories of multiplicative unitaries and their actions on c algebras abstract a conjugation functor f on a full subcategory of r v the representation category of a multiplicative unitaryv is defined ifvhas a conjugate it is also regular and the domain of f is all r v examples of selfconjugate multiplicative unitaries are discussed a coaction of the hopfc algebra associated withvon the cuntz algebra o dis canonically defined by a unitary objectwof r v acting on ad dimensional hilbert space as in the group action case ifd andwbelongs to the domain of f ergodic coactions are often characterized by the absence of finite dimensional subrepresentations ofw furthermore model actions of compact quantum group duals onc algebras are defined

evolutionary dynamics of single species model with allee effect abstract by considering a continuous strategy evolutionary game theory egt a single species population subject to additive allee effect is investigated we assume that the carrying capacity and predator evasion ability following a gaussian distribution this assumption shows that evolution prevents extinction even if population has strong allee effect the ratio of competition and anti predation phenotypes has an important effect on determining global dynamics of the egt model the numerical simulations present the model can have nine equilibria and the model has multiple evolutionarily stable strategy equilibria ess

complete minimal varieties in hyperbolic space it is a basic problem in the subject of minimal varieties to determine the class of complete minimal and area minimizing varieties m k in a given riemannian manifold n besides being of their own intrinsic interest the cases r of euclidean space and mn sn of the sphere are fundamental in understanding the local structure of minimal varieties due to the existence of tangent cones to general minimal varieties there has been much study of the complete areaminimizing varieties in these cases in particular relating to the bernstein conjecture and minimizing cones e g l2 f1 nevertheless many deep problems remain unsolved this paper is centered around the question of existence of complete areaminimizing varieties in hyperbolic space h here by way of contrast to the situation in ir n or s we find a comparatively complete solution to the problem of existence in fact the main result of this paper exhibits a wealth of complete area minimizing varieties in h in all dimensions and codimensions more precisely we have