the global structure of a spatial model of infectious disease in this paper we study an si model of infectious diseases that takes into account spatial inhomogeneities resulting in a system of reaction convection diffusion equations on a bounded domain the convection process is included to account for social interaction as modelled by the location of a focal point or den where the population will tend to aggregate we show that a vertical bifurcation of steady state solutions occurs in this model when birth rate is taken as the bifurcation parameter from which emanates a global secondary branch which then bifurcates at infinity subsequently we use singular perturbation techniques to give a description of the limiting spatial structure along this branch in large and small parameter limits finally the results are illustrated numerically on some biologically relevant cases

error bounds for 2 regular mappings with lipschitzian derivatives and their applications we obtain local estimates of the distance to a set defined by equality constraints under assumptions which are weaker than those previously used in the literature specifically we assume that the constraints mapping has a lipschitzian derivative and satisfies a certain 2 regularity condition at the point under consideration this setting directly subsumes the classical regular case and the twice differentiable 2 regular case for which error bounds are known but it is significantly richer than either of these two cases when applied to a certain equation based reformulation of the nonlinear complementarity problem our results yield an error bound under an assumption more general than b regularity the latter appears to be the weakest assumption under which a local error bound for complementarity problems was previously available we also discuss an application of our results to the convergence rate analysis of the exterior penalty method for solving irregular problems

existence and bifurcation of solutions for an elliptic degenerate problem abstract we investigate the existence multiplicity and bifurcation of solutions of a model nonlinear degenerate elliptic differential equation x 2 u u u p 1 u in 0 1 u 0 u 1 0 this model is related to a simplified version of the nonlinear wheeler dewitt equation as it appears in quantum cosmological models we prove the existence of multiple positive solutions more precisely we show that there exists an infinite number of connected branches of solutions which bifurcate from the bottom of the essential spectrum of the corresponding linear operator nous etudions ici l existence multiplicite et proprietes de bifurcation des solutions d un probleme elliptique degenere x 2 u u u p 1 u in 0 1 u 0 u 1 0 ce probleme modele est proche d une version simplifiee et non lineaire de l equation de wheeler dewitt utilisee dans des modeles de cosmologie quantique nous prouvons l existence d une infinite de branches de solutions qui bifurquent a partir de l infimum du spectre continu de l operateur lineaire correspondant

weak c cleft extensions weak entwining structures and weak hopf algebras abstract we formulate the concept of weak cleft extension for a weak entwining structure in a braided monoidal category c with equalizers and coequalizers we prove that if a is a weak c cleft extension then there is an isomorphism of algebras between a and a subobject of the tensor product of a c and c where a c is a subalgebra of a also we prove the corresponding dual results and linking the information of this two parts we obtain a general property for a pair morphisms f c a and g a c of algebras and coalgebras satisfying certain conditions finally as particular instances we get the results of fernandez and rodriguez the theorems of radford majid and bespalov in the case of hopf algebras with projection and the ones obtained by alonso and gonzalez for weak hopf algebras living in a symmetric category with split idempotents for example the weak theorem of blattner cohen and montgomery for weak hopf algebras with coalgebra splitting is one of them

fourier integral operators on lie groupoids abstract as announced in 36 we develop a calculus of fourier integral g operators on any lie groupoid g for that purpose we study lagrangian conic submanifolds of the symplectic groupoid t g this includes their product transposition and inversion we also study the relationship between these lagrangian submanifolds and the equivariant families of lagrangian submanifolds of t g x t g x parametrized by the units x g 0 of g this allows us to select a subclass of lagrangian distributions on any lie groupoid g that deserve the name of fourier integral g operators g fios by construction the class of g fios contains the class of equivariant families of ordinary fourier integral operators on the manifolds g x x g 0 we then develop for g fios the first stages of the calculus in the spirit of hormander s work finally we illustrate this calculus in the case of manifolds with boundary

multiparameter local bifurcation on considere l equation l 0 u l 1 n u f 1 n u 0 sur un espace de banach reel u on etudie des solutions non triviales bifurcant a l origine

topological gauge theories and group cohomology we show that three dimensional chern simons gauge theories with a compact gauge groupg not necessarily connected or simply connected can be classified by the integer cohomology grouph4 bg z in a similar way possible wess zumino interactions of such a groupg are classified byh3 g z the relation between three dimensional chern simons gauge theory and two dimensional sigma models involves a certain natural map fromh4 bg z toh3 g z we generalize this correspondence to topological spin theories which are defined on three manifolds with spin structure and are related to what might be calledz2 graded chiral algebras or chiral superalgebras in two dimensions finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group establishing links with two dimensional holomorphic orbifold models

bifurcation in lp r for a semilinear equation keywords weak solution second order differential equation bifurcations reference ana article 1986 001doi 10 1016 0022 0396 86 90077 x record created on 2008 12 10 modified on 2016 08 08

unbounded pseudodifferential calculus on lie groupoids abstract we develop an abstract theory of unbounded longitudinal pseudodifferential calculus on smooth groupoids also called lie groupoids with compact basis we analyze these operators as unbounded operators acting on hilbert modules over c g and we show in particular that elliptic operators are regular we construct a scale of sobolev modules which are the abstract analogues of the ordinary sobolev spaces and analyze their properties furthermore we show that complex powers of positive elliptic pseudodifferential operators are still pseudodifferential operators in a generalized sense

new bifurcation theorems via the second order optimality conditions we derive new sufficient conditions for bifurcation relying on subtle second order necessary optimality conditions for abnormal equality constrained optimization problems we relate these conditions to the known ones and demonstrate the cases when the new conditions are easier to verify

classification and unfoldings of degenerate hopf bifurcations abstract this paper initiates the classification up to symmetry covariant contact equivalence of perturbations of local hopf bifurcation problems which do not satisfy the classical non degeneracy conditions the only remaining hypothesis is that i should be simple eigenvalues of the linearized right hand side at criticality then the lyapunov schmidt method allows a reduction to a scalar equation g x 0 where g x g x a definition is given of the codimension of g and a complete classification is obtained for all problems with codimension 3 together with the corresponding universal unfoldings the perturbed bifurcation diagrams are given for the cases with codimension 2 and for one case with codimension 3 for this last case one of the unfolding parameters is a modal parameter such that the topological codimension equals in fact 2 formulas are given for the calculation of the taylor coefficients needed for the application of the results and finally the results are applied to two simple problems a model of glycolytic oscillations and the fitzhugh nerve equations

a geometric framework for the numerical study of singular points while bifurcation theory has developed rapidly in recent years there appears to be a need for a tighter framework for the numerical analysis of bifurcation problems this paper presents such a mathematical framework for the numerical study of the bifurcation phenomena associated with a parameter dependent equation f z lambda 0 the presentation draws from differential geometry and singularity theory and provides a basis for various numerical methods used to detect and compute certain types of bifurcation points

drinfeld center of enriched monoidal categories abstract we define the drinfeld center of a monoidal category enriched over a braided monoidal category and show that every modular tensor category can be realized in a canonical way as the drinfeld center of a self enriched monoidal category we also give a generalization of this result for important applications in physics

tangent vectors to a zero set at abnormal points we are concerned with sharp characterization of the contingent cone to the set defined by a finite number of equality constraints in the absence of classical regularity constrained qualification

on a computational method for the second fundamental tensor and its application to bifurcation problems an algorithm is presented for the computation of the second fundamental tensorv of a riemannian submanifoldm ofr n fromv the riemann curvature tensor ofm is easily obtained moreover v has a close relation to the second derivative of certain functionals onm which in turn provides a powerful new tool for the computational determination of multiple bifurcation directions frequently in applications thed dimensional manifoldm is defined implicitly as the zero set of a submersionf onr n in this case the principal cost of the algorithm for computingv p at a given pointp m involves only the decomposition of the jacobiandf p off atp and the projection ofd d 1 neighboring points ontom by means of a local iterative process usingdf p several numerical examples are given which show the efficiency and dependability of the method

on the frobenius schur indicators for quasi hopf algebras abstract mason and ng have given a generalization to semisimple quasi hopf algebras of linchenko and montgomery s generalization to semisimple hopf algebras of the classical frobenius schur theorem for group representations we give a simplified proof in particular a somewhat conceptual derivation of the appropriate form of the frobenius schur indicator that indicates if and in which of two possible fashions a given simple module is self dual

global bifurcation of periodic solutions in nonlinear evolution problems with periodic forcing abstract this paper discusses the global bifurcation of 2 periodic solutions of u t p x u f t u with a homogeneous dirichlet boundary condition where p x is linear elliptic and the nonlinearity f is 2 periodic in t the main differences from existing theories devoted to this type of problem can roughly be summarized as follows i the bifurcation analysis makes no use of evolution operators or related concepts poincare maps floquet multipliers etc ii the bifurcation nonbifurcation points are characterized through an associated stationary problem iii the functional setting allows for nonlinearities f exhibiting time discontinuities among other things the results include various partial generalizations of the bifurcation from the principal eigenvalue theorem which unlike the classical version do not require linear parameter dependence

global secondary bifurcation in a non linear boundary value problem we consider a steady state non linear boundary value problem which arises in modelling the formation of vascular networks in response to tumour growth global bifurcation from both trivial and non trivial solution branches is considered with emphasis on the latter by investigating such secondary bifurcation it is shown that positive bounded solutions exist for all physically relevant values of a critical parameter a certain class of these solutions is discussed with respect to the application to tumour growth

integrability of lie brackets in this paper we present the solution to a longstanding problem of differential geometry lie s third theorem for lie algebroids we show that the integrability problem is controlled by two computable obstructions as applications we derive explain and improve the known integrability results we establish integrability by local lie groupoids we clarify the smoothness of the poisson sigma model for poisson manifolds and we describe other geometrical applications

radford s biproducts and yetter drinfeld modules for monoidal hom hopf algebras let h be a monoidal hom bialgebra and b be a left h hom module algebra and also a left h hom comodule coalgebra then in this paper we first introduce the notion of a hom smash coproduct which is a monoidal hom coalgebra second we find sufficient and necessary conditions for the hom smash product algebra structure and the hom smash coproduct coalgebra structure on b h to afford b h a monoidal hom bialgebra structure generalizing the well known radford s biproduct where the conditions are equivalent to that b is a bialgebra in the category of hom yetter drinfeld modules hydhh finally we illustrate the category of hom yetter drinfeld modules hydhh and prove that the category hydhh is a braided monoidal category

holonomy transformations for singular foliations abstract in order to understand the linearization problem around a leaf of a singular foliation we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations to this aim we introduce the notion of holonomy transformation unlike the regular case holonomy transformations cannot be attached to classes of paths in the foliation but rather to elements of the holonomy groupoid of the singular foliation

on right equivalence a c m a p g e r m g n xo p yo is an m approximation to f w r t y if g is an eb m approximat ion to f w r t 2 iii let m i or m i 0s for some ideal i c cn we will then write iapp rox ima t ion instead of m approx ima t ion no ment ion of coord ina te choice need be made since as follows at once f rom 4 1 14 this not ion is independent of co ordinate choice for general m or m the not ion of m a p p r o x i m a t i o n or m a p p r o x i m a tion is not independent of the choice of coordinates made however the results of this article will be concerned with m or m where these not ions are independent of co ordinate choice

milnor moore categories and monadic decomposition abstract in this paper monoidal hom lie algebras lie color algebras lie superalgebras and other type of generalized lie algebras are recovered by means of an iterated construction known as monadic decomposition of functors which is based on eilenberg moore categories to this aim we introduce the notion of milnor moore category as a monoidal category for which a milnor moore type theorem holds we also show how to lift the property of being a milnor moore category whenever a suitable monoidal functor is given and we apply this technique to provide examples

on the asymptotic properties of solutions to a differential equation in a case of bifurcation without eigenvalues the semi linear equation u u h x u 0 is studied on all of d dimensional euclidean space in the bifurcation problem a non trivial solution is sought for small which tends to zero with the asymptotic dependence of the solution on is examined for fixed 1 the existence of non degenerate non trivial solutions is proved for generic measurable h x sufficiently near to a constant provided d 1 or 3 the two problems are seen to be interdependent the bifurcation problem at 0 is particularly interesting as the linearised equation is of non fredholm type

second order necessary conditions for nonlinear optimization problems with abstract constraints the degenerate case in this paper we derive second order necessary conditions for optimality for an optimization problem with abstract constraints in banach spaces results for the nondegenerate case derived earlier h gfrerer siam j control optim 45 2006 pp 972 997 are extended to the degenerate case for the mathematical programming problem where the constraints are given by equality and finitely many inequality constraints our approach applies to the degenerate case when the equality constraints are not regular our results appear to be new even in this special case our second order necessary conditions are contained in the gap between the standard necessary and sufficient conditions where the only difference is the change from a nonstrict to a strict inequality our results are formulated in such a way to be applicable also to vector optimization problems

bifurcation at multiple eigenvalues and stability of bifurcating solutions if k is a bounded linear operator from the real banach space u into the real banach space v and u r v has the value zero at 0 0 the existence and linear stability of the equilibrium solutions of the dynamical system k dudt u which are close to the origin in u r are studied it is assumed that u 0 0 u v is a freholm operator of index zero the only restriction on the dimension of the null space of u 0 0 and the order of vanishing at 0 0 of restricted to the null space of d 0 0 u r v is that they both be finite positive integers the main result gives conditions under which the equation which determines the equilibrium solutions in a neighborhood of the origin also determines the stability of these equilibrium solutions

idempotents and one sided units lattice invariants and a semigroup of functors on the category of monoids abstract for a monoid m we denote by g m the group of units e m the submonoid generated by the idempotents and g l m and g r m the submonoids consisting of all left or right units writing m for the monoidal category of monoids g e g l and g r are all monoidal functors m m there are other natural functors associated to submonoids generated by combinations of idempotents and one or two sided units the above functors generate a monoid with composition as its operation we show that this monoid has size 15 and describe its algebraic structure we also show how to associate certain lattice invariants to a monoid and classify the lattices that arise in this fashion a number of examples are discussed throughout some of which are essential for the proofs of the main theoretical results

on the computation of manifolds of foldpoints for parameter dependent problems for parameter dependent nonlinear equations in r n a new augmentation method for computing submanifolds of foldpoints is presented the underlying theory is based on a characterization developed earlier of foldpoints on solution manifolds of parameterized equations the method allows for a locally convergent iterative computation of foldpoints of a certain class for a continuation along paths of such foldpoints and for a computation of simplicial approximations of higher dimensional submanifolds of foldpoints of the same type

symmetries and the u condition in hom yetter drinfeld categories let h s be a monoidal hom hopf algebra and hydhh the hom yetter drinfeld category over h then in this paper we first find sufficient and necessary conditions for hydhh to be symmetric and pseudosymmetric respectively second we study the u condition in hydhh and show that the hom yetter drinfeld module h adjoint resp h m coadjoint satisfies the u condition if and only if s2 id finally we prove that hydhh over a triangular resp cotriangular hom hopf algebra contains a rich symmetric subcategory

regular representation of groupoid c algebras and applications to inverse semigroups the analogue of the left regular representation of a locally compact groupoid is constructed in the hausdoras well as in the non hausdorcase a necessary and su cient condition for a locally compact groupoid with a cocycle to be morita equi valent to a group action is obtained as an application the c algebras of a class of inverse semigroups is shown to be morita equivalent to crossed products of groups by abelian c

numerical liapunov schmidt spectral methods for k determined problems we describe several generalized liapunov schmidt methods in the bordered systems formulation for operator equations and collect information concerning classification of bifurcation functions we present a short outline of spectral methods in this bifurcation context and show the convergence of the discrete defining equations and nondegeneracy conditions for spectral finite element and difference methods to the counterparts of the original operator for k determined problems this result is then applied to a model for turing patterns in a two component mixture

on the brauer picard group of a finite symmetric tensor category let cn denote the representation category of finite supergroup kn z 2z we compute the brauer picard group brpic cn of cn this is done by identifying brpic cn with the group of braided tensor autoequivalences of the drinfeld center of cn and studying the action of the latter group on the categorical lagrangian grassmannian of cn we show that this action corresponds to the action of a projective symplectic group on a classical lagrangian grassmannian

determinacy of sufficiently differentiable maps variants of the algebraic conditions of mather are shown to be sufficient for the k determinacy of cu maps with respect to j flat contact or right cr equivalence relations where u k k the algebraic conditions are seen to be necessary

double layer potentials on three dimensional wedges and pseudodifferential operators on lie groupoids abstract let w be a three dimensional wedge and k be the double layer potential operator associated to w and the laplacian we show that 1 2 k are isomorphisms between suitable weighted sobolev spaces which implies a solvability result in weighted sobolev spaces for the dirichlet problem on w furthermore we show that the double layer potential operator k is an element in c g m 2 c where g is the action transformation groupoid m g with g 1 0 a b a r b r which is a lie group and m is a kind of compactification of g this result can be used to prove the fredholmness of 1 2 k where is a domain with edge singularities and k the double layer potential operator associated to the laplacian and

reflection fusion categories abstract we introduce the notion of a reflection fusion category which is a type of a g crossed category generated by objects of frobenius perron dimension 1 and p where p is an odd prime we show that such categories correspond to orthogonal reflection groups over f p this allows us to use the known classification of irreducible reflection groups over finite fields to classify irreducible reflection fusion categories

loop spaces and coherence for monoidal and braided monoidal bicategories abstract we prove a coherence theorem for braided monoidal bicategories and relate it to the coherence theorem for monoidal bicategories we show how coherence for these structures can be interpreted topologically using up to homotopy operad actions and the algebraic classification of surface braids

the holonomy groupoid of a singular foliation we construct the holonomy groupoid of any singular foliation in the regular case this groupoid coincides with the usual holonomy groupoid of winkelnkemper h e winkelnkemper the graph of a foliation ann glob anal geom 1 3 1983 51 75 the same holds in the singular cases of j pradines how to define the differentiable graph of a singular foliation c top geom diff cat xxvi 4 1985 339 381 b bigonnet j pradines graphe d un feuilletage singulier c r acad sci paris 300 13 1985 439 442 c debord local integration of lie algebroids banach center publ 54 2001 21 33 c debord holonomy groupoids of singular foliations j diff geom 58 2001 467 500 which from our point of view can be thought of as being almost regular in the general case the holonomy groupoid can be quite an ill behaved geometric object on the other hand it often has a nice longitudinal smooth structure nonetheless we use this groupoid to generalize to the singular case connes construction of the c algebra of the foliation we also outline the construction of a longitudinal pseudo differential calculus the analytic index of a longitudinally elliptic operator takes place in the k theory of our c algebra in our construction the key notion is that of a bi submersion which plays the role of a local lie groupoid defining the foliation our groupoid is the quotient of germs of these bi submersions with respect to an appropriate equivalence relation

weak hopf algebras and weak yang baxter operators abstract in this paper we introduce the notions of weak yang baxter operator and weak braided hopf algebra we prove that it is possible to obtain examples of these notions working with yetter drinfeld modules associated to a weak hopf algebra h with invertible antipode finally we complete the study of the structure of weak hopf algebras with a projection obtaining a categorical equivalence between the category of weak hopf algebra projections associated to h and the category of hopf algebras in the non strict braided monoidal category of left left yetter drinfeld modules over h

on finite determinacy of formal vector fields it is widely understood that finite determinacy plays an important role for studies of various singularities for instance deformation theory of singularities of map germs depends deeply on the algebraic characterization of finitely determined map germs in 1 we defined finite determinacy for singularities of formal vector fields in the same way as for map germs under some conditions we gave characterizations of finitely determined formal vector fields first we state briefly the results of 1 let k be the field of real numbers r or complex numbers c a formal vector field x is a derivation of o k x 1 x n i e x is a k linear mapping of into itself which satisfies x f g x f g f x g where f ge we say that two formal vector fields x and y are equivalent if there is a k algebra automorphism q of z such that q y 0 1 yq x a formal vector field x is called k determined if any formal vector field y with the same k jet as x is equivalent to x a formal vector field x is called finitely determined if there is a positive integer k such that x is k determined a k jet z is called wild if for any formal vector field x such that the k jet of x equals z x is not finitely determined now we state several conditions on the eigenvalues for a 1 jet x

on the central charge of a factorizable hopf algebra abstract for a semisimple factorizable hopf algebra over a field of characteristic zero we show that the value that an integral takes on the inverse drinfel d element differs from the value that it takes on the drinfel d element itself by at most a fourth root of unity this can be reformulated by saying that the central charge of the hopf algebra is an integer if the dimension of the hopf algebra is odd we show that these two values differ by at most a sign which can be reformulated by saying that the central charge is even we give a precise condition on the dimension that determines whether the plus sign or the minus sign occurs to formulate our results we use the language of modular data

a generalization of the implicit function theorem for mappings from rn 1 into rn and its applications abstract some regularity results about the local structure of the zero set of a mapping of n 1 real variables with values in r n are presented they all provide improved and generalized versions of the morse lemma for plane curves as well as generalizations of the implicit function theorem we describe their applications to one parameter nonlinear problems including an analysis of bifurcation phenomena at simple or multiple eigenvalues

hopf bifurcation at multiple eigenvalues with zero eigenvalue on donne des resultats locaux relies a la bifurcation de hopf pour des equations paraboliques la partie lineaire autour du point d equilibre peut avoir des valeurs propres nulles

differential graded categories and deligne conjecture abstract we prove a version of the deligne conjecture for n fold monoidal abelian categories a over a field k of characteristic 0 assuming some compatibility and non degeneracy conditions for a the output of our construction is a weak leinster n 1 algebra over k a relaxed version of the concept of leinster n algebra in a lg k the difference between the leinster original definition and our relaxed one is apparent when n 1 for n 1 both concepts coincide we believe that there exists a functor from weak leinster n 1 algebras over k to c e n 1 k algebras well defined when k q and preserving weak equivalences for the case n 1 such a functor is constructed in 31 by elementary simplicial methods providing together with this paper a complete solution for 1 monoidal abelian categories our approach to deligne conjecture is divided into two parts the first part completed in the present paper provides a construction of a weak leinster n 1 algebra over k out of an n fold monoidal k linear abelian category provided the compatibility and non degeneracy condition are fulfilled the second part still open for n 1 is a passage from weak leinster n 1 algebras to c e n 1 k algebras as an application we prove in theorem 8 1 that the gerstenhaber schack complex of a hopf algebra over a field k of characteristic 0 admits a structure of a weak leinster 2 1 algebra over k extending the yoneda structure it relies on our earlier construction 30 of a 2 fold monoidal structure on the abelian category of tetramodules over a bialgebra

adiabatic groupoid crossed product by r and pseudodifferential calculus abstract let g be a lie groupoid recall that the associated adiabatic groupoid g ad is the groupoid obtained by the deformation to the normal cone construction corresponding to the inclusion g 0 g in the present paper we consider the crossed product g ga of the natural action of r on the adiabatic groupoid g ad associated with any lie groupoid g we construct an explicit morita equivalence between the exact sequence of order 0 pseudodifferential operators on g and a restriction of the natural exact sequence associated with g ga as an important intermediate step we express a pseudodifferential operator on g as an integral associated with a smoothing operator on the adiabatic groupoid g ad of g

application of elliptic regularity to bifurcation in stationary nonlinear schrodinger equations keywords bifurcation elliptic regularity fredholm operator morse index reference ana article 2003 003doi 10 1016 s0362 546x 02 00138 4view record in web of science record created on 2008 12 10 modified on 2016 08 08

global bifurcation analysis and uniqueness for a semilinear problem we study the bifurcation diagram and uniqueness of solutions of by using a rescaling technique and the implicit function theorem we establish the global bifurcation diagram uniqueness is proved by a separation argument to complete the bifurcation picture of the problem our study suggests that the bifurcation diagrams have different behaviour at 0 depending on whether g 0 or g l norm but quite similar behaviour in l p or w 2 1

group cohomology and gauge equivalence of some twisted quantum doubles the purpose of the present paper is to investigate relationships that exist between certain quasi hopf algebras namely twisted quantum doubles of a finite abelian group and their module categories this is closely related to aspects of group cohomology concerning the relationship of the bar complex to some other complexes defined and studied by eilenberg and maclane mac52 em50a and em50b although our results are purely homological and algebraic in nature the motivation for studying these questions derives mainly from connections with conformal field theory cft and vertex operator algebras dw90 dpr92 ms89 dl93 we will thus review background motivation although it is hardly necessary for an understanding of our main results and then give a more detailed overview of the paper it is not necessary for the reader to appreciate what a vertex operator algebra voa is cf bor86 flm88 fhl93 but only to understand this voas have a representation theory hence a linear module category and it is important to understand the nature of this category it is expected that the module category v mod for a voa v has the structure of a braided monoidal category js93 roughly this means that there is a notion of tensor product of v modules and that the tensor product of three modules is associative by an isomorphism that depends on the particular modules moreover tensor product of modules is commutative again via an isomorphism that depends on the particular modules particularly nice voas called rational have the additional property that v mod is a semisimple category so that v has only a finite number of isomorphism classes of simple modules and every object in v mod is a direct sum of simple objects the simplest voas of all from this perspective are called holomorphic they are rational and have but one simple module namely the adjoint module v itself thus if v is a holomorphic voa then v mod is equivalent as a semi simple braided monoidal category to the category of vector spaces

holonomy groupoids of singular foliations we give a new construction of lie groupoids which is particularly well adapted to the generalization of holonomy groupoids to singular foliations given a family of local lie groupoids on open sets of a smooth manifold m satisfying some hypothesis we construct a lie groupoid which contains the whole family this construction involves a new way of considering local morita equivalences not only as equivalence relations but also as generalized isomorphisms in particular we prove that almost injective lie algebroids are integrable

higher algebraic structures and quantization we derive quasi quantum groups in 2 1 dimensional topological field theory directly from the classical action and the path integral detailed computations are carried out for the chern simons theory with finite gauge group the principles behind our computations are presumably more general we extend the classical action in ad 1 dimensional topological theory to manifolds of dimension less thand 1 we then construct a generalized path integral which ind 1 dimensions reduces to the standard one and ind dimensions reproduces the quantum hilbert space in a 2 1 dimensional topological theory the path integral over the circle is the category of representations of a quasi quantum group in this paper we only consider finite theories in which the generalized path integral reduces to a finite sum new ideas are needed to extend beyond the finite theories treated here

the theory of 2 regularity for mappings with lipschitzian derivatives and its applications to optimality conditions we study local structure of a nonlinear mapping near points where standard regularity and or smoothness assumptions need not be satisfied we introduce a new concept of 2 regularity a certain kind of second order regularity for a once differentiable mapping whose derivative is lipschitz continuous under this 2 regularity condition we obtain the representation theorem and the covering theorem i e stability with respect to right hand side perturbations under assumptions that are weaker than those previously employed in the literature for results of this type these results are further used to derive a constructive description of the tangent cone to a set defined by 2 regular equality constraints and optimality conditions for related optimization problems the class of mappings introduced and studied in the paper appears to be a convenient tool for treating complementarity structures by means of an appropriate equation based reformulation optimality conditions for mathematical programs with equivalently reformulated complementarity constraints are also discussed

more on the determinacy of smooth map germs they don t in this situation and i r determinacy will for notational convenience be written approximation and determinacy this notation was introduced in 4 together with some motivation brief ly ranges of determinacy give a useful way of dexcribing which map germs are equivalent to a given one

bifurcation theorems via second order optimality conditions abstract we present a new approach to bifurcation study that relies on the theory of second order optimality conditions for abnormal constrained optimization problems developed earlier by the first author this theory does not subsume the primal description of the feasible set in terms of tangent vectors or in any other way as a result we obtain new sufficient conditions for bifurcation which are to some extent complementary with respect to the known bifurcation theory

variational perturbative methods and bifurcation of bound states from the essential spectrum this paper consists of two main parts the first deals with a perturbative method in critical point theory and can be seen as the generalisation and completion of some earlier results the second part is concerned with applications of the abstract setup to the existence of bound states of a class of elliptic differential equations that branch off from the infimum of the essential spectrum

quivers quasi quantum groups and finite tensor categories we study finite quasi quantum groups in their quiver setting developed recently by the first author we obtain a classification of finite dimensional pointed majid algebras of finite corepresentation type or equivalently a classification of elementary quasi hopf algebras of finite representation type over the field of complex numbers by the tannaka krein duality principle this provides a classification of the finite tensor categories in which every simple object has frobenius perron dimension 1 and there are finitely many indecomposable objects up to isomorphism some interesting information of these finite tensor categories is given by making use of the quiver representation theory

an analytical study of bifurcation problems for equations involving fredholm mappings on considere des equations de la forme t v l v m v v d 0 ou est un sous ensemble ouvert d un espace norme pour un fixe t l et m sont des applications de la fermeture d 0 d un voisinage d 0 de l origine dans un espace de banach x dans un autre espace de banach y avec t 0 l 0 m 0 0 on etudie l existence de points de bifurcation

monoidal 2 structure of bimodule categories abstract we define a notion of tensor product of bimodule categories and prove that with this product the 2 category of c bimodule categories for fixed tensor c is a monoidal 2 category in the sense of kapranov and voevodsky 1991 1 we then provide a monoidal structure preserving 2 equivalence between the 2 category of c bimodule categories and z c module categories module categories over the center of c for a finite group g we show that de equivariantization is equivalent to the tensor product over rep g we derive rep g module fusion rules and show that the group of invertible rep g module categories is isomorphic to h 2 g k extending results in etingof et al 2

butterflies i morphisms of 2 group stacks abstract weak morphisms of non abelian complexes of length 2 or crossed modules are morphisms of the associated 2 group stacks or gr stacks we present a full description of the weak morphisms in terms of diagrams we call butterflies we give a complete description of the resulting bicategory of crossed modules which we show is fibered and biequivalent to the 2 stack of 2 group stacks as a consequence we obtain a complete characterization of the non abelian derived category of complexes of length 2 deligne s analogous theorem in the case of picard stacks and abelian sheaves becomes an immediate corollary commutativity laws on 2 group stacks are also analyzed in terms of butterflies yielding new characterizations of braided symmetric and picard 2 group stacks furthermore the description of a weak morphism in terms of the corresponding butterfly diagram allows us to obtain a long exact sequence in non abelian cohomology removing a preexisting fibration condition on the coefficients short exact sequence

a modular invariant bulk theory for the c 0 triplet model a proposal for the bulk space of the logarithmic cal w 2 3 triplet model at central charge zero is made the construction is based on the idea that one may reconstruct the bulk theory of a rational conformal field theory from its boundary theory the resulting bulk space is a quotient of the direct sum of projective representations which is isomorphic as a vector space to the direct sum of tensor products of the irreducible representations with their projective covers as a consistency check of our analysis we show that the partition function of the bulk theory is modular invariant and that the boundary state analysis is compatible with the proposed annulus partition functions of this model

dg analogues of the zuckerman functors and the dual zuckerman functors i abstract we study the category of dg harish chandra modules over arbitrary commutative rings and generalize the induction functor the production functor the zuckerman functor and the dual zuckerman functor

smoothness of holonomy covers for singular foliations and essential isotropy given a singular foliation we attach an essential isotropy group to each of its leaves and show that its discreteness is the integrability obstruction of a natural lie algebroid over the leaf we show that a condition ensuring discreteness is the local surjectivity of a transversal exponential map associated with the maximal ideal of vector fields prescribed to be tangent to the foliation the essential isotropy group is also shown to control the smoothness of the holonomy cover of the leaf the associated fiber of the holonomy groupoid as well as the smoothness of the associated isotropy group namely the topological closeness of the essential isotropy group is a necessary and sufficient condition for the holonomy cover to be a smooth finite dimensional manifold and the isotropy group to be a lie group these results are useful towards understanding the normal form of a singular foliation around a compact leaf at the end of this article we briefly outline work of ours on this normal form to be presented in a subsequent paper

homological epimorphisms recollements and hochschild cohomology with a conjecture by snashall solberg in view abstract we show that recollements of module categories give rise to homomorphisms between the associated hochschild cohomology algebras which preserve the strict gerstenhaber structure i e the cup product the graded lie bracket and the squaring map we review various long exact sequences in hochschild cohomology and apply our results in order to realise that the occurring maps preserve the strict gerstenhaber structure as well as a byproduct we generalise a known long exact cohomology sequence of koenig nagase to arbitrary surjective homological epimorphisms we use our observations to motivate and formulate a variation of the finite generation conjecture by snashall solberg

applications of the blowing up construction and algebraic geometry to bifurcation problems a generalization of the morse lemma to vector valued functions is proved by a blowing up argument this is combined with a theorem from algebraic geometry on the number of real solutions of a system of homogeneous equations of even degree to yield a new bifurcation theorem bifurcation in a one or multi parameter problem is guaranteed if the leading term is of even degree it is often two and satisfies a regularity condition applications are given to nonlinear eigenvalue problems and to the hopf bifurcation

global bifurcation for neumann problems without eigenvalues the spectrum of this linear problem consists of the half line 0 co and contains no eigenvalue corresponding to an eigenfunction in l because of this the nonlinear sturm liouville problem 1 1 is not one to which standard bifurcation theory applies nevertheless the question of bifurcation of nontrivial solutions from the line k a 0 a e ir of trivial solutions has been considered and we shall be concerned here with some further developments of the theory in a recent paper 5 kupper and riemer proved among other things that if y is a constant then nontrivial solutions of 1 1 bifurcate from g at 0 o in r x w2 2 0 a if and only if 0 u 4 their methods however depend crucially on the autonomous nature of the problem when r is constant in 7 and 81 stuart and in lo chiapinelli and stuart have considered the general question of the bifurcation of solutions of nonlinear operator equaions when the linearised problem about the trivial solution has no eigenvalues the variational approach of 7 8 has no difficulty in treating 82 0022 0396 82 040082 29 02 00 o

on perturbations of a translationally invariant differential equation on etudie certaines perturbations de l equation differentielle u u up 0 sur tout l espace euclidien a n dimensions on obtient des conditions qui assurent l existence d une solution a l equation perturbee pres d une solution donnee de l equation non perturbee

infinite loop spaces and coherence for symmetric monoidal bicategories abstract this paper proves three different coherence theorems for symmetric monoidal bicategories first we show that in a free symmetric monoidal bicategory every diagram of 2 cells commutes second we show that this implies that the free symmetric monoidal bicategory on one object is equivalent as a symmetric monoidal bicategory to the discrete symmetric monoidal bicategory given by the disjoint union of the symmetric groups third we show that every symmetric monoidal bicategory is equivalent to a strict one we give two topological applications of these coherence results first we show that the classifying space of a symmetric monoidal bicategory can be equipped with an e structure second we show that the fundamental 2 groupoid of an e n space n 4 has a symmetric monoidal structure these calculations also show that the fundamental 2 groupoid of an e 3 space has a sylleptic monoidal structure

periodic solutions of a forced lotka volterra equation abstract for a 2 species predator prey model the effect of a periodic forcing dependent on two parameters is studied a description is given for the local bifurcation curves of periodic solutions near a fixed family of solutions of the free equation

integrability of poisson brackets we discuss the integration of poisson brackets motivated by our recent solution to the integrability problem for general lie brackets we give the precise obstructions to integrating poisson manifolds describing the integration as a symplectic quotient in the spirit of the poisson sigma model of cattaneo and felder for regular poisson manifolds we express the obstructions in terms of variations of symplectic areas improving on results of alcalde cuesta and hector we apply our results and our point of view to decide about the existence of complete symplectic realizations to the integrability of submanifolds of poisson manifolds and to the study of dual pairs morita equivalence and reduction

a global branch of solutions to a semilinear equation on an unbounded interval keywords semilinear second order differential equation bifurcation asymptotic bifurcation neumann problem global branch reference ana article 1985 001view record in web of science record created on 2008 12 10 modified on 2016 08 08