zappa szep products of semigroups and their c algebras abstract zappa szep products of semigroups provide a rich class of examples of semigroups that include the self similar group actions of nekrashevych we use li s construction of semigroup c algebras to associate a c algebra to zappa szep products and give an explicit presentation of the algebra we then define a quotient c algebra that generalises the cuntz pimsner algebras for self similar actions we indicate how known examples previously viewed as distinct classes fit into our unifying framework we specifically discuss the baumslag solitar groups the binary adding machine the semigroup n n and the a x b semigroup z z

on the definition of the strategic stability of equilibria a new definition of strategic stability is shown to satisfy all of the requirements given by elon kohlberg and jean francois mertens 1986 the definition follows the general form of the original definition of kohlberg and mertens but rather than working with perturbations of the payoffs or strategy space works directly with perturbations to the best reply correspondence with the appropriate topology on this space of perturbations the resulting definition does satisfy all of the requirements given by kohlberg and mertens it is shown that one does not have much freedom in the topology one uses

on essential components of the solution set of generalized games in this paper we prove that for any generalized game there exists at least one essential connected component of the set of it s equilibrium points

essential components of nash equilibria for games parametrized by payoffs and strategies abstract we study the stability of nash equilibria for games in normal form parameterized by continuous and quasi concave payoffs and compact convex strategy sets in euclidean spaces and we establish an existence theorem for essential connected components of nash equilibria which includes corresponding results in the literature as special cases

codimension 2 hopf bifurcation of a two degree of freedom vibro impact system abstract codimension 2 hopf bifurcation problem of a two degree of freedom system vibrating against a rigid surface is investigated in this paper the four dimensional poincare map of the vibro impact system is reduced to a two dimensional normal form by virtue of a center manifold reduction and a normal form technique then the theory of hopf bifurcation of maps in r 2 is applied to conclude the existence of codimension 2 hopf bifurcation of the vibro impact system the quasi periodic response of the system by theoretical analysis is well supported by numerical simulations it is shown that there exists codimension 2 hopf bifurcation in multi degree of freedom vibro impact systems the codimension 2 tori doubling phenomenon and the routes of quasi periodic impacts to chaos are reported briefly

differential equations on variable time scales abstract we introduce a class of differential equations on variable time scales with a transition condition between two consecutive parts of the scale conditions for existence and uniqueness of solutions are obtained periodicity boundedness and stability of solutions are considered the method of investigation is by means of two successive reductions b equivalence of the system e akalin m u akhmet the principles of b smooth discontinuous flows computers and mathematics with applications 49 2005 981 995 m u akhmet perturbations and hopf bifurcation of the planar discontinuous dynamical system nonlinear analysis 60 2005 163 178 m u akhmet n a perestyuk the comparison method for differential equations with impulse action differential equations 26 9 1990 1079 1086 on a variable time scale to a system on a time scale a reduction to an impulsive differential equation m u akhmet perturbations and hopf bifurcation of the planar discontinuous dynamical system nonlinear analysis 60 2005 163 178 m u akhmet m turan the differential equations on time scales through impulsive differential equations nonlinear analysis 65 2006 2043 2060 appropriate examples are constructed to illustrate the theory

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

discrete product systems and twisted crossed products by semigroups a product systemeover a semigrouppis a family of hilbert spaces es s p together with multiplicationses et est we vieweas a unitary valued cocycle onp and consider twisted crossed productsa e pinvolvingeand an action ofpby endomorphisms of ac algebraa whenpis quasi lattice ordered in the sense of nica we isolate a class of covariant representations ofe and consider a twisted crossed productbp e pwhich is universal for covariant representations ofewhenehas finite dimensional fibres and in general is slightly larger in particular whenp nand dim e1 our algebrabn e n is a new infinite analogue of the toeplitz cuntz algebras ton our main theorem is a characterisation of the faithful representations ofbp e p

product system models for twisted c algebras of topological higher rank graphs abstract we use product systems of c correspondences to introduce twisted c algebras of topological higher rank graphs we define the notion of a continuous t valued 2 cocycle on a topological higher rank graph and present examples of such cocycles on large classes of topological higher rank graphs to every proper source free topological higher rank graph and continuous t valued 2 cocycle c on we associate a product system x of c 0 0 correspondences built from finite paths in we define the twisted cuntz krieger algebra c c to be the cuntz pimsner algebra o x and we define the twisted toeplitz algebra t c c to be the nica toeplitz algebra nt x we also associate to and c a product system y of c 0 correspondences built from infinite paths we prove that there is an embedding of t c c into nt y and an isomorphism between c c and o y

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

product systems over right angled artin semigroups we build upon mac lane s definition of a tensor category to introduce the concept of a product system that takes values in a tensor groupoid g we show that the existing notions of product systems fit into our categorical framework as do the k graphs of kumjian and pask we then specialize to product systems over right angled artin semigroups these are semigroups that interpolate between free semigroups and free abelian semigroups for such a semigroup we characterize all product systems which take values in a given tensor groupoid g in particular we obtain necessary and sufficient conditions under which a collection of k 1 graphs form the coordinate graphs of a k graph

strongly essential set of ky fan s points and the stability of nash equilibrium abstract in this paper a stronger perturbation of inequality functions and set valued mappings is proposed by means of the hausdorff upper semi metric which includes the perturbations defined by sup norm of function and the maximum hausdorff metric of section mapping based on this perturbation a class of strongly essential sets of ky fan s points is introduced and the existence of the strongly essential component of ky fan s points is proved as an application we use the equivalence of nash equilibrium with ky fan s points to obtain the existence of the strongly essential component of equilibrium which not only give a class of stronger essential sets but also provide a method to discuss the stability with respect to the perturbation of strategic sets

nuclearity of semigroup c algebras and the connection to amenability abstract we study c algebras associated with subsemigroups of groups for a large class of such semigroups including positive cones in quasi lattice ordered groups and left ore semigroups we describe the corresponding semigroup c algebras as c algebras of inverse semigroups groupoid c algebras and full corners in associated group crossed products these descriptions allow us to characterize nuclearity of semigroup c algebras in terms of faithfulness of left regular representations and amenability of group actions moreover we also determine when boundary quotients of semigroup c algebras are uct kirchberg algebras this leads to a unified approach to cuntz algebras and ring c algebras

corner bifurcations in non smoothly forced impact oscillators abstract we consider an impacting mechanical system in which a particle at position u t impacts with a periodically moving obstacle at position z t the motion of which is non smooth in particular we look at corner events when u impacts with z very close to a point where z loses smoothness we show that this leads through a corner bifurcation to complex dynamics in u which can include periodic orbits of arbitrary period and period adding cascades by analysing associated maps close to the corner event we show that this dynamics can be understood in terms of the iterations of a two dimensional piecewise linear discontinuous map we also show some links between this analysis and the difficult problem of understanding the motion of three objects which may have simultaneous impacts

existence of solutions for generalized variational inequality problems abstract this paper aims to investigate the solvability of generalized variational inequalities specifically we give some conditions that guarantee the existence of solutions of generalized variational inequalities with upper semicontinuous and compact contractible valued correspondence over unbounded closed convex subsets in finite dimensional spaces our results include the corresponding results in the literature as special cases

semigroup crossed products and the toeplitz algebras of nonabelian groups abstract we consider the quasi lattice ordered groups g p recently introduced by nica we realise their universal toeplitz algebra as a crossed product b p p by a semigroup of endomorphisms and show that the toeplitz representation is faithful precisely when an amenability condition is satisfied we then show directly that many interesting free products are amenable the final result contains theorems of cuntz and dinh on the uniqueness of toeplitz cuntz algebras as special cases

closed form solutions for oscillators with inelastic impacts abstract a class of vibrating systems with perfectly stiff amplitude limiters is considered by means of non smooth time substitutions the motion is represented as a combination of oscillating component which is due to cyclic collisions with the limiters and a slow decay caused by the gradual energy loss at collision times a specific modification of the two variable expansions is used where the non smooth triangle wave temporal argument is viewed as a fast time while the energy decay is described in a slow time scale as a result closed form analytical solutions are obtained that automatically satisfy collision conditions with the energy loss three qualitatively different basic types of vibrations are considered to cover periodic frequency modulated and amplitude frequency modulated motions

generic uniqueness of equilibrium points abstract let x be a nonempty convex and compact subset of normed linear space e respectively let x be a nonempty bounded closed and convex subset of banach space e and a be a nonempty convex and compact subset of x and f x x r be a given function the uniqueness of equilibrium point for equilibrium problem which is to find x x respectively x a such that f x y 0 for all y x respectively f x y 0 for all y a is studied with varying f respectively with both varying f and varying a the results show that most of equilibrium problems in the sense of baire category have unique equilibrium point

stability of solutions for ky fan s section theorem with some applications abstract in this paper we prove that most of problems in ky fan s section theorem in the sense of baire category are essential and that for any problem in ky fan s section theorem there exists at least one essential component of its solution set as applications we deduce both the existence of essential components of the set of ky fan s points based on ky fan s minimax inequality theorem and the existence of essential components of the set of nash equilibrium points for general n person non cooperative games with non concave payoffs

hadamard well posedness of the α core abstract in this paper we discuss the continuity property of the core with respect to data perturbations in different environments we show that some collections of abstract economies or normal games with the nonempty core have the hadamard well posedness property we also show that the core points of every game in a dense residual subset are essential

hadamard well posedness in discontinuous non cooperative games abstract we consider some recent classes of discontinuous games with nash equilibria and we prove that such classes have the hadamard well posedness property this means that given a game y a net y of games converging to y and a net x such that x is a nash equilibrium of any y then at least a cluster point of x is a nash equilibrium of y in order to obtain this property we prove that the map of nash equilibria is upper semicontinuous using the pseudocontinuity a generalization of the continuity we improve previous results obtained with continuous functions

stability of solutions for variational relation problems with applications abstract in this paper we prove that most of problems in variational relations in the sense of baire category are essential and that for any problem in variational relations there exists at least one essential component of its solution set as applications we deduce the existence of essential components of the set of ky fan s points based on ky fan s minimax inequality theorem the existence of essential components of the set of nash equilibrium points for general n person non cooperative games the existence of essential component of the set of solutions for vector ky fan s minimax inequality the existence of essential components of the set of kkm points and the existence of essential components of the set of solutions for ky fan s section theorem

pure infiniteness and ideal structure of c algebras associated to fell bundles abstract we investigate structural properties of the reduced cross sectional algebra c r b of a fell bundle b over a discrete group g conditions allowing one to determine the ideal structure of c r b are studied notions of aperiodicity paradoxicality and b infiniteness for the fell bundle b are introduced and investigated by themselves and in relation to the partial dynamical system dual to b several criteria of pure infiniteness of c r b are given it is shown that they generalize and unify corresponding results obtained in the context of crossed products by the following duos laca spielberg 34 jolissaint robertson 21 sierakowski rordam 47 giordano sierakowski 18 and ortega pardo 39 for exact separable fell bundles satisfying the residual intersection property primitive ideal space of c r b is determined the results of the paper are shown to be optimal when applied to graph c algebras applications to a class of exel larsen crossed products are presented

well posed ky fan s point quasi variational inequality and nash equilibrium problems abstract we give a unified approach to hadamard well posedness for some nonlinear problems such as those of ky fan s point and quasi variational inequality as applications we obtain some well posed theorems for nash equilibrium points

continuity properties of the nash equilibrium correspondence in a discontinuous setting abstract we introduce a new complete metric space of discontinuous normal form games and prove that the nash equilibrium correspondence is upper semicontinuous with non empty and compact values so using the theorem of fort 1949 we obtain that the correspondence is also lower semicontinuous in a dense subset we introduce new topological assumptions on the payoff functions and a strengthening of standard quasi concavity properties examples show that our results cannot be obtained from the previous ones

on the origin and bifurcations of stick slip oscillations a recently proposed model of macroscopic friction is investigated using methods of dynamical systems analysis particular emphasis is put on the bifurcations associated with the appearance of stick

unified approach to existence and stability of essential components abstract we give a unified approach to essential components for some nonlinear problems such as fixed points ky fan s points and nash equilibrium points etc

existence and stability of the α core for fuzzy games abstract in this study we establish the existence of the core in fuzzy games using the existence results we identify a class of fuzzy games comprising a dense residual subset of fuzzy games such that every point of the core is essential we also show that every fuzzy game in this class has an essential component of its core

bifurcations in nonsmooth dynamical systems a review is presented of the one parameter nonsmooth bifurcations that occur in a variety of continuous time piecewise smooth dynamical systems motivated by applications a pragmatic approach is taken to defining a discontinuity induced bifurcation dib as a nontrivial interaction of a limit set with respect to a codimension one discontinuity boundary in phase space only dibs that are local are considered that is bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows three classes of systems are considered involving either state jumps jumps in the vector field or jumps in some derivative of the vector field a rich array of dynamics are revealed involving the sudden creation or disappearance of attractors jumps to chaos bifurcation diagrams with sharp corners and cascades of period adding for each kind of bifurcation identified where possible a kind of normal form or discontinuity mapping dm is given together with a canonical example and an application the goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators impact oscillators dc dc converters and problems in control theory

on existence and essential components of the solution set for the system of vector quasi equilibrium problems abstract in this paper we study the existence and essential components of the solution set for the system of vector quasi equilibrium problems and establish some new results by defining the best reply map

on essential sets and essential components of efficient solutions for vector optimization problems in this paper we first introduce the notions of an essential set and an essential component of the set of efficient solutions for continuous vector optimizations on a nonempty compact subset of a metric space then we show that for each of these vector optimizations each set of all efficient solutions corresponding to the same optimal values is essential basing on this result we give full characterizations of an essential point an essential set and an essential component respectively as an application we prove that for continuous quasiconvex vector optimization problems on a nonempty compact subset of a metric vector space each component of the set of efficient solutions is essential even though the efficient solution set is not connected

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

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 closed form stationary probability distribution of the stochastically excited vibro impact oscillators abstract the response of vibro impact oscillators under random excitations has been studied using various techniques in the last three decades however the results available were smooth approximations of the intrinsically non smooth response of vibroimpact oscillators this paper proposes a new procedure for the closed form stationary probability density function pdf of the response of single degree of freedom sdof vibro impact system under gaussian white noise excitation first the zhuravlev ivanov transformation is adopted to convert a vibro impact oscillator with one side barrier into an oscillator without barrier the probabilistic description of the system is subsequently defined through the corresponding fokker planck kolmogorov fpk equation the closed form stationary pdf of the response is obtained by solving the reduced fpk equation using the iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow two examples are examined to illustrate the effectiveness of the proposed procedure good agreements are found between the analytical solutions and the simulated results of the pdfs and logarithmic pdfs of the examples the reported studies also show that the proposed procedure can deal with case of small restitution factor in particular the closed form solution for the case of small restitution factor is firstly obtained in literature and can be used as the benchmark problem to examine the other method in random vibration furthermore the approximate solutions obtained with the proposed procedure are piece wise form reflecting the true nature of the intrinsically discontinuous vibro impact oscillators

topological freeness for c correspondences abstract we study conditions that ensure uniqueness theorems of cuntz krieger type for relative cuntz pimsner algebras o j x associated to a c correspondence x over a c algebra a we give general sufficient conditions phrased in terms of a multivalued map x acting on the spectrum a of a when x j is of type i we construct a directed graph dual to x and prove a uniqueness theorem using this graph when x j is liminal we show that topological freeness of this graph is equivalent to the uniqueness property for o j x as well as to an algebraic condition which we call j acyclicity of x as an application we improve the fowler raeburn uniqueness theorem for the toeplitz algebra t x we give new simplicity criteria for o x we generalize and enhance uniqueness results for relative quiver c algebras of muhly and tomforde we also discuss applications to crossed products by endomorphisms

the essential components of the set of equilibrium points for set valued maps in this article we discuss the stability of equilibrium points for set valued maps we introduce the notion of essential components of the set of equilibrium points for set valued maps and prove an existence theorem of essential components as applications we deduce the existence of essential components of the set of coincidence points and show that every marchaud dynamical economy cf j p aubin dynamic economic theory springer verlag 1997 possesses at least one essential component of the set of its viable equilibrium points

bifurcations caused by grazing incidence in many degrees of freedom impact oscillators the transition from stable periodic non impacting motion to impacting motion is analysed for a mechanical oscillator by using local methods it is shown that a grazing impact leads to an almost one dimensional stretching in state space a condition can then be formulated such that a grazing trajectory will be stable if the condition is fulfilled if this is the case the bifurcation will be continuous and the motion after the bifurcation can be understood by a one dimensional mapping this mapping is known to exhibit chaotic solutions as well as arbitrary long stable cycles depending on parameters

modal analysis of mechanical systems with impact non linearities limitations to a modal superposition this paper presents an attempt to generalize the modal superposition formula to mechanical systems with impact type non linearities following the procedure introduced for smooth non linearities the study is restricted to simple one and two degree of freedom systems with a unilateral constraint on one of the degrees of freedom for which the response can be analytically determined generalized frequencies modes and masses are built in the procedure the results obtained for various sets of parameters point out some limitations to the validity of a general modal superposition formula

semigroup c algebras and amenability of semigroups we construct reduced and full semigroup c algebras for left cancellative semigroups our new construction covers particular cases already considered by a nica and also toeplitz algebras attached to rings of integers in number fields due to j cuntz moreover we show how left amenability of semigroups can be expressed in terms of these semigroup c algebras in analogy to the group case

impact oscillations linear theory of stability and bifurcations abstract a unified approach to analysis of impact oscillations is proposed its mathematical essence is the continuous representation of the impulsive motion in some auxiliary variables as a result an explicit formula for the fundamental matrix is obtained which allows one to construct the characteristic equation then the stability and bifurcations can be studied by the usual techniques the exceptional case of bifurcations related to grazing impacts is investigated by taking into account a non zero impact duration due to this approach linearization is also possible and the complex bifurcation becomes a sequence of ordinary ones some algebraic conditions are obtained which allow one to determine the type of the resulting motion a mechanical example is considered a disc with an offset centre of gravity bouncing on an oscillating surface