vanishing viscosity for hemivariational inequalities modeling dynamic problems in elasticity abstract in this paper we consider a mathematical model describing a dynamic linear elastic contact problem with nonmonotone skin effects the subdifferential multivalued and multidimensional reaction displacement law is employed we treat an evolution hemivariational inequality of hyperbolic type which is a weak formulation of this mechanical problem we establish a result on the existence of solutions to the cauchy problem for the hemivariational inequality this result is a consequence of an existence theorem for second order evolution inclusion for the latter using the parabolic regularization method we obtain the solution as a limit when the viscosity term tends to zero

symmetry and phase locking in a ring of pulse coupled oscillators with distributed delays abstract phase locking in a ring of pulse coupled integrate and fire oscillators with distributed delays is analysed using group theory the period of oscillation of a solution and those related by symmetry is determined self consistently numerical continuation of maximally symmetric solutions in characteristic system length and timescales yields bifurcation diagrams with spontaneous symmetry breaking the stability of phase locked solutions is determined via a linearisation of the oscillator firing map in the weak coupling regime averaging leads to an effective phase coupled model with distributed phase shifts and the analysis of the system is considerably simplified in particular the collective period of a solution is now slaved to the relative phases for odd numbered rings spontaneous symmetry breaking can lead to a change of stability of a travelling wave state via a simple hopf bifurcation the resulting non phase locked solutions are constructed via numerical continuation at these bifurcation points the corresponding behaviour in the integrate and fire system is explored with simulations showing bifurcations to quasiperiodic firing patterns

abelianisation of orthogonal groups and the fundamental group of modular varieties abstract we study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms we show that the index of this commutator is 2 for many groups that occur in the construction of moduli spaces in algebraic geometry in particular the moduli of k3 surfaces we give applications to modular forms and to computing the fundamental groups of some moduli spaces

dynamic contact problem for viscoelastic piezoelectric materials with slip dependent friction abstract in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the friction condition is described to be the clarke subdifferential relations of nonmonotone and multivalued character in the tangential directions on the boundary the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

moduli spaces of polarized symplectic o grady varieties and borcherds products we study moduli spaces of o grady s ten dimensional irreducible symplectic manifolds these moduli spaces are covers of modular varieties of dimension 21 namely quotients of hermitian symmetric domains by a suitable arithmetic group the interesting and new aspect of this case is that the group in question is strictly bigger than the stable orthogonal group this makes it different from both the k3 and the k3 n case which are of dimension 19 and 20 respectively

patterns at primary hopf bifurcations at a plexus of identical oscillators mathematically an oscillator is a system of ordinary differential equations with a periodic limit cycle usually arising from a hopf bifurcation for a stationary solution a plexus is a collection of such oscillators coupled to each other via one way or two way communication channels plexuses model a wide number of phenomena in the mathematically oriented sciences the primary hopf bifurcation theory of such a plexus is developed there are features of the bifurcating solutions which depend only on the combinatorics of the plexus and not on the details of the individual oscillators such features are called the pattern of the bifurcation the relation of patterns to the modes of small oscillations of mechanical systems is discussed more detailed information is developed for weak coupling the theory is used to analyze two particular types of plexuses viz rings and lines of oscillators it is then shown that the structure of a plexus permits numerical bifurcation computations to be made more efficien

hemivariational inequalities modeling dynamic contact problems with adhesion abstract this paper deals with the mathematical modelling of viscoelastic frictional contact processes in mechanics which involve adhesion the model consists of a coupled system of the hemivariational inequality of hyperbolic type for the displacement and the ordinary differential equation for the bonding field the frictional forces are derived from nonconvex superpotentials through the generalized clarke subdifferential the properties of the body are described by a modified kelvin voigt constitutive law the existence of weak solution to the problem is proved by embedding it into a class of second order evolution inclusions and by applying a surjectivity result for multivalued pseudomonotone operators we also establish a result on the regularity of weak solution to the model finally examples of subdifferential boundary conditions which include the functions of d c type are provided

boundary hemivariational inequality of parabolic type abstract in this paper we consider a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time dependent pseudomonotone operator we establish the existence of solutions for such inequality our proof is based on a known surjectivity result for operators of pseudomonotone type we present an example of semipermeability heat conduction problem to which the result applies

hemivariational inequality for viscoelastic contact problem with slip dependent friction abstract in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction law is described by a multivalued subdifferential relation which includes the slip displacement dependent friction and the tresca models we establish the existence of weak solutions to the problem by using a surjectivity result for pseudomonotone mappings

existence results for quasilinear parabolic hemivariational inequalities abstract this paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance by use of the theory of multi valued pseudomonotone operators the notion of generalized gradient of clarke and the property of the first eigenfunction we build a landesman lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities

slip dependent friction in dynamic elasticity the dynamic evolution with frictional contact of an elastic body is considered in modeling the contact the tresca model and a slip dependent friction law are used the existence of a solution is proved in the two dimensional case the uniqueness is proved for the one dimensional shearing problem the convergence for a vanishing viscosity of the unique solution of the viscoelastic problem to a solution of the elastic problem is obtained

on the kodaira dimension of orthogonal modular varieties we prove that up to scaling there are only finitely many integral lattices l of signature 2 n with n ge 21 or n 17 such that the modular variety defined by the orthogonal group of l is not of general type in particular when n ge 108 every modular variety defined by an arithmetic group for a rational quadratic form of signature 2 n is of general type we also obtain similar finiteness in n ge 9 for the stable orthogonal groups as a byproduct we derive finiteness of lattices admitting reflective modular form of bounded vanishing order which proves a conjecture of gritsenko and nikulin

hemivariational inequality approach to the dynamic viscoelastic sliding contact problem with wear abstract the dynamic contact problem of sliding contact with wear between a viscoelastic body and a foundation is formulated as a hemivariational inequality the contact is modeled with a general normal damped response condition which is nonmonotone possibly multivalued and has the subdifferential form we establish the existence of weak solutions by using a surjectivity result for a class of pseudomonotone operators we also deliver conditions under which the solution of the evolution inclusion associated with the hemivariational inequality is unique

a dynamic model with friction and adhesion with applications to rocks abstract dynamic frictional contact with adhesion of a viscoelastic body and a foundation is formulated as a hemivariational inequality this may model the dynamics of rock layers the normal stress displacement relation on the contact boundary is nonmonotone and nonconvex because of the adhesion process a sequence of regularized problems is considered the necessary a priori estimates are obtained and the existence of a weak solution for the hemivariational inequality is established by passing to the limit as the regularization parameter vanishes

a system of evolution hemivariational inequalities modeling thermoviscoelastic frictional contact abstract in this paper we prove the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation we employ the kelvin voigt viscoelastic law include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions the model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the parabolic hemivariational inequality for the temperature the existence of solutions is proved by using a surjectivity result for operators of pseudomonotone type the uniqueness is obtained for a large class of operators of subdifferential type satisfying a relaxed monotonicity condition

dynamic contact problem for viscoelastic piezoelectric materials with normal damped response and friction in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the contact is modeled by a general normal damped response condition and a friction law which are nonmonotone possibly multivalued and have the subdifferential form the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

the kodaira dimension of the moduli of k3 surfaces the global torelli theorem for projective k3 surfaces was first proved by piatetskii shapiro and shafarevich 35 years ago opening the way to treating moduli problems for k3 surfaces the moduli space of polarised k3 surfaces of degree 2d is a quasi projective variety of dimension 19 for general d very little has been known hitherto about the kodaira dimension of these varieties in this paper we present an almost complete solution to this problem our main result says that this moduli space is of general type for d 61 and for d 46 50 54 57 58 60

evolution hemivariational inequality for a class of dynamic viscoelastic nonmonotone frictional contact problems in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction condition is described by a multivalued subdifferential relation which includes both the slip displacement and the slip rate dependent friction and the tresca models the existence of weak solutions to the problem is proved by exploiting a surjectivity result for a class of pseudomonotone mappings

non symplectic involutions of irreducible symplectic manifolds of k3 n type this paper is concerned with non symplectic involutions of irreducible symplectic manifolds of k3 n type we will give a criterion for deformation equivalence and use this to give a lattice theoretic description of all deformation types while moduli spaces of k3 n type manifolds with non symplectic involutions are not necessarily hausdorff we will construct quasi projective moduli spaces for a certain well behaved class of such pairs

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

on the moduli space of pairs consisting of a cubic threefold and a hyperplane abstract we study the moduli space of pairs x h consisting of a cubic threefold x and a hyperplane h in p 4 the interest in this moduli comes from two sources the study of certain weighted hypersurfaces whose middle cohomology admit hodge structures of k3 type and on the other hand the study of the singularity o 16 the cone over a cubic surface in this paper we give a hodge theoretic construction of the moduli space of cubic pairs by relating x h to certain lattice polarized cubic fourfolds y a period map for the pairs x h is then defined using the periods of the cubic fourfolds y the main result is that the period map induces an isomorphism between a git model for the pairs x h and the baily borel compactification of some locally symmetric domain of type iv

one dimensional dynamic thermoviscoelastic contact with damage abstract the problem of thermoviscoelastic dynamic contact between a rod and a rigid obstacle when the material damage is taken into account is modeled and analyzed the contact is modeled by the normal compliance condition and the stress strain constitutive equation is of kelvin voigt type the damage which describes the reduction of the load carrying capacity of the rod evolves because of the opening of microcracks as a result of tension or compression when the damage reaches a critical value at a point on the rod the material cannot carry any load and the system breaks down mathematically this is expressed by the quenching of the solution the existence of a local weak solution is established using penalization and a priori estimates

dynamic hemivariational inequalities in contact mechanics abstract this paper gives a review of results on the existence and uniqueness of solutions to some mechanical contact problems the second order evolution problems with a general normal compliance response condition and a normal damped response one in viscoelasticity are discussed finally a new result for a problem which includes the slip displacement dependent friction and the tresca model is provided

moduli spaces of twisted k3 surfaces and cubic fourfolds motivated by the relation between twisted k3 surfaces and special cubic fourfolds we construct moduli spaces of polarized twisted k3 surfaces of any fixed degree and order we do this by mimicking the construction of the moduli space of untwisted polarized k3 surfaces as a quotient of a bounded symmetric domain

periods of double epw sextics we study the period map for double epw sextics which are varieties making up a locally versal family of polarized hyperkahler fourfolds double epw sextics are parametrized by lagrangian subspaces of the third wedge product of a 6 dimensional complex vector space we prove that lagrangians in the indeterminacy locus of the period map contain a decomposable 3 vector enjoying very special properties in addition we prove a result about periods of double epw sextics which are either smooth or have isolated singular points with projectivized tangent cone isomorphic to the incidence variety in mathbb p 2 times mathbb p 2 vee

stability analysis of synchronous oscillations in a weakly coupled integrodifferential system abstract it is shown that synchronous oscillations arising via a hopf bifurcation in a class of weakly coupled integrodifferential systems are destabilised by a weak difference coupling of the oscillators

time dependent implicit evolution equations on presente des theoremes d existence et d unicite pour des problemes de cauchy correspondant aux equations abstraites de la forme d b t u t dt a t u t f t ou b t est une famille dependante du temps d operateurs lineaires

abelian quotients of mapping class groups of highly connected manifolds we compute the abelianisations of the mapping class groups of the manifolds w g 2n g s n times s n for n ge 3 and g ge 5 the answer is a direct sum of two parts the first part arises from the action of the mapping class group on the middle homology and takes values in the abelianisation of the automorphism group of the middle homology the second part arises from bordism classes of mapping tori and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable j homomorphism we relate its calculation to a purely homotopy theoretic problem

modelling of nonconvex nonsmooth energy problems dynamic hemivariational inequalities with impact effects nonconvex nonsmooth energy functions lead to hemivariational inequalities the subjects of the present paper are dynamic hemivariational inequalities without and with impact effects first some existence and approximation results are obtained for dynamic hemivariational inequalities without impact effects then for the case of impact a new type of variational expressions has been obtained including variations of the time and the place of impact and the corresponding dynamic hemivariational inequalities have been formulated

boundary control problems with nonlinear state equation first order necessary conditions of optimality are obtained for boundary control problems governed by parabolic equations with nonlinear boundary value conditions

hemivariational inequalities in thermoviscoelasticity abstract in this paper we present the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation we employ the kelvin voigt viscoelastic law which includes the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions the model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the parabolic hemivariational inequality for the temperature the existence of solutions is obtained from a surjectivity result for operators of pseudomonotone type the uniqueness holds for a large class of operators of subdifferential type satisfying a relaxed monotonicity condition