l 1 stability estimates for n x n conservation laws let u t f u x 0 be a strictly hyperbolic n times n system of conservation laws each characteristic field being linearly degenerate or genuinely nonlinear in this paper we explicitly define a functional phi phi u v equivalent to the l 1 distance which is almost decreasing i e phi big u t v t big phi big u s v s big leq o ve cdot t s quad hbox for all t s geq 0 for every pair of e approximate solutions u v with small total variation generated by a wave front tracking algorithm the small parameter e here controls the errors in the wave speeds the maximum size of rarefaction fronts and the total strength of all non physical waves in u and in v from the above estimate it follows that front tracking approximations converge to a unique limit solution depending lipschitz continuously on the initial data in the vec l 1 norm this provides a new proof of the existence of the standard riemann semigroup generated by a n n system of conservation laws

vanishing viscosity solutions of nonlinear hyperbolic systems we consider the cauchy problem for a strictly hyperbolic n n system in one space dimension ut a u ux 0 assuming that the initial data have small total variation we show that the solutions of the viscous approximations ut a u ux euxx are defined globally in time and satisfy uniform bv estimates independent of e moreover they depend continuously on the initial data in the l 1 distance with a lipschitz constant independent of t e letting e 0 these viscous solutions converge to a unique limit depending lipschitz continuously on the initial data in the conservative case where a df is the jacobian

weightless cohomology of algebraic varieties abstract using morel s weight truncations in categories of mixed sheaves we attach to varieties over finite fields or the complex numbers a series of groups called the weightless cohomology groups these lie between the usual cohomology and intersection cohomology have natural ring structures and are functorial for certain morphisms

weak solutions of general systems of hyperbolic conservation laws in this paper we establish the existence theory for general system of hyperbolic conservation laws and obtain the uniform l1 boundness for the solutions the existence theory generalizes the classical glimm theory for systems for which each characteristic field is either genuinely nonlinear or linearly degenerate in the sense of lax we construct the solutions by the glimm scheme through the wave tracing method one of the key elements is a new way of measuring the potential interaction of the waves of the same characteristic family involving the angle between waves a new analysis is introduced to verify the consistency of the wave tracing procedure the entropy functional is used to study the l1 boundedness

motivic weightless complex and the relative artin motive abstract we construct a motivic analogue of the weightless cohomology groups 18 and demonstrate several expected properties ring structure kunneth functoriality for certain morphisms etc we also demonstrate the expected relationship with the motivic intersection complex of wildeshaus 26 25 whenever it exists the methods also give another construction of the weightless cohomology groups over any base field in characteristic 0 this motive coincides with the motive e x of ayoub zucker 3 and recovers the motivic construction of the reductive borel serre compactification of shimura varieties

the unique limit of the glimm scheme we introduce the definitions of a standard riemann semigroup and of a viscosity solution for a nonlinear hyperbolic system of conservation laws for a class including general 2 2 systems it is proved that the solutions obtained by a wavefront tracking algorithm or by the glimm scheme are precisely the semigroup trajectories in particular these solutions are unique and depend lipschitz continuously on the initial data in the l1 norm

existence theory for hyperbolic systems of conservation laws with general flux functions to begin with we assume that the flux function f u is piecewise genuinely nonlinear in the sense that it exhibits finitely many at most p say points of lack of genuine nonlinearity along each wave curve importantly our analysis applies to arbitrary large p in the sense that the constant c restricting the total variation is independent of p second by an approximation argument we prove that the existence theory above extends to general flux functionsf u that can be approached by a sequence of piecewise genuinely nonlinear flux functions fe u

idempotent completion of triangulated categories we show that the idempotent completion of a triangulated category has a natural structure of a triangulated category the idempotent completion of the bounded derived category of an exact category gives the derived category of the idempotent completion in particular the derived category of an idempotent complete exact category is idempotent complete

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

decay estimate for a new measure of rarefaction waves in general systems of conservation laws abstract the sharp decay estimate of rarefaction waves in terms of a partial ordering among positive measures is not only interesting in itself but also crucial in the study of convergence rate of vanishing viscosity approximations cf bressan and yang 2004 10 such an estimate is well established for genuinely nonlinear system of conservation laws cf bressan and yang 2004 9 but similar result is not available for non genuinely nonlinear system in this paper we give a new measure about the rarefaction waves in addition a sharp decay estimate of the new measure is given for the cubic nonlinear system of conservation laws

indecomposable higher chow cycles on jacobians we construct some natural indecomposable elements of ch g j c 1 with trivial regulator and in particular prove that ch g ind j c 1 mb q is uncountable for c a generic curve or a generic hyperelliptic curve of genus g geq 3

the n motivic t structures for n 0 1 and 2 abstract for a field k and an integer n 0 1 2 we construct a t structure t 0 m n k t 0 m n k on voevodsky s triangulated category of motives dm eff k which we call the n motivic t structure when n 0 this is simply the usual homotopy t structure but for n 1 2 these are new t structures we will show that the category of deligne s 1 motives can be embedded as a full subcategory in the heart of the 1 motivic t structure by a rather straightforward analogy we are led to specify a class of objects in the heart of the 2 motivic t structure which we call mixed 2 motives we will also check that these objects form an abelian category

well posedness theory for hyperbolic conservation laws the paper presents a well posedness theory for the initial value problem for a general system of hyperbolic conservation laws we will start with the refinement of glimm s existence theory and discuss the principle of nonlinear through wave tracing our main goal is to introduce a nonlinear functional for two solutions with the property that it is equivalent to the l1 x distance between the two solutions and is time decreasing moreover the functional is constructed explicitly in terms of the wave patterns of the solutions through the nonlinear superposition it consists of a linear term measuring the l1 x distance a quadratic term measuring the coupling of waves and distance and a generalized entropy functional 1999 john wiley sons inc

on the riemann problem for non conservative hyperbolic systems we consider the construction and the properties of the riemann solver for the hyperbolic system

self triggered consensus for multi agent systems with zeno free triggers in this technical note a self triggered consensus algorithm for multi agent systems has been proposed each agent receives the state information of its neighbors and computes the average state of its neighborhood based on this average state the event trigger is designed to determine when the agent updates its control input and transmits the average state to its neighbors by specifying a strictly positive minimal inter event time for each agent zeno behavior can be avoided then by solving quadratic equations related to the event condition the self triggered consensus algorithm is developed by directly computing the event time instants with a set of iterative procedures it has been proved that with the proposed zeno free algorithm the agent group can achieve consensus asymptotically compared with the existing works the proposed algorithm is simpler in formulation and computation moreover it has been showed that agents need less time to achieve consensus with considerable reduction of the number of triggering events controller updates and information transmission as a result more energy can be saved using the proposed algorithm in practical multi agent systems

decay estimation in nonlinear hyperbolic system of conservation laws abstract in this paper we study some decay estimates in nonlinear hyperbolic system of conservation laws this research is not only interesting in itself but also crucial in studying the large time behavior problem by introducing a proper glimm functional we obtain some useful decay estimates which are proved helpful in obtaining decay rates of the admissible solutions to nonlinear hyperbolic conservation laws as t

on the chow group of zero cycles of a generalized kummer variety abstract for a generalized kummer variety x of dimension 2n we will construct for each 0 i n some co isotropic subvarieties in x foliated by i dimensional constant cycle subvarieties these subvarieties serve to prove that the rational orbit filtration introduced by voisin on the chow group of zero cycles of a generalized kummer variety coincides with the induced beauville decomposition from the chow ring of abelian varieties as a consequence the rational orbit filtration is opposite to the conjectural bloch beilinson filtration for generalized kummer varieties

motives and filtrations on chow groups in this paper sequential to sa we discuss a philosophy of bloch and beilinson concerning filtrations on chow groups of algebraic vareties which provides us with a good understanding on the structure of at least certain portions of chow groups let k be a fixed ground field and let c be the category of smooth projective schemes over k with a fixed suitable weil cohomology theory cf notations x in mathcal c rightsquigarrow h x mathop oplus limits i in z h i x

murre s conjectures and explicit chow kunneth projectors for varieties with a nef tangent bundle in this paper we investigate murre s conjectures on the structure of rational chow groups and exhibit explicit chow kiinneth projectors for some examples more precisely the examples we study are the varieties which have a nef tangent bundle for surfaces and threefolds which have a nef tangent bundle explicit chow kunneth projectors are obtained which satisfy murre s conjectures and the motivic hard lefschetz theorem is verified

borel moore motivic homology and weight structure on mixed motives by defining and studying functorial properties of the borel moore motivic homology we identify the heart of bondarko hebert s weight structure on beilinson motives with corti hanamura s category of chow motives over a base therefore answering a question of bondarko

a wavefront tracking algorithm for n n nongenuinely nonlinear conservation laws we introduce a wavefront tracking algorithm for n n hyperbolic systems of conservation lawsut f u x 0 that admits characteristic fields that are neither genuinely nonlinear nor linearly degenerate in the sense of lax instead we assume that for any nongenuinely nonlinear ith characteristic family the derivative of the ith eigenvalue i u of df u in the direction of the ith right eigenvector ri u vanishes on a single n 1 dimensional hypersurface in the u space transversal to the field ri u systems that fulfill this type of assumptions are of particular interest in studying elastodynamic or rigid heat conductors at low temperature the first proof of the existence of weak solutions for nongenuinely nonlinear systems was given by t p liu mem amer math soc 30 1981 no 240 based on a glimm scheme our construction here provides an alternative method for establishing the global existence of weak solutions for such systems moreover relying on the stability analysis developed in ancona and marson preprint s i s s a i s a s 27 99 11 1999 and preprint 2000 we show that these solutions are entropy admissible in the sense of lax

relative artin motives and the reductive borel serre compactification of a locally symmetric variety we introduce the notion of artin motives and cohomological motives over a scheme x given a cohomological motive m over x we consider the universal artin motive mapping to m and denote it omega 0 x m we use this to define a motive mathbb e x over x which is an invariant of the singularities of x the first half of the paper is devoted to the study of the functors omega 0 x and the computation of the motives mathbb e x

realisation l adique des motifs triangules geometriques ii for geometrical triangulated motives with rational coefficients over a ground field of characteristic zero which is embeddable into mathbb c huber j algebraic geom 9 4 755 799 2000 j algebraic geom 13 1 195 207 2004 has constructed a realization functor with values in the category of mixed realization of huber mixed motives and their realization in derived categories lecture notes in mathematics vol 1604 springer berlin 1995 in this sequel to ivorra doc math 12 607 671 2007 we prove that the l adic realization functor obtained in theorem 4 3 of ivorra doc math 12 607 671 2007 is the same up to a canonical isomorphism as the l adic component of a huber s construction in this way ivorra in doc math 12 607 671 2007 might be viewed as an integral generalization to all noetherian separed schemes of the work huber in j algebraic geom 9 4 755 799 2000 j algebraic geom 13 1 195 207 2004 as far as the l adic setting is concerned we also prove a comparison theorem with the classical l adic cycle class map over a perfect field using a naive motivic cycle class map

dynamical properties of hybrid automata hybrid automata provide a language for modeling and analyzing digital and analogue computations in real time systems hybrid automata are studied here from a dynamical systems perspective necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized the results on existence uniqueness and continuity serve as a starting point for stability analysis lyapunov s theorem on stability via linearization and lasalle s invariance principle are generalized to hybrid automata

distributed event triggered coordination for average consensus on weight balanced digraphs this paper proposes a novel distributed event triggered algorithmic solution to the multi agent average consensus problem for networks whose communication topology is described by weight balanced strongly connected digraphs the proposed event triggered communication and control strategy does not rely on individual agents having continuous or periodic access to information about the state of their neighbors in addition it does not require the agents to have a priori knowledge of any global parameter to execute the algorithm we show that under the proposed law events cannot be triggered an infinite number of times in any finite period i e no zeno behavior and that the resulting network executions provably converge to the average of the initial agents states exponentially fast we also provide weaker conditions on connectivity under which convergence is guaranteed when the communication topology is switching finally we also propose and analyze a periodic implementation of our algorithm where the relevant triggering functions do not need to be evaluated continuously simulations illustrate our results and provide comparisons with other existing algorithms

the zero section of the universal semiabelian variety and the double ramification cycle we study the chow ring of the boundary of the partial compactification of the universal family of principally polarized abelian varieties ppav we describe the subring generated by divisor classes and we compute the class of the partial compactification of the universal zero section which turns out to lie in this subring our formula extends the results for the zero section of the universal uncompactified family the partial compactification of the universal family of ppav can be thought of as the first two boundary strata in any toroidal compactification of ag our formula provides a first step in a program to understand the chow groups of a g especially of the perfect cone compactification by induction on genus by restricting to the image of mg under the torelli map our results extend the results of hain on the double ramification cycle answering eliashberg s question

correspondences to abelian varieties i when s is an algebraic scheme and x s and y s proper schemes over s we define the notion of correspondences from x to y over s and when y s is a relative abelian scheme and x is a normal variety we give a charac terization for a correspondence from x to y over s to be a graph of some morphism x y over s which is a generalization of the result for classical correspondences in 4

toroidal and reductive borel serre compactifications of locally symmetric spaces by hermitian locally symmetric space we mean an arithmetic quotient of a bounded symmetric domain both the toroidal and the reductive borel serre compactifications of such a space come equipped with canonical mappings to the baily borel satake compactification in this article we show that there is a mapping from the toroidal compactification to the reductive borel serre compactification whose composition with the projection to the baily borel compactification agrees with the canonical projection up to an arbitrarily small homotopy we also consider arithmetic quotients of a self adjoint homogeneous cone there is a canonical mapping from the reductive borel serre compactification to the standard compactification of such a locally symmetric cone we show that this projection when restricted to the closure of a polyhedral cone has contractible fibers

the geisser levine method revisited and algebraic cycles over a finite field we reformulate part of the arguments of t geisser and m levine relating motivic cohomology with finite coefficients to truncated etale cohomology with finite coefficients 9 10 this reformulation amounts to a uniqueness theorem for motivic cohomology and shows that the geisser levine method can be applied generally to compare motivic cohomology with other types of cohomology theories we apply this to prove an equivalence between conjectures of tate and beilinson on cycles in characteristic p and a vanishing conjecture for continuous etale cohomology

the bloch kato conjecture and a theorem of suslin voevodsky we give a new proof of the theorem of suslin voevodsky which shows that the bloch kato conjecture implies a portion of the beilinsonlichtenbaum conjectures our proof does not rely on resolution of singularities and thereby extends the suslin voevodsky theorem to positive characteristic

the semigroup generated by 2 2 conservation laws consider the cauchy problem for a strictly hyperbolic 2 2 system of conservation laws in one space dimension ie1 01 assuming that each characteristic field is either linearly degenerate or genuinely nonlinear this paper develops a new algorithm based on wave front tracking which yields a cauchy sequence of approximate solutions converging to a unique limit depending continuously on the initial data the solutions that we obtain constitute a semigroup s defined on a set ie1 02 of integrable functions with small total variation for some lipschitz constant l we have the estimate ie1 03

on weight truncations in the motivic setting abstract using punctual gluing of t structures we construct an analogue of s morel s weight truncation functors for certain weight profiles in the setting of motivic sheaves as an application we construct a canonical motivic analogue of the intersection complex for an arbitrary threefold over any field k we are also able to recover certain invariants of singularities motivically

on the tautological ring of mg we prove that any product of tautological classes of g of degreed in the chow ring of g with rational coefficients vanishes ford g 2 and is proportional to the class of the hyperelliptic locus in degreeg 2

event based robust control for uncertain nonlinear systems using adaptive dynamic programming in this paper the robust control problem for a class of continuous time nonlinear system with unmatched uncertainties is investigated using an event based control method first the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function under the event based mechanism we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition that is the designed event based controller is robust to the original uncertain system note that the event based controller is updated only when the triggering condition is satisfied which can save the communication resources between the plant and the controller then a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies the stability of the closed loop system with the event based control policy and the augmented control policy is analyzed using the lyapunov approach furthermore we prove that the minimal intersample time is bounded by a nonzero positive constant which excludes zeno behavior during the learning process finally two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme

dimensional homotopy t structures in motivic homotopy theory the aim of this work is to construct certain homotopy t structures on various categories of motivic homotopy theory extending works of voevodsky morel deglise and ayoub we prove these t structures possess many good properties some analogous to those of the perverse t structure of beilinson bernstein and deligne we compute the homology of certain motives notably in the case of relative curves we also show that the hearts of these t structures provide convenient extensions of the theory of homotopy invariant sheaves with transfers extending some of the main results of voevodsky these t structures are closely related to gersten weight structures as defined by bondarko

action of correspondences on filtrations on cohomology and 0 cycles of abelian varieties we prove that given a symmetrically distinguished correspondence of a suitable complex abelian variety which includes any abelian variety of dimension at most 5 powers of complex elliptic curves etc that vanishes as a morphism on a certain quotient of its middle singular cohomology then it vanishes as a morphism on the deepest part of a particular filtration on the chow group of 0 cycles of the abelian variety as a consequence we prove that an automorphism of such an abelian variety that acts as the identity on a certain quotient of its middle singular cohomology acts as the identity on the deepest part of this filtration on the chow group of 0 cycles of the abelian variety as an application we prove that for the generalized kummer variety associated to a complex abelian surface and the automorphism induced from a symplectic automorphism of the complex abelian surface the automorphism of the generalized kummer variety acts as the identity on a certain subgroup of its chow group of 0 cycles

optimal sampling and performance comparison of periodic and event based impulse control in this technical note several issues of periodic and event based impulse control for a class of second order stochastic systems are considered including the optimal sampling and performance comparison the procedures are provided to design the optimal sampling period for periodic sampling and optimal threshold for event based sampling it is demonstrated that event based impulse control outperforms periodic impulse control in terms of mean square state variations while both having the same average control rate

event based agreement protocols for multi agent networks abstract this paper considers an average consensus problem for multiple integrators over fixed or switching undirected and connected network topologies event based control is used on each agent to drive the state to their initial average eventually an event triggering scheme is designed based on a quadratic lyapunov function the derivative of the lyapunov function is made negative by an appropriate choice of the event condition for each agent the event condition is sampled data and distributed in the sense that the event detector uses only neighbor information and local computation at discrete sampling instants the event based protocol design is illustrated with simulations

simple hironaka resolution in characteristic zero building upon work of villamayor and bierstone milman we give a proof of the canonical hironaka principalization and desingularization the idea of homogenized ideals introduced in the paper gives a priori the canonicity of algorithm and radically simplifies the proof

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

intermediate extension of chow motives of abelian type abstract in this article we give an unconditional construction of a motivic analogue of the intermediate extension in the context of chow motives of abelian type our main application concerns intermediate extensions of chow motives associated to kuga families to the baily borel compactification of a shimura variety

on the convergence rate of vanishing viscosity approximations given a strictly hyperbolic genuinely nonlinear system of conservation laws we prove the a priori boundu t u e t l1 o 1 1 t e ln e on the distance between an exact bv solution u and a viscous approximation u e letting the viscosity coefficient e 0 in the proof starting from u we construct an approximation of the viscous solution u e by taking a mollification u e and inserting viscous shock profiles at the locations of finitely many large shocks for each fixed e error estimates are then obtained by introducing new lyapunov functionals that control interactions of shock waves in the same family and also interactions of waves in different families c 2004 wiley periodicals inc

some new examples in the theory of quadratic forms we construct a 6 dimensional anisotropic quadratic form phi and a 4 dimensional quadratic form psi over some fieldf such that phi becomes isotropic over the function field f psi but every proper subform of phi is still anisotropic over f psi it is an example of non standard isotropy with respect to some standard conditions of isotropy for 6 dimensional forms over function fields of quadrics known previously besides of that we produce an 8 dimensional quadratic form phi with trivial determinant such that the index of the clifford invariant of phi is 4 but phi can not be represented as a sum of two 4 dimensional forms with trivial determinants using this we find a 14 dimensional quadratic form with trivial discriminant and clifford invariant which is not similar to a difference of two 3 fold pfister forms the proofs are based on computations of the topological filtration on the grothendieck group of certain projective homogeneous varieties to do these computations we develop several methods covering a wide class of varieties and being to our mind of independent interest

chow groups are finite dimensional in some sense when s is a surface with pg s 0 mumford proved that its chow group a s is not finite dimensional in some sense in this paper we propose another definition of finite dimensionality for the chow groups using this new definition at least the chow group of some surface s with pg s 0 for example the product of two curves becomes finite dimensional the finite dimensionality of the chow groups follows from the finite dimensionality of the chow motives it turns out that the finite dimensionality of the chow motives is a very strong property for example we can prove bloch s conjecture representability of the chow groups of surfaces with pg s 0 under the assumption that the chow motive of s is finite dimensional

bv solutions of the semidiscrete upwind scheme consider the strictly hyperbolic system of conservation laws u t f u x 0 1 where u n f n n smooth the system is said to be strictly hyperbolic provided that the jacobian matrix a u df u has n distinct eigenvalues 1 u n u

dirac operators in tensor categories and the motive of quaternionic modular forms we define a motive whose realizations afford modular forms of arbitrary weight on an indefinite division quaternion algebra this generalizes work of iovita spiess to odd weights in the spirit of jordan livne it also generalizes a construction of scholl to indefinite division quaternion algebras and provides the first motivic construction of new subspaces of modular forms

weights on cohomology invariants of singularities and dual complexes we study the weight filtration on the cohomology of a proper complex algebraic variety and obtain natural upper bounds on its size when it is the exceptional divisor of a singularity we also give bounds for the cohomology of links the invariants of singularities introduced here gives rather strong information about the topology of rational and related singularities

on the chow motive of an abelian scheme with non trivial endomorphisms let x be an abelian scheme over a base variety s with endomorphism algebra d we prove that the relative chow motive r x s has a canonical decomposition as a direct sum of motives r whereruns over an explicitly determined finite set of irreducible representations of the group d op such that r seen as a functor from chow motives to d op representations is isotypic our decomposition refines the motivic decomposition of deninger and murre as well as beauville s decomposition of the chow group the second main result is that we construct a canonical generalized motivic lefschetz decomposition inspired by work of looijenga and lunts in 17 the role of sl2 in the classical theory is here replaced by a larger lie algebra generated by all lefschetz and lambda operators associated to non degenerate line bundles we construct an action of this larger lie algebra on r x s and deduce from this a generalized lefschetz decomposition we also give a precise structure result for the lefschetz components that arise as an application of our techniques we provide a positive answer to a question of claire voisin concerning the analogue for abelian varieties of a conjecture of beauville ams 2010 mathematics subject classification 14c15 14k05