the critical behavior of dimer dimer surface reaction models monte carlo and finite size scaling investigation two models based upon the well known mechanism for the oxidation of hydrogen on transition metal surfaces which may also apply to generic dimerdimer surface reaction processes of the type 1 2 a2 b2 b2a are proposed and studied on the square lattice of sidel l 600 by means of monte carlo simulations and finite size analysis both models exhibit irreversible kinetic phase transitions ipt from a reactive state with sustained production of b2a molecules to off equilibrium surface poisoned states with the reactants i e without production the location of the critical points at which the ipts take place in thel limit is determined by means of a finite size scaling analysis also it is shown that at criticality some relevant quantities such as the rate of b2a production and the coverage with the reactants exhibit simple power law behavior which allow us to determine the corresponding critical exponents

asymptotic expansion of complex integrals via mellin transform soit x une variete complexe connexe a n 1 dimensions et f une fonction holomorphe non constante sur x avec 0 comme seule valeur critique possible on demontre un theoreme de developpement asymptotique d integrales complexes par la transformation de mellin

regularizations of residue currents under assumptions about complete intersection we prove that coleff herrera type currents satisfy a robust calculus in the sense that natural regularizations of such currents can be multiplied to yield regularizations of the coleff herrera product of the currents

regularizations of products of residue and principal value currents let f 1 and f 2 be two functions on some complex n manifold and let be a test form of bidegree n n 2 assume that f 1 f 2 defines a complete intersection the integral of f 1 f 2 on f 1 2 e lunate 1 f 2 2 e lunate 2 is the residue integral i f1 f 2 e lunate 1 e lunate 2 it is in general discontinuous at the origin let 1 and 2 be smooth functions on 0 such that j 0 0 and j 1 we prove that the regularized residue integral defined as the integral of over 1 over 2 f 1 f 2 where j j f j 2 e lunate j is holder continuous on the closed first quarter and that the value at zero is the coleff herrera residue current acting on in fact we prove that if is a test form of bidegree n n 1 then the integral of 1 over 2 f 1 f 2 is holder continuous and tends to the over potential 1 f 1 over 1 f 2 of the coleff herrera current acting on more generally let f 1 and f 2 be sections of some vector bundles and assume that f 1 f 2 defines a complete intersection there are associated principal value currents u f and u g and residue currents r f and r g the residue currents equal the coleff herrera residue currents locally one can give meaning to formal expressions such as e g u f r g in such a way that formal leibnitz rules hold our results generalize to products of these currents as well 2006 elsevier inc all rights reserved

supervisory control of families of linear set point controllers 2 robustness a simply structured high level controller called a supervisor has recently been proposed in part i of this article ibid vol 41 1996 for the purpose of orchestrating the switching of a sequence of candidate set point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input the process is assumed to be modeled by an siso linear system whose transfer function is in the union of a number of subclasses each subclass being small enough so that one of the candidate controllers would solve the set point tracking problem if the process transfer function was to be one of the subclass members this paper proves that without any further modification the same supervisor described in part i can also perform this function in the face of norm bounded unmodeled dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs whether they are constant or not

explicit serre duality on complex spaces abstract in this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization as well as a new analytic proof of serre duality on any reduced pure n dimensional paracompact complex space x at the core of the paper is the introduction of certain fine sheaves b x n q of currents on x of bidegree n q such that the dolbeault complex b x n becomes in a certain sense a dualizing complex in particular if x is cohen macaulay then b x n is an explicit fine resolution of the grothendieck dualizing sheaf

abelian differentials on singular varieties and variations on a theorem of lie griffiths we compare various notions of meromorphic and holomorphic differential forms on singular analytic varieties in particular we find that every meromorphic form gives rise to a canonical principal value current with support in the variety demanding that this current be closed we obtain a useful analytic description of the dualizing sheaf we then go on to generalize the lie griffiths theorem on one hand it is shown that a rational trace is enough to ensure algebraicity of the data on the other hand we prove that zero trace implies that the form is holomorphic in the sense of currents in fact we prove a more general local version of the theorem

ideals of smooth functions and residue currents abstract let f f 1 f m be a holomorphic mapping in a neighborhood of the origin in c n we find sufficient condition in terms of residue currents for a smooth function to belong to the ideal in c or ck generated by f if f is a complete intersection the condition is necessary more generally we give a sufficient condition for an element of class c or ck in the koszul complex induced by f to be exact for the proofs we introduce explicit homotopy formulas for the koszul complex induced by f

the bar partial equation on a non reduced analytic space let x be a possibly non reduced analytic space of pure dimension we introduce a notion of overline partial equation on x and prove a dolbeault grothendieck lemma we obtain fine sheaves mathcal a x q of 0 q currents so that the associated dolbeault complex yields a resolution of the structure sheaf mathscr o x our construction is based on intrinsic semi global koppelman formulas on x

various approaches to products of residue currents abstract we describe various approaches to coleff herrera products of residue currents r j of cauchy fantappie leray type associated to holomorphic mappings f j more precisely we study to which extent exterior products of natural regularizations of the individual currents r j yield regularizations of the corresponding coleff herrera products our results hold globally on an arbitrary pure dimensional complex space

residue currents with prescribed annihilator ideals on singular varieties given an ideal mathcal j on a complex manifold andersson and wulcan constructed explicitly a current r mathcal j such that the annihilator of r mathcal j is mathcal j generalizing the duality theorem for coleff herrera products we describe a way to generalize this construction to ideals on singular varieties

integral formulas and an explicit version of the fundamental principle soit p c n c m une application polynomiale et on considere le systeme d equations differentielles p j d f t 0 j 1 m ou d i t et f est une fonction lisse dans un domaine convexe borne r n on presente une version explicite qui emploie des formules integrales et des courants residus du principe fondamental de ehrenpreis et palamodov

decomposition of residue currents given a submodule j o r 0 and a free resolution of j one can de ne a certain vector valued residue current whose annihilator is j we make a decomposition of the current with respect to assj that corresponds to a primary decomposition of j as a tool we introduce a class of currents that includes usual residue and principal value currents in particular these currents admit a certain type of restriction to analytic varieties and more generally to constructible sets

brief paper tracking and synchronisation for a class of pwa systems in this paper the tracking problem for a class of discontinuous piecewise affine pwa systems is addressed we propose an observer based output feedback control design consisting of a feedforward a piecewise affine feedback law and a model based observer solving the tracking problem these synthesis results can also be employed to tackle the master slave synchronisation problem for pwa systems it is shown that for certain classes of pwa systems the design is characterised in terms of linear matrix inequalities the results are illustrated by application to mechanical systems with discontinuous friction characteristics

dynamic critical exponents of discontinuous kinetic phase transitions in surface reaction models abstract dynamical critical exponents of three surface reaction models a monomer monomer process and two variants of the dimer dimer process which exhibit discontinuous kinetics phase transitions kpts are evaluated the obtained exponents differ from those characteristic of continuous kpts and suggest that the three models belongs to distinct universality classes

maximum rank of a legendrian web abstract we propose the legendrian web in a contact three manifold as a second order generalization of the planar web an abelian relation for a legendrian web is analogously defined as an additive equation among the first integrals of its foliations for a class of legendrian d webs defined by simple second order ode s we give an algebraic construction of d d 1 d 2 2 d 3 6 linearly independent abelian relations we then employ the method of local differential analysis and the theory of linear differential systems to show that d is the maximum rank of a legendrian d web in the complex analytic category we give a possible projective geometric interpretation of d as an analogue of castelnuovo bound for degree 2 d surfaces in the 3 quadric q 3 p 4 via the duality between p 3 and q 3 associated with the rank two complex simple lie group sp 2 c the legendrian 3 webs of maximum rank three are analytically characterized and their explicit local normal forms are found for an application we give an alternative characterization of a darboux super integrable metric as a two dimensional riemannian metric g which admits a mate metric g such that a legendrian 3 web naturally associated with the geodesic foliations of the pair g has maximum rank

the algorithmic analysis of hybrid systems we present a general framework for the formal specification and algorithmic analysis of hybrid systems a hybrid system consists of a discrete program with an analog environment we model hybrid systems as finite automata equipped with variables that evolve continuously with time according to dynamical laws for verification purposes we restrict ourselves to linear hybrid systems where all variables follow piecewise linear trajectories we provide decidability and undecidability results for classes of linear hybrid systems and we show that standard program analysis techniques can be adapted to linear hybrid systems in particular we consider symbolic model checking and minimization procedures that are based on the reachability analysis of an infinite state space the procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space we also present approximation techniques for dealing with systems for which the iterative procedures do not converge

weighted koppelman formulas and the equation on an analytic space let x be an analytic space of pure dimension we introduce a formalism to generate intrinsic weighted koppelman formulas on x that provide solutions to the partial derivative over bar equation we obtain new existence results for the partial derivative over bar equation as well as new proofs of various known results c 2011 elsevier inc all rights reserved

koppelman formulas on flag manifolds and harmonic forms we construct koppelman formulas on manifolds of flags in mathbb c n for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals as an application we obtain new explicit proofs of some vanishing theorems of the bott borel weil type by solving the corresponding bar partial equation we also construct reproducing kernels for harmonic p q forms in the case of grassmannians

sparse effective membership problems via residue currents we use residue currents on toric varieties to obtain bounds on the degrees of solutions to polynomial ideal membership problems our bounds depend on the volume of the newton polytope of the polynomial system and are therefore well adjusted to sparse polynomial systems we present sparse versions of max nother s af bg theorem macaulay s theorem and kollar s effective nullstellensatz as well as recent results by hickel and andersson gotmark

piecewise linear quadratic optimal control the use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control lower bounds on the optimal control cost are obtained by semidefinite programming based on the bellman inequality this also gives an approximation to the optimal control law an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law a compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

residue currents constructed from resolutions of monomial ideals given a free resolution of an ideal j of holomorphic functions one can construct a vector valued residue current r whose annihilator is precisely j in this paper we compute r in case j is a monomial ideal and the resolution is a cellular resolution in the sense of bayer and sturmfels a description of r is given in terms of the underlying polyhedral cell complex and it is related to irreducible decompositions of j

on the duality theorem on an analytic variety the duality theorem for coleff herrera products on a complex manifold says that if f f 1 f p defines a complete intersection then the annihilator of the coleff herrera product f equals locally the ideal generated by f this does not hold unrestrictedly on an analytic variety z we give necessary and in many cases sufficient conditions for when the duality theorem holds these conditions are related to how the zero set of f intersects certain singularity subvarieties of the sheaf mathcal o z

asymptotic stability of piecewise affine systems with filippov solutions via discontinuous piecewise lyapunov functions asymptotic stability of continuous time piecewise affine systems defined over a polyhedral partition of the state space with possible discontinuous vector field on the boundaries is considered in the first part of the paper the feasible filippov solution concept is introduced by characterizing single mode caratheodory sliding mode and forward zeno behaviors then a global asymptotic stability result through a possibly discontinuous piecewise lyapunov function is presented the sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing unreachable and caratheodory boundaries it is shown that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic lyapunov functions and using the cone copositivity approach several examples illustrate the theoretical arguments and the effectiveness of the stability result

existence and uniqueness of solutions of piecewise nonlinear systems abstract in this paper we consider the existence and the uniqueness of solutions of piecewise nonlinear systems we will present some necessary and sufficient conditions for the existence and the uniqueness of solutions of this class of systems

residue current approach to ehrenpreis malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags abstract we introduce a ring h of partial difference differential operators with constant coefficients initially defined by h glusing lursen for ordinary difference differential operators and investigate its cohomological properties combining this ring theoretic observation with the integral representation technique developed by m andersson we solve a certain type of division with bounds in the last section we deduce from this injectivity properties of various function modules over h as well as the density results of exponential polynomial solutions for partial difference differential equations

koppelman formulas on grassmannians we construct koppelman formulas on grassmannians for forms with values in any holomorphic line bundle as well as in the tautological vector bundle and its dual as an application we obtain new explicit proofs of some vanishing theorems of the bott borel weil type by solving the corresponding equation we also relate the projection part of our formulas to the bergman kernels associated to the line bundles

trajectory tracking control of bimodal piecewise affine systems this paper deals with a trajectory tracking problem for a class of bimodal piecewise affine systems which is inherently difficult because of the discontinuous changes of their vector fields first we introduce an error variable and an error system as a generalization of the tracking error and its system as an error variable a function switched by the mode of a piecewise affine system is adopted to overcome the inherent difficulty in trajectory tracking control of piecewise affine systems next we design a tracking controller which stabilizes the error system using a lyapunov like function which can be applied to systems including state jumps furthermore the feasibility condition of tracking for siso piecewise linear systems is simplified finally a numerical example is given to illustrate the effectiveness of the proposed method

regulator synthesis for bimodal linear systems this technical note presents a regulator synthesis approach for switched bimodal linear systems where it is desired to achieve regulation against known disturbance or reference signals first a set of observer based q parameterized stabilizing controllers for the switched system is constructed then regulation conditions for the switched system are obtained and a regulator synthesis method is derived based on iteratively solving a set of linear matrix inequalities finally a numerical example is presented to illustrate the effectiveness of the proposed method

division formulas on projective varieties we introduce a division formula on a possibly singular projective subvariety x of complex projective space mathbb p n which e g provides explicit representations of solutions to various polynomial division problems on the affine part of x especially we consider a global effective version of the briancon skoda huneke theorem

global effective versions of the briancon skoda huneke theorem we prove global effective versions of the briancon skoda huneke theorem our results extend to singular varieties a result of hickel on the membership problem in polynomial ideals in cn and a related theorem of ein and lazarsfeld for smooth projective varieties the proofs rely on known geometric estimates and new results on multivariable residue calculus

courants du type residuel attaches a une intersection complete abstract we construct in complete intersection s case elementary currents which describe the local ideal and give a decomposition in it for holomorphic function

tissus algebriques exceptionnels in pirio and trepreau int math res not imrn doi 10 1093 imrn rnu066 2014 it has been proved that for r 1 n ge 2 and d ge r 1 n 1 2 a d web of t ype r n with maximal rank is algebraizable in the classical sense except maybe when n ge 3 and d r 2 n 1 1 in the present paper one considers this particular case under these hypotheses on n and d one constructs some examples of exceptional algebraic webs these are generalized algebraic webs of maximal rank that are not algebraizable in the classical sense

on the intersection of algebraic curves and hypersurfaces many classical theorems about the intersection of plane algebraic curves can be derived from and generalized by the algebraic theory of residues in higher dimensional spaces one obtains results about the intersection of curves and hypersurfaces in various degrees of generality this was pointed out f i in s gh k2 and hu in the present note we wish to prove higher dimensional analogues of theorems of waring g humbert and reiss for arbitrary curves in affine n space and their intersection with hypersurfaces see theorems 4 1 5 1 and 6 2 below by a curve hypersurface we mean a closed subscheme in projective or affine n space of pure dimension 1 pure codimension 1 having no embedded components our considerations are based on the residue theorem for complete integral algebraic curves

integral representation with weights ii division and interpolation let f be a r m matrix of holomorphic functions that is generically surjective we provide explicit integral representation of holomorphic such that f provided that is holomorphic and annihilates a certain residue current with support on the set where f is not surjective we also consider formulas for interpolation as applications we obtain generalizations of various results previously known for the case r 1

critical exponents for a dimer dimer irreversible surface reaction abstract a dimer dimer reaction model of the type a2 b2 2ab is investigated by means of computer simulations the desorption of b2 dimer with probability p is studied here we investigate the critical behaviour the critical exponents of our model do not fall into the reggeon field theory or directed percolation universality class the universality class of the reaction changes with changes in p

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

residual bar partial cohomology and the complex radon transform on subvarieties of mathbb c p n we show that the complex radon transform realizes an isomorphism between the quotient space of residual bar partial cohomologies of a locally complete intersection algebraic subvariety in a linearly concave domain of mathbb c p n and the space of holomorphic solutions of the associated homogeneous system of differential equations with constant coefficients in the dual domain in mathbb c p n

estimates of solutions of the h p and bmoa corona problem we prove new sharper estimates of solutions to the h p corona problem in strictly pseudoconvex domains in particular we show that the constant is independent of the number of generators we also obtain sharper estimates for solutions to the bmoa corona problem the proofs also lead to new results about the taylor spectrum of analytic toeplitz operators on h p and bmoa

universal computation and other capabilities of hybrid and continuous dynamical systems we explore the simulation and computational capabilities of hybrid and continuous dynamical systems the continuous dynamical systems considered are ordinary differential equations odes for hybrid systems we concentrate on models that combine odes and discrete dynamics e g finite automata we review and compare four such models from the literature notions of simulation of a discrete dynamical system by a continuous one are developed we show that hybrid systems whose equations can describe a precise binary timing pulse exact clock can simulate arbitrary reversible discrete dynamical systems defined on closed subsets of r n the simulations require continuous odes in ir2n with the exact clock as input all four hybrid systems models studied here can implement exact clocks we also prove that any discrete dynamical system in rn can be simulated by continuous odes in rt2n 1 we use this to show that smooth odes in ri3 can simulate arbitrary turing machines and hence possess the power of universal computation we use the famous asynchronous arbiter problem to distinguish between hybrid and continuous dynamical systems we prove that one cannot build an arbiter with devices described by a system of lipschitz odes on the other hand all four hybrid systems models considered can implement arbiters even if their odes are lipschitz

complementarity modeling of hybrid systems a complementarity framework is described for the modeling of certain classes of mixed continuous discrete dynamical systems the use of such a framework is well known for mechanical systems with inequality constraints but we give a more general formulation which also applies for instance to switching control systems the main theoretical results in the paper are concerned with uniqueness of smooth continuations the solution of this problem requires the construction of a map from the continuous state to the discrete state a crucial technical tool is the so called linear complementarity problem from mathematical programming and we introduce various generalizations of this problem

effective bezout identities in q z1 zn abstract if p sub 1 p sub m are n variate polynomials with integral coefficients and no common zeros in c exp n brownawell has shown in 1986 that there exist q sub 1 q sub m polynomials with integral coefficients and nu is an element of z such that p sub 1 q sub 1 p sub m q sub m nu and max deg q sub j max deg p sub j exp n on the other hand if h logarithm of the largest coefficient of all the p sub j and h sub 1 is the corresponding quantity for the q sub j then there is no sharp estimate of h sub 1 in terms of h and max deg p sub j in this paper we show that when the variety of common zeros at infinity of the p sub j is discrete then essentially we have h sub 1 d exp cn h for an absolute constant c if there were an algorithm to compute the q sub j in d exp cn time one would obtain exactly the above estimate current algorithms require about d exp n squared operations

integral representation with weights i we describe a new approach to representation formulas for holomorphic functions including the cauchy fantappie leray formula and provide a general method to generate weighted formulas

hybrid model reference adaptive control of piecewise affine systems this paper is concerned with the derivation of a model reference adaptive control mrac scheme for multimodal piecewise affine pwa and piecewise linear systems the control allows the plant to track asymptotically the states of a multimodal piecewise affine or smooth reference model the reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

characterization of well posedness of piecewise linear systems one of the basic issues in the study of hybrid systems is the well posedness existence and uniqueness of solutions problem of discontinuous dynamical systems the paper addresses this problem for a class of piecewise linear discontinuous systems under the definition of solutions of caratheodory the concepts of jump solutions or of sliding modes are not considered here in this sense the problem to be discussed is one of the most basic problems in the study of well posedness for discontinuous dynamical systems first we derive necessary and sufficient conditions for bimodal systems to be well posed in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions next its extensions to the multimodal case are discussed as an application to switching control in the case that two state feedback gains are switched according to a criterion depending on the state we give a characterization of all admissible state feedback gains for which the closed loop system remains well posed

on the universality classes of the discontinuous irreversible phase transitions of a multicomponent reaction system discontinuous irreversible phase transitions ipts from active states to absorbing poisoned states in a trimolecular irreversible reaction model which involves one monomer and two different dimers are studied by means of monte carlo simulations evaluated dynamic critical exponents strongly suggest that each first order ipt has its own universality class

explicit representation of membership in polynomial ideals we introduce a new division formula on projective space which provides explicit solutions to various polynomial division problems with sharp degree estimates we consider simple examples as the classical macaulay theorem as well as a quite recent result by hickel related to the effective nullstellensatz we also obtain a related result that generalizes max noether s classical af bg theorem

a dolbeault grothendieck lemma on complex spaces via koppelman formulas let x be a complex space of pure dimension we introduce fine sheaves a x q of 0 q currents which coincides with the sheaves of smooth forms on the regular part of x so that the associated dolbeault complex yields a resolution of the structure sheaf hol x our construction is based on intrinsic and quite explicit semi global koppelman formulas

segre numbers a generalized king formula and local intersections let mathcal j be an ideal sheaf on a reduced analytic space x with zero set z we show that the lelong numbers of the restrictions to z of certain generalized monge ampere products dd c log f 2 k where f is a tuple of generators of mathcal j coincide with the so called segre numbers of mathcal j introduced independently by tworzewski achilles manaresi and gaffney gassler more generally we show that these currents satisfy a generalization of the classical king formula that takes into account fixed and moving components of vogel cycles associated with mathcal j a basic tool is a new calculus for products of positive currents of bochner martinelli type we also discuss connections to intersection theory

controllability and observability of hybrid systems abstract a special class of hybrid systems is considered whose state space is a cross product space of a euclidean space and a finite state space such models may be used to represent systems subject to known abrupt parameter variations such as commu tated networks they may also be used to approximate some types of time varying systems controllability observability and stability of hybrid systems are inves tigated in particular a necessary and sufficient algebraic condition a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived moreover a simple sufficient stability condition is provided

the kashiwara conjugation and wave front sets of regular holonomic distributions on a complex manifold if a distributionu on a complex manifoldx is a solution of a regular holonomicdx module one shows that its wave front sets coincide with the characteristic variety of thedx module generated byu the proof relies essentially on a microlocal form of kashiwara s conjugation functor as a byproduct regular holonomicex modules are locally embedded into the sheaf of temperate microfunctions