cartan decomposition subgroups of 2 for g sl 3 r and g so 2 n we give explicit practical conditions that determine whether or not a closed connected subgroup h of g has the property that there exists a compact subset c of g with chc g to do this we fix a cartan decomposition g ka k of g and then carry out an approximate calculation of khk n a for each closed connected subgroup h of g

a preparation theorem for weierstrass systems it is shown that lion and rolin s preparation theorem for globally subanalytic functions holds for the collection of definable functions in any expansion of the real ordered field by a weierstrass system

approximate generalizations and computational experiments in this paper i demonstrate how one can generalize finitely many examples to statements about infinite classes of economic models if there exist upper bounds on the number of connected components of one dimensional linear subsets of the set of parameters for which a conjecture is true one can conclude that it is correct for all parameter values in the class considered except for a small residual set once one has verified the conjecture for a predetermined finite set of points i show how to apply this insight to computational experiments and spell out assumptions on the economic fundamentals that ensure that the necessary bounds on the number of connected components exist

distributed model predictive control of linear systems with stochastic parametric uncertainties and coupled probabilistic constraints this paper investigates the distributed stochastic model predictive control dsmpc for multiple constrained dynamically decoupled subsystems subject to stochastic uncertainties in the parameters to obtain a computationally tractable formulation for real control applications a spectral method called generalized polynomial chaos expansions gpces is utilized to propagate the stochastic parametric uncertainties through the system model by using gpces combined with the probabilistic information on the uncertainties both local probabilistic constraints and coupled probabilistic constraints are converted explicitly into deterministic convex second order cone constraints the constraints can achieve satisfaction of coupled probabilistic constraints in a distributed way by permitting a single subsystem to optimize a local cost function at each time step while freezing the plans of others the proposed gpces based dsmpc algorithm guarantees recursive feasibility with respect to both local and coupled prob

on the stability and instability regions of non conservative continuous system under partially follower forces abstract the transition between stability and instability of a uniform cantilever beam subjected to a partially follower load is discussed by means of the finite element method the stability diagram in terms of the load versus the non conservativeness loading parameter is obtained both in the hypothesis of linearized small displacements and non linearized large displacements analysis it is found that the regions of divergence and flutter instability of the finite element model of continuous system are quite different from the corresponding ones obtained for the classical 2 degrees of freedom ziegler s model i e the inverted double pendulum both quantitatively and qualitatively the transition from the 2 degrees of freedom model to the continuous model is investigated through the study of some multi degrees of freedom approximation models i e the 3 4 5 and 10 degrees of freedom models of the continuous column finally the effect of damping in the stability diagram of the finite element model of continuous system is discussed and the destabilizing effect of small damping is emphasized

on the failure of static stability analyses of nonconservative systems in regions of divergence instability abstract the stability of perfect bifurcational discrete dissipative systems under follower loads in regions of existence non existence of adjacent equilibria is thoroughly re examined in the light of recent progress in nonlinear dynamics a general theory for such nongradient systems described by autonomous ordinary differential equations is developed conditions for the existence of adjacent equilibria the stability of precritical critical and postcritical states as well as for different types of local bifurcations are established focusing attention on the interaction of geometric nonlinearities and vanishing damping new findings contradicting widely accepted results of the classical linear analysis are discovered in a small region of adjacent equilibria near a compound branching point which is explicitly determined an interaction of two consecutive postbuckling modes occurs related to the following phenomena in case of vanishing damping loss of stability may occur via a hopf dynamic bifurcation prior to static divergence buckling moreover the critical states of divergence instability may be associated with a double zero jacobian eigenvalue satisfying also the conditions of a hopf local bifurcation besides local dynamic bifurcations global bifurcations are also found an example is used to illustrate the qualitative findings

non fragile observer based sliding mode control for markovian jump systems with mixed mode dependent time delays and input nonlinearity this paper is concerned with the state estimation and the sliding mode control smc for a class of markovian jump systems with mixed mode dependent time delays and input nonlinearity a non fragile observer is designed to estimate the system states and an observer based smc is synthesized to ensure the reachability of the sliding surfaces in the state estimation space by constructing a novel mode dependent lyapunov krasovskii functional some new criteria are established for the existence and the solvability of the desired observer based sliding mode controller finally numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results

extended variational formulations and f e models for nonlinear beams under nonconservative loading abstract for nonconservative mechanical systems classical variational principles do not hold true hence the principle of incremental virtual work is usually taken as a convenient foundation for finite element solution methods 2 8 9 recent results on the so called inverse problem of calculus of variations however lead to extended variational formulations which can be provided even for nonconservative systems in the present paper this approach is used for the particular case of a nonlinear beam subjected to a co planar follower static loading suitable finite element models are deduced from the extended variational principle and their numerical performance is assessed by means of some meaningful examples

integrability of oscillatory functions on local fields transfer principles for oscillatory functions on local fields coming from motivic exponential functions we show that integrability over q n p implies integrability over f p t n for large p and vice versa more generally the integrability only depends on the isomorphism class of the residue field of the local field once the characteristic of the residue field is large enough this principle yields general local integrability results for harish chandra characters in positive characteristic as we show in other work transfer principles for related conditions such as boundedness and local integrability are also obtained the proofs rely on a thorough study of loci of integrability to which we give a geometric meaning by relating them to zero loci of functions of a specific kind

valuation theory of exponential hardy fields i we describe the valuation theoretic properties of the hardy fields associated to models of t exp where t is the theory of a polynomially bounded o minimal expansion of the reals and exp is the real exponential function we deduce that t exp has levels with parameters and is exponentially bounded we establish a maximality property of h mathbb r rm an powers the hardy field of the expansion by the restricted analytic functions and power functions

relational queries over interpreted structures we rework parts of the classical relational theory when the underlying domain is a structure with some interpreted operations that can be used in queries we identify parts of the classical theory that go through as before when interpreted structure is present parts that go through only for classes of nicely behaved structures and parts that only arise in the interpreted case the first category include a number of results on language equivalence and expressive power characterizations for the active domain semantics for a variety of logics under this semantics quantifiers range over elements of a relational database the main kind of results we prove here are generic collapse results for generic queries adding operations beyond order does not give us extra power the second category includes results on the natural semantics under which quantifiers range over the entire interpreted structure we prove for a variety of structures natural active collapse results showing that using unrestricted quantification does not give us any extra power moreover for a variety of structures including the real field we give a set of algorithms for eliminating unbounded quantifications in favor of bounded ones furthermore we extend these collapse results to a new class of higher order logics that mix unbounded and bounded quantification we give a set of normal forms for these logics under special conditions on the interpreted structures as a by product we obtain an elementary proof of the fact that parity test is not definable in the relational calculus with polynomial inequality constraints we also give examples of structures with nice model theoretic properties over which the natural active collapse fails

definable sets in ordered structures i this paper introduces and begins the study of a well behaved class of linearly ordered structures the minimal structures the definition of this class and the corresponding class of theories the strongly dlminlmal theories is made in analogy with the notions from stability theory of minimal structures and strongly minimal theories theorems 2 1 and 2 3 respectively provide characterizations of 41 minimal ordered groups and rings several other simple results are collected in 3 the primary tool in the analysis of minimal structures is a strong analogue of ii forking symmetry given by theorem 4 2 this result states that any parametri cally definable unary function in an yminimal structure is piecewise either constant or an ore er preserving or reversing bijection of intervals the results that follow include the existence and uniqueness of prime models over sets theorem 5 1 and a characterization of all bto categorical aminimal structures theorem 6 1 1 introduction the class of linearly ordered structures has long been an im portant subject of concern to model theorists impressive results have been obtained in the study of models of several particular theories that extend the theory of linear order among those theories that have been approached successfully are peano arithmetic the theory of ordered abelian groups that of real closed fields and that of linear order itself yet very little has been done in the way of developing a general model theory for ordered structures in this paper we develop the model theory for a class of linearly ordered structures that we isolate by demanding that a structure in this class satisfy a condition whose effect is that the linear ordering and the algebraic part of the structure behave quite well with respect to one another let l be a finitary first order language and w an l structure a set of n tuples a c x is said to be parametrically definable if there is some l formula

tropical totally positive matrices abstract we investigate the tropical analogues of totally positive and totally nonnegative matrices these arise when considering the images by the nonarchimedean valuation of the corresponding classes of matrices over a real nonarchimedean valued field like the field of real puiseux series we show that the nonarchimedean valuation sends the totally positive matrices precisely to the monge matrices this leads to explicit polyhedral representations of the tropical analogues of totally positive and totally nonnegative matrices we also show that tropical totally nonnegative matrices with a finite permanent can be factorized in terms of elementary matrices we finally determine the eigenvalues of tropical totally nonnegative matrices and relate them with the eigenvalues of totally nonnegative matrices over nonarchimedean fields

tangent cones and c 1 regularity of definable sets abstract let x r n be a connected locally closed set which is definable in an o minimal structure we prove that the following three statements are equivalent i x is a c 1 manifold ii the tangent cone and the paratangent cone of x coincide at every point in x iii for every x x the tangent cone of x at the point x is a k dimensional linear subspace of r n k does not depend on x varies continuously in x and the density x x 3 2

the field of reals with multisummable series and the exponential function we show that the field of real numbers with multisummable real power series is model complete o minimal and polynomially bounded further expansion by the exponential function yields again a model complete and o minimal structure which is exponentially bounded and in which the gamma function on the positive real line is definable 2000 mathematics subject classification primary 03c10 32b05 32b20 secondary 26e05

on the elastic stability of uniform beams and circular arches under nonconservative loading the infinitesimal local stability of uniform beams and circular arches under the terminal nonconservative loading is studied the nonlinear equilibrium with large deflections is expressed in a closed form then the equations which govern a free motion about the equilibrium position are constructed the eigenvalue analysis of the linearized system of differential equations with varying coefficients is performed by the finite element concept and the subdomain collocation method

chaotic dynamics of the partially follower loaded elastic double pendulum abstract the non linear dynamics of the elastically restrained double pendulum with non conservative follower type loading and linear damping is re examined with specific reference to the occurrence of chaotic motion a local non linear perturbation analysis is performed showing that in three distinct regions of loading parameter space small initial disturbances will result in respectively 1 static equilibrium solutions 2 stable periodic motion and 3 initially large changes in amplitude due to a destabilizing effect of both linear and non linear forces a global numerical analysis confirms the theoretical findings for regions 1 and 2 and shows that in region 3 almost all solutions are chaotic it is suggested that chaos is triggered by a bifurcating cascade of large amplitude stable and unstable equilibrium points which may be explored by orbits only when the zero solution is destabilized by both linear and non linear forces although heuristically based this may be used as a practical and rather accurate predictive criterion for chaos to appear in the specific system

definable sets in ordered structures on introduit la notion de theorie o minimale des structures ordonnees une telle theorie etant telle que les sous ensembles definissables de ses modeles soient particulierement simples

stability of a stochastic two dimensional non hamiltonian system we study the top lyapunov exponent of the response of a two dimensional non hamiltonian system driven by additive white noise the origin is not a fixed point for the system however there is an invariant measure for the one point motion of the system in this paper we consider the stability of the two point motion by khasminskii s method of linearization along trajectories the specific system we consider is the third order truncated normal form of the unfolding of a hopf bifurcation we show that in the small noise limit the top lyapunov exponent always approaches zero from below and is thus negative for noise sufficiently small we also show that there exist open sets of parameters for which the top lyapunov exponent is positive thus the two point motion can be either stable or unstable while the stationary density that describes the one point motion always exists

smooth functions in o minimal structures abstract fix an o minimal expansion of the real exponential field that admits smooth cell decomposition we study the density of definable smooth functions in the definable continuously differentiable functions with respect to the definable version of the whitney topology this implies that abstract definable smooth manifolds are affine moreover abstract definable smooth manifolds are definably c diffeomorphic if and only if they are definably c 1 diffeomorphic

o minimal hauptvermutung for polyhedra i milnor discovered two compact polyhedra which are homeomorphic but not pl homeomorphic a counterexample to the hauptvermutung he constructed the homeomorphism by a finite procedure repeated infinitely often informally we call a procedure constructive if it consists of an explicit procedure that is repeated only finitely many times in this sense milnor did not give a constructive procedure to define the homeomorphism between the two polyhedra in the case where the homeomorphism is semialgebraic the author and yokoi proved that the polyhedra in r n are pl homeomorphic in that article the required pl homeomorphism was not constructively defined from the given homeomorphism in the present paper we obtain the pl homeomorphism by a constructive procedure starting from the homeomorphism we prove in fact that for any ordered field r equipped with any o minimal structure two definably homeomorphic compact polyhedra in r n are pl homeomorphic the o minimal hauptvermutung theorem 1 1 together with the fact that any compact definable set is definably homeomorphic to a compact polyhedron we can say that o minimal topology is tame

geometrically non linear formulation for three dimensional curved beam elements with large rotations this paper presents a geometrically non linear formulation gnl for the three dimensional curved beam elements using the total lagrangian approach the element geometry is constructed using co ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions the element displacement field is described using three translations at the element nodes and three rotations about the local axes the gnl three dimensional beam element formulations based on these element approximations are restricted to small nodal rotations between two successive load increments the element formulation presented here removes such restrictions this is accomplished by retaining non linear nodal terms in the definition of the element displacement field and the consistent derivation of the element properties the formulation presented here is very general and yet can be made specific by selecting proper non linear functions representing the effects of nodal rotations the details of the element properties are presented and discussed numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements a comparison of the results obtained from the present formulation with those available in the literature using a linearized element approximation clearly demonstrate the superiority of the formulation in terms of large load steps large rotations between two load steps and extremely good convergence characteristics during equilibrium iterations the displacement approximation of these elements is fully compatible with the isoparametric curved shell elements with large rotations and since the elements possess offset capability these elements can also serve as stiffeners for the curved shells

ilyashenko algebras based on transserial asymptotic expansions abstract we construct a hardy field that contains ilyashenko s class of germs at of almost regular functions found in 12 as well as all log exp analytic germs this implies non oscillatory behaviour of almost regular germs with respect to all log exp analytic germs in addition each germ in this hardy field is uniquely characterized by an asymptotic expansion that is an le series as defined by van den dries et al 7 as these series generally have support of order type larger than the notion of asymptotic expansion itself needs to be generalized

a game theoretic approach to fault diagnosis and identification of hybrid systems physical systems can fail for this reason the problem of identifying and reacting to faults has received a lot of attention in the control and computer science communities in this paper we study the fault diagnosis problem for hybrid systems from a game theoretical point of view a hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modelled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics we model hybrid systems as hybrid automata and add distinguished actions to describe faults we define a fault identification game on them using two players the environment and the identifier the environment controls the evolution of the system and chooses whether and when a fault occurs the identifier observes the external behaviour of the system and announces whether a fault has occurred or not existence of a winning strategy for the identifier implies that faults can be detected correctly while computing such a winning strategy corresponds to implementing an identifier for the system we will show how to determine the existence of a winning strategy and how to compute it for all decidable classes of hybrid automata that admit a finite bisimulation quotient

comparison theorems for o minimal singular co homology fct grant sfrh bpd 6015 2001 european research and training network hprn ct 2001 00271 raag

dissipativity analysis for stochastic memristive neural networks with time varying delays a discrete time case in this paper the dissipativity problem of discrete time memristive neural networks dmnns with time varying delays and stochastic perturbation is investigated a class of logical switched functions are put forward to reflect the memristor based switched property of connection weights and the dmnns are then recast into a tractable model based on the tractable model the robust analysis method and refined jensen based inequalities are applied to establish some sufficient conditions that ensure the mathcal q mathcal s mathcal r gamma text disspativity of dmnns two numerical examples are presented to illustrate the effectiveness of the obtained results

the real field with convergent generalized power series we construct a model complete and o minimal expansion of the field of real numbers in which each real function given on 0 1 by a series cnxn with 0 n and cn r n 1 is definable this expansion is polynomially bounded

the six grothendieck operations on o minimal sheaves in this paper we develop the formalism of the grothendieck six operations on o minimal sheaves the grothendieck formalism allows us to obtain o minimal versions of i derived projection formula ii universal coefficient formula iii derived base change formula iv kunneth formula v local and global verdier duality

characteristic cycles of constructible sheaves in his paper k kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds let x be a real analytic manifold and f a complex of sheaves of c vector spaces on x whose cohomology is constructible with respect to a subanalytic strati cation the characteristic cycle cc f is a subanalytic lagrangian cycle with in nite support and with values in the orientation sheaf of x in the cotangent bundle t x the de nition of cc f is morse theoretic heuristically cc f encodes the in nitesimal change of the euler characteristic of the stalks of f along the various directions in x it tends to be di cult in practice to calculate cc f explicitly for all but the simplest complexes f on the other hand the characteristic cycle construction has good functorial properties the behavior of cc f with respect to the operations of proper direct image verdier duality and non characteristic inverse image of f is well understood ks in this paper we describe the e ect of the operation of direct image by an open embedding combining our result with those that were previously known we obtain descriptions of cc rf f and cc f f analogous to those in ks for arbitrary morphisms f x y in the semi algebraic category and complexes f with semi algebraically constructible cohomology in e ect this provides an axiomatic characterization of the functor cc at least in the semi algebraic context our arguments do apply more generally in the subanalytic case but because statements become quite convoluted we shall not strive for the greatest degree of generality as a concrete application we consider the case of the ag manifold x of a complex semisimple lie algebra g here the weyl group w of g operates

ax lindemann for mathcal a _g we prove the ax lindemann theorem for the coarse moduli space a g of principally polarized abelian varieties of dimension g 1 we affirm the andre oort conjecture unconditionally for a g for g 6 and under grh for all g

global exponential stability in continuous time and discrete time delayed bidirectional neural networks convergence dynamics of continuous time bidirectional neural networks with constant transmission delays are studied without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions lyapunov functionals and halanay type inequalities are constructed and employed to derive delay independent sufficient conditions under which the continuous time networks converge exponentially to the equilibria associated with temporally uniform external inputs to the networks discrete time analogues of the continuous time networks are formulated and we study their dynamical characteristics it is shown that the convergence dynamics of the continuous time networks are preserved by the discrete time analogues without any restriction on the discretization step size several examples are given to illustrate the advantages of the discrete time analogues in numerically simulating the continuous time networks

exponential state estimation for stochastically disturbed discrete time memristive neural networks multiobjective approach the state estimation of the discrete time memristive model is studied in this article by applying the stochastic analysis technique sufficient formulas are established to ensure the exponentially mean square stability of the error model moreover the derived control gain matrix can be calculated via the linear matrix inequality lmi it should be mentioned that by extending the derived conclusion to a multiobjective optimization problem the maximum bound of the active function and the minimum bound of the disturbance attenuation are derived the corresponding simulation figures are provided in the end

isomorphism theorem for bss recursively enumerable sets over real closed fields the main result of this paper lies in the framework of bss computability it shows roughly that any recursively enumerable set s in rn n where r is a real closed field is isomorphic to rdims by a bijection which is decidable over s moreover the map s is computable some related matters are also considered like characterization of the real closed fields with a r e set of infinitesimals and the dimension of r e sets

a geometrically exact rod model incorporating shear and torsion warping deformation abstract a fully nonlinear three dimensional rod model is developed that incorporates transverse shear and torsion warping deformation the geometric setting is that of a constrained body model with configuration space modeled on r3 so 3 r a differentiable manifold the proposed model incorporates the classical notion of bi moment and bi shear in a fully nonlinear geometrically exact context explicit properly invariant constitutive equations that generalize those of the linearized theory are developed the underlying variational formulation of the model is discussed and computational procedures employing a galerkin projection are addressed numerical examples are presented that illustrate the performance of the formulation

attractivity analysis of memristor based cellular neural networks with time varying delays this paper presents new theoretical results on the invariance and attractivity of memristor based cellular neural networks mcnns with time varying delays first sufficient conditions to assure the boundedness and global attractivity of the networks are derived using state space decomposition and some analytic techniques it is shown that the number of equilibria located in the saturation regions of the piecewise linear activation functions of an n neuron mcnn with time varying delays increases significantly from 2n to 22n2 n 22n2 times compared with that without a memristor in addition sufficient conditions for the invariance and local or global attractivity of equilibria or attractive sets in any designated region are derived finally two illustrative examples are given to elaborate the characteristics of the results in detail

some phenomena for lateral flutter of beams under follower load abstract simple model of a slender beam loaded by a transverse follower force and undergoing a lateral flutter is used to demonstrate the following phenomena 1 if an analysis does not include any damping an extraction of only two lowest eigenvalues can lead to a wrong conclusion that the critical load is infinite this is so because when the ratio of two principal rigidities of a beam is not small the eigenvalue with a positive real part emerges first not at the very beginning of the spectrum 2 for the kelvin type material and with no external damping the critical load becomes infinitely small when the damping in the normal stress vanishes while the shear stress damping is finite 3 when the external damping is increased the critical load approaches the value calculated with no internal damping the nonlinear equilibrium is presented in the closed form and the eigenvalues of the torsional flexural dynamic perturbed equations are found by the finite element approach and subdomain collocation method

the rational points of a definable set let x r n be a set that is definable in an o minimal structure over r this article shows that in a suitable sense there are very few rational points of x which do not lie on some connected semialgebraic subset of x of positive dimension

o minimality and the andre oort conjecture for mathbb c n we give an unconditional proof of the andre oort conjecture for arbitrary products of modular curves we establish two generalizations the first includes the manin mumford conjecture for arbitrary products of elliptic curves defined over q as well as lang s conjecture for torsion points in powers of the multiplicative group the second includes the manin mumford conjecture for abelian varieties defined over q our approach uses the theory of o minimal structures a part of model theory and follows a strategy proposed by zannier and implemented in three recent papers a new proof of the manin mumford conjecture by pila zannier a proof of a special but new case of pink s relative manin mumford conjecture by masser zannier and new proofs of certain known results of andre oort manin mumford type by pila 2010 mathematics subject classification 11g18 03c64

local classical and global bifurcations in non linear non gradient autonomous dissipative structural systems abstract a general analysis for non linear non gradient multiple parameter structural systems with or without damping described by autonomous ordinary differential equations is comprehensively presented attention is focused on bifurcational systems under follower loading exhibiting a trivial stable fundamental path from which a post divergence or post oscillatory instability may occur conditions for establishing regions of existence of adjacent equilibria critical and stability conditions as well as different types of bifurcations with zero double zero and pure imaginary eigenvalues for a smooth variation of the control parameter are thoroughly explored and discussed global dynamic bifurcations associated with stable limit cycles irrelevant to any characteristic properties of the jacobian eigenvalues are discovered in a certain small neighborhood of a compound branching it seems that such global bifurcations with trajectories passing through the saddles of the trivial path are due to the interaction of the first and second buckling modes which occur in the aforementioned small region of adjacent equilibria loading discontinuity phenomena for values of the control parameter defining the foregoing compound branching are detected the effect of damping and other findings based on local classical analyses are compared with the results of this nonlinear analysis and serious discrepancies are observed showing that a precise modelling must be generic including both non linearities and damping the analysis is illustrated by using as a model ziegler s classical model the response of which is fully assessed

finite time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities this paper is concerned with the finite time stochastically stability ftss analysis of markovian jump memristive neural networks with partly unknown transition probabilities in the neural networks there exist a group of modes determined by markov chain and thus the markovian jump was taken into consideration and the concept of ftss is first introduced for the memristive model by introducing a markov switching lyapunov functional and stochastic analysis theory an ftss test procedure is proposed from which we can conclude that the settling time function is a stochastic variable and its expectation is finite the system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases more importantly a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point compared with the fixed point theorem that has been widely used in the existing results this method is more easy to implement besides the delay interval was divided into four subintervals which make full use of the information of the subsystems upper bounds of the time varying delays finally the effectiveness and superiority of the proposed method is demonstrated by two simulation examples

new delay dependent non fragile h observer based control for continuous time delay systems the problem of the delay dependent non fragile h observer based control for a class of continuous time delay systems is investigated in this paper the additive gain variations under consideration are contained in both the controller gain and obhsiunserver gain delay dependent criteria are derived to guarantee the stability of the non fragile h observer based control system using the lyapunov functional approach the controller and observer gains are given from the lmi feasible solutions based on the result of this paper the constraint of matrix equality is not necessary for designing the non fragile h observer based controls computer software matlab can be applied to solve all the proposed results finally a numerical example is illustrated to show the improvement of this paper

remez type inequality on sets with cusps abstract a remez type inequality is proved for a large family of sets with cusps in r n including compact fat and semialgebraic or subanalytic sets

exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method this paper is concerned with the exponential stability and stabilization of memristive neural networks mnns with delays first we present some generalized double integral inequalities which include some existing inequalities as their special cases second combining with quadratic convex combination method these double integral inequalities are employed to formulate a delay dependent stability condition for mnns with delays third a state dependent switching control law is obtained for mnns with delays based on the proposed stability conditions the desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

definable zero sum stochastic games definable zero sum stochastic games involve a finite number of states and action sets and reward and transition functions that are definable in an o minimal structure prominent examples of such games are finite semi algebraic or globally subanalytic stochastic games we prove that the shapley operator of any definable stochastic game with separable transition and reward functions is definable in the same structure definability in the same structure does not hold systematically we provide a counterexample of a stochastic game with semi algebraic data yielding a non semi algebraic but globally subanalytic shapley operator our definability results on shapley operators are used to prove that any separable definable game has a uniform value in the case of polynomially bounded structures we also provide convergence rates using an approximation procedure we actually establish that general zero sum games with separable definable transition functions have a uniform value these results highlight the key role played by the tame structure of transition functions as particular cases of our main results we obtain that stochastic games with polynomial transitions definable games with finite actions on one side and definable games with perfect information or switching controls have a uniform value applications to nonlinear maps arising in risk sensitive control and perron frobenius theory are also given

the elementary theory of restricted analytic fields with exponentiation numbers with exponentiation is model complete when we combine this with hovanskii s finiteness theorem 9 it follows that the real exponential field is o minimal in o minimal expansions of the real field the definable subsets of r share many of the nice structural properties of semialgebraic sets for example definable subsets have only finitely many connected components definable sets can be stratified and triangulated and continuous definable maps are piecewise trivial see 5 in this paper we will prove a quantifier elimination result for the real field augmented by exponentiation and all restricted analytic functions and use this result to obtain o minimality we were led to this while studying work of ressayre 13 and several of his ideas emerge here in simplified form however our treatment is formally independent of the results of 16 17 9 and 13

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

global stabilty analysis of a classical non conservative system under a follower load abstract the bifurcations critical conditions and global stability of the classical two degree of freedom ziegler s dissipative model under a partial follower load are thoroughly discussed with the aid of a complete non linear dynamic analysis attention is mainly focused on the range of values of the non conservativeness loading parameter for which adjacent equilibria do not exist various characteristic findings are established by studying the nature of the jacobian matrix eigenvalues associated with the above non linear autonomous dissipative system it is found that the system exhibits stable hopf bifurcations global stability for the entire region of non adjacent equilibria while the classical linear stability analysis leads to flutter instability local instability moreover in an explicit general form the significant effect of damping on the critical dynamic bifurcation load is established on the basis of the latter the critical loads for the case of vanishing damping are found to be completely different from those of the classical local stability analysis all findings of this analysis are checked against numerical solution of the equations of motion

a note on divisible points of curves let c be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3 we partially answer a question posed by levin on points on c for which a non trivial power lies again on c our results have connections to zilber s conjecture on intersections with tori and yield to methods arising in transcendence theory and the theory of o minimal structures

output feedback stabilization of stochastic high order nonlinear systems under weaker conditions under the weaker conditions on the power order and the nonlinear functions this paper investigates the output feedback stabilization problem for a class of stochastic high order nonlinear systems based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally asymptotically stable in probability

tropical varieties for exponential sums we study the complexity of approximating complex zero sets of certain n variate exponential sums we show that the real part r of such a zero set can be approximated by the n 1 dimensional skeleton t of a polyhedral subdivision of mathbb r n in particular we give an explicit upper bound on the hausdorff distance delta r t o left t 3 5 delta right where t and delta are respectively the number of terms and the minimal spacing of the frequencies of g on the side of computational complexity we show that even the n 2 case of the membership problem for r is undecidable in the blum shub smale model over mathbb r whereas membership and distance queries for our polyhedral approximation t can be decided in polynomial time for any fixed n

finite element solution of the stability problem for nonlinear undamped and damped systems under nonconservative loading a nonlinear finite element analysis of elastic structures which can be studied by a 3d beam theory subjected to conservative as well as to nonconservative forces is presented the stability behaviour of the system is studied by means of an eigenvalue analysis the stiffness matrix of the eigenvalue problem is asymmetric i e non self adjoint system the flutter and divergence modes of instability as well as the values of the critical load are identified for a number of numerical examples belonging to the benchmark tests proposed by nafems 1990 the results demonstrate the reliability of this finite element formulation in particular the effect of damping on the stability behaviour of such structures is investigated and the destabilizing effect of small damping is underlined finally the need to define a number of benchmark tests for nonlinear nonconservative analyses in presence of damping is included

counting special points logic diophantine geometry and transcendence theory we expose a theorem of pila and wilkie on counting rational points in sets definable in o minimal structures and some applications of this theorem to problems in diophantine geometry due to masser peterzil pila starchenko and

relational expressive power of constraint query languages the expressive power of first order query languages with several classes of equality and inequality constraints is studied in this paper we settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomial inequality constraints over the reals furthermore noting that relational queries exhibit several forms of genericity we establish a number of collapse results of the following form the class of generic boolean queries expressible in the relational calculus augmented with a given class of constraints coincides with the class of queries expressible in the relational calculus with or without an order relation we prove such results for both the natural and active domain semantics as a consequence the relational calculus augmented with polynomial inequalities expresses the same classes of generic boolean queries under both the natural and active domain semantics in the course of proving these results for the active domin semantics we establish ramsey type theorems saying that any query involving certain kinds of constraints coincides with a constraint free query on databases whose elements come from a certain infinite subset of the domain to prove the collapse results for the natural semantics we make use of techniques from nonstandard analysis and from the model theory of ordered structures

inclusion dynamics hybrid automata hybrid systems are dynamical systems with the ability to describe mixed discrete continuous evolution of a wide range of systems consequently at first glance hybrid systems appear powerful but recalcitrant neither yielding to analysis and reasoning through a purely continuous time modeling as with systems of differential equations nor open to inferential processes commonly used for discrete state transition systems such as finite state automata a convenient and popular model called hybrid automata was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting intuitively a hybrid automaton is simply a finite state automaton with each state augmented by continuous variables which evolve according to a set of well defined continuous laws each specified separately for each state this article investigates both the notion of hybrid automaton and the model checking problem over such a structure in particular it relates first order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions x f x t to a decidability problem for first order formulaeover the reals furthermore the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first order formulaeover the reals despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite we show that our techniques permit effective model checking for a nontrivial fragment of ctl

quasianalytic denjoy carleman classes and o minimality we show that the expansion of the real field generated by the functions of a quasianalytic denjoy carleman class is model complete and o minimal provided that the class satisfies certain closure conditions some of these structures do not admit analytic cell decomposition and they show that there is no largest o minimal expansion of the real field

schubert calculus on the grassmannian of hermitian lagrangian spaces abstract with an eye towards index theoretic applications we describe a schubert like stratification on the grassmannian of hermitian lagrangian spaces in c n c n this is a natural compactification of the space of hermitian n n matrices the closures of the strata define integral cycles and we investigate their intersection theoretic properties we achieve this by blending morse theoretic ideas with techniques from o minimal or tame geometry and geometric integration theory

on pillay s conjecture in the general case abstract let m be an arbitrary o minimal structure let g be a definably compact definably connected abelian definable group of dimension n here we compute i the new intrinsic o minimal fundamental group of g ii for each k 0 the k torsion subgroups of g iii the o minimal cohomology algebra over q of g as a corollary we obtain a new uniform proof of pillay s conjecture an o minimal analogue of hilbert s fifth problem relating definably compact groups to compact real lie groups extending the proof already known in o minimal expansions of ordered fields