strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

some proximity and sensitivity results in quadratic integer programming we show that for any optimal solution bar z for a given separable quadratic integer programming problem there exist an optimal solution bar x for its continuous relaxation such that parallel bar z bar x parallel infty leqslant n delta a wheren is the number of variables and a is the largest absolute subdeterminant of the integer constraint matrixa also for any feasible solutionz which is not optimal for the separable quadratic integer programming problem there exists a feasible solution bar z having greater objective function value and with parallel bar z z parallel infty leqslant n delta a we further prove under some additional assumptions that the distance between a pair of optimal solutions to an integer quadratic programming problem with right hand side vectorsb andb respectively depends linearly on b b 1 finally the validity of all the results for nonseparable mixed integer quadratic programs is established the proximity results obtained in this paper are extensions of some of the results described in cook et al 1986 for linear integer programming

refined proximity and sensitivity results in linearly constrained convex separable integer programming abstract we define a new measure of the structure of a linear constraint matrix and establish some propertie we then use the measure to refine proximity and sensitivity results in the literature in particular we refine bounds on the distance between continuous and discrete optima of linearly constrained convex separable programming problems and on the size of the feasible region for a linear program we apply the results to improve the computational complexity of hochbaum and shanthikumar s algorithm for integer nonlinear programming reducing the computational effort for certain problems from exponential to polynomial

convex separable optimization is not much harder than linear optimization the polynomiality of nonlinear separable convex concave optimization problems on linear constraints with a matrix with small subdeterminants and the polynomiality of such integer problems provided the inteter linear version of such problems ins polynomial is proven this paper presents a general purpose algorithm for converting procedures that solves linear programming problems the conversion is polynomial for constraint matrices with polynomially bounded subdeterminants among the important corollaries of the algorithm is the extension of the polynomial solvability of integer linear programming problems with totally unimodular constraint matrix to integer separable convex programming an algorithm for finding a e accurate optimal continuous solution to the nonlinear problem that is polynomial in log 1 e and the input size and the largest subdeterminant of the constraint matrix is also presented these developments are based on proximity results between the continuous and integral optimal solutions for problems with any nonlinear separable convex objective function the practical feature of our algorithm is that is does not demand an explicit representation of the nonlinear function only a polynomial number of function evaluations on a prespecified grid

torsion points on families of squares of elliptic curves in a recent paper we proved that there are at most finitely many complex numbers 0 1 such that the points 2 sqrt 2 2 lambda and 3 sqrt 6 3 lambda are both torsion on the elliptic curve defined by y 2 x x 1 x here we give a generalization to any two points with coordinates algebraic over the field q and even over c this implies a special case of a variant of pink s conjecture for a variety inside a semiabelian scheme namely for any curve inside any scheme isogenous to a fibred product of two isogenous elliptic schemes

dwell time based observer design for unknown input switched linear systems without requiring strong detectability of subsystems this paper investigates the state observer design of a class of unknown input switched linear systems via mode dependent dwell time switchings the distinguishing feature of the proposed method is that strong detectability condition of subsystems of the switched systems is unnecessarily required first a time varying coordinate transformation is introduced to design a suitable reduced order observer for each subsystem then computable sufficient conditions on the synthesis of the observers are proposed in the framework of a mode dependent dwell time technique since the observer of an individual subsystem cannot be designed due to unavailability of strong detectability condition of the subsystem the state of the switched system is estimated under the condition of confining the dwell time by a pair of upper and lower bounds restricting the growth of the lyapunov function of the active subsystem and forcing energy of the overall switched system to decrease at switching instants finally an example is presented to demonstrate the effectiveness of the proposed method

interval estimation for lpv systems applying high order sliding mode techniques in this paper the problem of design of interval observers for linear parameter varying lpv systems containing non detectable or non strongly observable parts is addressed firstly a high order sliding mode hosm method is applied to the strongly observable subsystem obtained by an appropriate change of coordinates to estimate the state and its derivative secondly this information is used to decrease the level of uncertainty in the rest of the system which leads to improvement of accuracy of the set membership estimates generated by an interval observer moreover it is shown that hosm techniques allows us to relax the applicability conditions of standard interval observer design methods the efficiency of the proposed approach is demonstrated through simulation examples

ranks of elliptic curves this paper gives a general survey of ranks of elliptic curves over the field of rational numbers the rank is a measure of the size of the set of rational points the paper includes discussions of the birch and swinnertondyer conjecture the parity conjecture ranks in families of quadratic twists and ways to search for elliptic curves of large rank

courbes algebriques et equations multiplicatives we study the intersection of an algebraic curve c lying in a multiplicative torus over bar mathbb q with the union of all algebraic subgroups of codimension 2 finiteness of this set has already been proved by bombieri masser and zannier under the assumption that c is not contained in a translate of a proper subtorus following this result the question of the minimal hypothesis implying finiteness has been raised by these authors giving rise to the conjecture finiteness holds precisely when c is not contained in a proper subgroup we prove here this statement which is also a special case of more general conjectures stated independently by zilber and pink our proof takes its inspiration from an article by remond and viada concerning the zilber pink conjecture for curves lying in a power of an elliptic curve hence it relies on a uniform version of the vojta inequality proven via the generalized vojta inequality of remond the main task is to establish a lower bound for some intersection numbers here on a whole family of surfaces obtained by blowing up a compactification of c c

adaptive fuzzy tracking control of switched uncertain nonlinear systems with unstable subsystems this paper is concerned with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems where the solvability of the fuzzy tracking control problem for subsystems is unnecessary fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a new adaptive fuzzy tracking control technique for the problem under study is set up based on the technique above we design a switching law and construct adaptive fuzzy controllers of subsystems explicitly by a recursive design algorithm to guarantee that all the signals in the resulting closed loop system remain bounded and the system output of the closed loop system converges to a small neighborhood of the reference signal multiple lyapunov functions are exploited to get out of the conservativeness caused by adoption of a common lyapunov function for all subsystems which is commonly required when applying the backstepping like recursive design scheme a mass spring damper system is provided to demonstrate the effectiveness of the proposed design method

sensitivity theorems in integer linear programming we consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right hand side vector among our results we show that for any optimal solution to a linear program max wx ax b the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixa using this we strengthen several integer programming proximity results of blair and jeroslow graver and wolsey we also show that the chvatal rank of a polyhedron x ax b can be bounded above by a function of the matrixa independent of the vectorb a result which as blair observed is equivalent to blair and jeroslow s theorem that each integer programming value function is a gomory function

unknown input and state estimation for unobservable systems the concept of strong detectability and its relation with the concept of invariant zeros is reviewed for strongly detectable systems which includes the strongly observable systems it is proposed a hierarchical design of a robust observer whose trajectories converge to those of the original state vector furthermore it is shown that neither left invertibility is a sufficient condition nor strong detectability is a necessary condition to estimate the unknown inputs it is shown that the necessary and sufficient condition for estimating the unknown inputs is that the set of the invariant zeros that do not belong to the set of unobservable modes be within the interior of the left half plane of the complex space this shows that the unknown inputs could be estimated even if it is impossible to estimate the entire state vector of the system two numerical examples illustrate the effectiveness of the proposed estimation schemes

root numbers and ranks in positive characteristic abstract for a global field k and an elliptic curve e over k t silverman s specialization theorem implies rank e k t rank e t k for all but finitely many t p 1 k if this inequality is strict for all but finitely many t the elliptic curve e is said to have elevated rank all known examples of elevated rank for k q rest on the parity conjecture for elliptic curves over q and the examples are all isotrivial some additional standard conjectures over q imply that there does not exist a non isotrivial elliptic curve over q t with elevated rank in positive characteristic an analogue of one of these additional conjectures is false inspired by this for the rational function field k u over any finite field with characteristic 2 we construct an explicit 2 parameter family e c d of non isotrivial elliptic curves over k t depending on arbitrary c d such that under the parity conjecture each e c d has elevated rank

the difference between the weil height and the canonical height on elliptic curves estimates for the difference of the weil height and the canonical height of points on elliptic curves are used for many purposes both theoretical and computational in this note we give an explicit estimate for this difference in terms of the j invariant and discriminant of the elliptic curve the method of proof suggested by serge lang is to use the decomposition of the canonical height into a sum of local heights we illustrate one use for our estimate by computing generators for the mordell weil group in three examples let e be an elliptic curve defined over a number field k say given by a weierstrass equation 1 y2 x ax b with a and b in the ring of integers of k the canonical height on e is a quadratic form h e k r for the definition and basic properties of h see 10 chapter viii 9 or 6 chapter vi the canonical height is determined by this property together with the fact that the difference

distances between optimal solutions of mixed integer programs a classic result of cook et al math program 34 251 264 1986 bounds the distances between optimal solutions of mixed integer linear programs and optimal solutions of the corresponding linear relaxations their bound is given in terms of the number of variables and a parameter vardelta which quantifies sub determinants of the underlying linear inequalities we show that this distance can be bounded in terms of vardelta and the number of integer variables rather than the total number of variables to this end we make use of a result by olson j number theory 1 8 10 1969 in additive combinatorics and demonstrate how it implies feasibility of certain mixed integer linear programs we conjecture that our bound can be improved to a function that only depends on vardelta in general

an integral type multiple lyapunov functions approach for switched nonlinear systems an integral type multiple lyapunov functions mlfs approach for switched nonlinear systems is set up for the first time which gives a more general condition for analyzing the behavior of switched nonlinear systems since the branicky s nonincreasing condition is no longer assumed and the generalized mlfs condition is a special case of the condition provided meanwhile based on the integral type mlfs approach global stabilization for a class of switched nonlinear systems in p normal form is achieved by constructing state feedback controllers of subsystems and a proper switching law where the solvability of the problem under study for individual subsystems is not assumed two examples are also provided to demonstrate the effectiveness of the proposed design method

unknown input observer design for fuzzy systems with uncertainties this paper investigates the problem of unknown input observer design for both discrete and continuous time t s fuzzy systems with uncertainties after doing appropriate processing to the model and reasonable analysis to the error expression of the system the observer design conditions are proposed in lmi form based on lyapunov theory more important is the introduction of a new decoupling method which can further reduce the conservatism the idea can eliminate the influence of the unknown inputs and guarantee the error of the state estimation is bounded when the uncertainties are nonzero finally an appropriate example is given to show the effectiveness of the algorithm especially the excellent estimate ability of the observer in initial time

preperiodic points and unlikely intersections in this article we combine complex analytic and arithmetic tools to study the preperiodic points of one dimensional complex dynamical systems we show that for any fixed a b c and any integer d 2 the set of c c for which both a and b are preperiodic for z c is infinite if and only if a b this provides an affirmative answer to a question of zannier which itself arose from questions of masser concerning simultaneous torsion sections on families of elliptic curves using similar techniques we prove that if rational functions c z have infinitely many preperiodic points in common then all of their preperiodic points coincide and in particular the maps must have the same julia set this generalizes a theorem of mimar who established the same result assuming that and are defined over q the main arithmetic ingredient in the proofs is an adelic equidistribution theorem for preperiodic points over number fields and function fields with non archimedean berkovich spaces playing an essential role

interval observer design for continuous time switched systems under known switching and unknown inputs this paper deals with unknown input estimation for switched linear systems in an unknown but bounded error ubbe framework based on a known switching signal and under the fulfilment of the relati

unlikely intersections with isogeny orbits in a product of elliptic schemes fix an elliptic curve e 0 without cm and a non isotrivial elliptic scheme over a smooth irreducible curve both defined over the algebraic numbers consider the union of all images of a fixed finite rank subgroup of arbitrary rank of e 0 g also defined over the algebraic numbers under all isogenies between e 0 g and some fiber of the g th fibered power mathcal a of the elliptic scheme where g is a fixed natural number as a special case of a slightly more general result we characterize the subvarieties of arbitrary dimension inside mathcal a that have potentially zariski dense intersection with this set in the proof we combine a generalized vojta remond inequality with the pila zannier strategy

special points on fibered powers of elliptic surfaces consider a fibered power of an elliptic surface we characterize its subvarieties that contain a zariski dense set of points that are torsion points in fibers with complex multiplication this result can be viewed as a mix of the manin mumford and andre oort conjecture and is related to a conjecture of pink the main technical tool is a new height inequality we also use it to give another proof of a case of gubler s result on the bogomolov conjecture over function fields

on mode reconstructability and reconstructability sets of piecewise linear systems this paper focuses on the problem of mode reconstructability of piecewise linear multi output systems for the case when a partition of the state space characterises the switching modes the partiti

stability analysis of switched linear singular systems this paper addresses the stability analysis problem for switched linear continuous time singular systems first based on the equivalent dynamics decomposition form a refined description for state jumps of the switched singular system is presented which indicates that overall state jumps are resulted by two sequential state jumps second sufficient conditions for exponential stability of the switched singular system with stable subsystems are presented it is shown that the stability property of the system is completely determined by the switched reduced order dynamic subsystem and the switching law induced state jumps then a sufficient stability condition for the switched singular system with both stable and unstable subsystems is obtained finally numerical examples are presented to illustrate the effectiveness of the proposed approach

existence of simple jacobian varieties of genus g with rank at least 4g 5 we prove the existence of infinitely many curves of genus g over the rational number field which have absolutely simple jacobian varieties with mordell weil rank at least 4 g 5

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

torsion anomalous points and families of elliptic curves we prove that there are at most finitely many complex lambda neq 0 1 such that two points on the legendre elliptic curve y 2 x x 1 x lambda with coordinates x 2 3 both have finite order this is a very special case of some conjectures on unlikely intersections in semiabelian schemes

multi modelling as new estimation schema for high gain observers the presented paper proposes a novel method of observer design a new two layer observer structure is introduced the first layer consists of multiple high gain observers the latter is built to connect the first layer observers into single one as the new contribution the new mapping is defined between an unknown state and measurable outputs allowing to explore new estimation schema hence the proposed method enhances the estimation process for linear and nonlinear systems furthermore it is shown that the introduced observation scheme improves the transients illustrative examples are calculated to show the properties of the new observation method

the number of integral points on arcs and ovals integral lattice points and that the exponent and constant are best possible however swinnerton dyer 10 showed that the preceding result can be substantially improved if we start with a fixed c strictly convex arc and consider the number of lattice points on t the dilation of by a factor t t 1 this of course is the same as asking for rational points mn n n on as n in fact swinnerton dyer proves a bound of type t zz c e t 3 5 e

the relationship between integer and real solutions of constrained convex programming we prove the following theorem which gives a bound on the proximity of the real and the integer solutions to certain constrained optimization programs

switched observers for switched linear systems with unknown inputs two state observers are designed for some classes of switched linear systems with unknown inputs the design of the proposed observers assumes that all switching subsystems fulfill a property of strong detectability that allows to implement suitable reduced order unknown input switched observers the synthesis of the observers is based on the feasibility of a certain system of lmis two main schemes are presented for the case when the set of possible unknown input distribution matrices are linearly dependent an observer is suggested that guarantees the asymptotic state reconstruction without imposing any slow switching dwell time constraint about the sequence of the switching times for the general case the existence of a minimal average dwell time for every switching sequence is assumed by appropriate lyapunov analysis the convergence of the state estimate is proven to be exponential in both cases simulation results confirm the predicted performance

a new design approach to unknown input observers this paper proposes a fundamentally new unknown input observer uio which has uniquely r decoupled modes provides r linearly independent combinations of plant system states and has zero gain to all p unknown inputs the parameter r is adjustable if the plant system satisfies the conditions of the existing uio then r n plant system order and there is no difference between our uio and the existing regular uio however if the plant system satisfies either of the following two significantly more general conditions m p m is the number of plant output measurements and at least one stable transmission zero then 1 n and our uio can still generate some constrained state feedback control signals hence this new uio can completely unify the regular uio r n and the static output feedback r m the two basic feedback structures of modern control theory far from being unified before

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

torsion points on families of products of elliptic curves abstract in a recent paper we proved a special case of a variant of pink s conjecture for a variety inside a semiabelian scheme namely for any curve inside any scheme isogenous to a fibred product of two isogenous elliptic schemes here we go ahead with the programme of settling the conjecture for general abelian surface schemes by completing the proof for all non simple surfaces this involves some entirely new and crucial issues

torsion points pell s equation and integration in elementary terms the main results of this paper involve general algebraic differentials omega on a general pencil of algebraic curves we show how to determine if omega is integrable in elementary terms for infinitely many members of the pencil in particular this corrects an assertion of james davenport from 1981 and provides the first proof even in rather strengthened form we also indicate analogies with work of andre and hrushovski and with the grothendieck katz conjecture to reach this goal we first provide proofs of independent results which extend conclusions of relative manin mumford type allied to the zilber pink conjectures we characterize torsion points lying on a general curve in a general abelian scheme of arbitrary relative dimension at least 2 in turn we present yet another application of the latter results to a rather general pencil of pell equations a 2 db 2 1 over a polynomial ring we determine whether the pell equation with squarefree d is solvable for infinitely many members of the pencil

torsion points and the lattes family we give a dynamical proof of a result of masser and zannier for any a neq b in overline bbb q setminus 0 1 there are only finitely many parameters t in bbb c for which points p a a sqrt a a 1 a t and p b b sqrt b b 1 b t are both torsion on the legendre elliptic curve e t y 2 x x 1 x t our method also gives the finiteness of parameters t where both p a and p b have small n eron tate height a key ingredient in the proof is an arithmetic equidistribution theorem on bbb p 1 for this we prove two statements about the degree 4 latt es family f t on bbb p 1 1 for each c in bbb c t the bifurcation measure mu c for the pair f t c has continuous potential across the singular parameters t 0 1 infty and 2 for distinct points a b in bbb c setminus 0 1 the bifurcation measures mu a and mu b cannot coincide combining our methods with the result of masser and zannier we extend their conclusion to points t of small height also for a b in bbb c t

neron models of jacobians over base schemes of dimension greater than 1 we investigate to what extent the theory of neron models of jacobians and of abel jacobi maps extends to relative curves over base schemes of dimension greater than 1 we give a necessary and sufficient criterion for the existence of a neron model we use this to show that in general neron models do not exist even after making a modification or even alteration of the base on the other hand we show that neron models do exist outside some codimension 2 locus

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

bounded height in pencils of finitely generated subgroups in this paper we prove a general bounded height result for specializations in finitely generated subgroups varying in families which complements and sharpens the toric mordell lang theorem by replacing finiteness by emptyness for the intersection of varieties and subgroups all moving in a pencil except for bounded height values of the parameters and excluding identical relations more precisely an instance of the results is as follows consider the torus scheme g r m c over a curve c defined over q and let be a subgroup scheme generated by finitely many sections satisfying some necessary conditions further let v be any subscheme then there is a bound for the height of the points p c q such that for some which does not generically lie in v p lies in the fiber vp we further offer some direct diophantine applications to illustrate once again that the results implicitly contain information absent from the previous bounds in this context

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

decentralized adaptive fuzzy output feedback control of switched large scale nonlinear systems in this paper a decentralized adaptive fuzzy output feedback control problem is discussed for a class of switched large scale nonlinear systems without the measurements of the system states fuzzy logic systems are used to approximate the unknown nonlinear functions and a switched observer is designed to avoid the conservativeness caused by adoption of a common observer for all subsystems a common coordinate transformation of all subsystems is constructed to get rid of individual coordinate transformations for subsystems that are required when applying the backstepping recursive design scheme meanwhile since the exponential decline property of lyapunov functions for individual subsystems is no longer satisfied in this paper the classical average dwell time method cannot be directly applied based on this a switched observer based decentralized adaptive fuzzy output feedback control technique is set up by exploiting the average dwell time method and backstepping it is proved that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded under a class of switching signals with average dwell time while the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed control scheme is illustrated by its applications to a two inverted pendulum system and a quadruple tank process system

specializations of finitely generated subgroups of abelian varieties given a generic mordell weil group over a function field we can specialize it down to a number field it has been known for some time that the resulting homomorphism of groups is injective infinitely often we prove that this is in fact true almost always in a sense that is quantitatively nearly best possible

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