on vanishing stability regions in nonlinear systems with high gain feedback when local stabilization of nonlinear systems is achieved by linear feedback the resulting stability region may vanish as the feedback gains increase this is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium as the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium if a feedback linearization design is applied the same instability mechanism may occur when the nonlinearities are not precisely known

time finite element methods a unified framework for numerical discretizations of odes abstract we present a unified framework for the numerical discretization of odes based on time finite element methods we relate time finite element methods to runge kutta methods with infinitely many stages by means of the corresponding numerical quadrature we establish the relation between time finite element methods and partitioned runge kutta methods we also provide order estimates and superconvergence of the corresponding numerical methods in use of the simplifying assumptions we apply time finite methods to hamiltonian systems and investigate the conservation of energy and symplectic structure for the resulting numerical discretizations for hamiltonian systems we also construct new classes of symplectic integrators by combining different time finite element methods and verify the results by performing some numerical experiments

averages and higher moments for the ell torsion in class groups we prove upper bounds for the average size of the ell torsion mathrm cl k ell of the class group of k as k runs through certain natural families of number fields and ell is a positive integer we refine a key argument used in almost all results of this type which links upper bounds for mathrm cl k ell to the existence of many primes splitting completely in k that are small compared to the discriminant of k our improvements are achieved through the introduction of a new family of specialised invariants of number fields to replace the discriminant in this argument in conjunction with new counting results for these invariants this leads to significantly improved upper bounds for the average and sometimes even higher moments of mathrm cl k ell for many families of number fields k considered in the literature for example for the families of all degree d fields for d in 2 3 4 5 and non d 4 if d 4 as an application of the case d 2 we obtain the best upper bounds for the number of d p fields of bounded discriminant for primes p 3

time finite element discretization of hamilton s law of varying action hamilton s law of varying action is used as a variational source for the derivation of finite element discretization procedure in the time domain three different versions of the proposed algorithms are presented and verified for accuracy and stability the first one is the high precision finite time element analogous to the standard finite elements with cutoff frequency the second version is the step by step one time element from which the unconditionally stable with slightly altered accuracy third algorithm is derived the new operator connected with the proposed algorithms bears attractive properties of much greater accuracy than other existing stable methods and easy computer implementation thus the work herein shows that the reservations expressed against the use of finite elements in time domain seem unjustified

on the transversal vibrations of a conveyor belt with a low and time varying velocity part ii the beam like case in this paper initial boundary value problems for a linear wave string equation are considered these problems can be used as simple models to describe the vertical vibrations of a conveyor belt for which the velocity is small with respect to the wave speed and is assumed to move with a time varying speed formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt it will also be shown that the truncation method cannot be applied to this problem in order to obtain approximations valid on long time scales

a stable neural network based observer with application to flexible joint manipulators a stable neural network nn based observer for general multivariable nonlinear systems is presented in this paper unlike most previous neural network observers the proposed observer uses a nonlinear in parameters neural network nlpnn therefore it can be applied to systems with higher degrees of nonlinearity without any a priori knowledge about system dynamics the learning rule for the neural network is a novel approach based on the modified backpropagation bp algorithm an e modification term is added to guarantee robustness of the observer no strictly positive real spr or any other strong assumption is imposed on the proposed approach the stability of the recurrent neural network observer is shown by lyapunov s direct method simulation results for a flexible joint manipulator are presented to demonstrate the enhanced performance achieved by utilizing the proposed neural network observer

hamilton s law of variable mass system and time finite element formulations for time varying structures based on the law summary traditional principles of mechanics are primarily conceived for constant mass systems which are only valid if mass is gained or lost at null velocity with respect to an inertial reference frame for variable mass systems thus the numerical algorithms for time varying structures based on these principles are only suitable for this special case in this paper hamilton s law of variable mass system is derived based on meshchersky s fundamental equation and two classes of novel time finite element formulations for linear systems with arbitrary continuous time varying parameters are developed based on the previous law the formulations are verified extensively through numerical examples in which the convergence and effectiveness of algorithms are evaluated numerical examples demonstrate that compared with the algorithms for time varying structures that developed based on traditional principles of mechanics the proposed algorithms provide extended capabilities in both time varying mass problems that mass is gained or lost at any velocity such as rocket problem and moving mass problems such as vehicle bridge interaction problem besides the time varying stiffness and damping problems the proposed algorithms have a wider range of application in particular hamilton s law of variable mass system provides a solid theoretical foundation for further research on the algorithm design for time varying structures copyright 2014 john wiley sons ltd

dynamic behaviour of beams and rectangular plates under moving loads abstract a theory concerning the dynamic response of finite elastic structures rayleigh beams and plates having arbitrary end supports and under an arbitrary number of moving masses is developed the versatile solution technique presented is based on modified generalized finite integral transforms and the modified struble s method various analytical results are presented numerical examples are given and the results compare favourably with existing ones the efficiency of the solution technique is demonstrated and discussed

output only identification and dynamic analysis of time varying mechanical structures under random excitation a comparative assessment of parametric methods this article addresses the problem of parametric time domain identification and dynamic analysis for time varying tv mechanical structures under unobservable random excitation the methods presented are based on time dependent autoregressive moving average tarma models and are classified according to the mathematical structure imposed on the tv parameter evolution as unstructured parameter evolution stochastic parameter evolution and deter ministic parameter evolution the features and relative merits of each class are outlined a representativ e method from each is then assessed through its application to the identification and dynamic analysis o f a laboratory tv structure consisting of a beam with a mass moving on it the results are mutually compared and contrasted to those obtained through frozen configuration multiple experiment bas eline identification

lyapunov based model predictive control of stochastic nonlinear systems in this work we design a lyapunov based model predictive controller lmpc for nonlinear systems subject to stochastic uncertainty the lmpc design provides an explicitly characterized region from where stability can be probabilistically obtained the key idea is to use stochastic lyapunov based feedback controllers with well characterized stabilization in probability to design constraints in the lmpc that allow the inheritance of the stability properties by the lmpc the application of the proposed lmpc method is illustrated using a nonlinear chemical process system example

the 4 class ranks of quadratic fields let k be a quadratic extension field of the rational numbers q let c k be the 2 class group of k in the narrow sense it is a classical result that rank c k t l where t is the number of primes that ramify in k q now let c ai a e ck and let r k denote the 4 class rank of k in the narrow sense i e rk rank kc z dimv2 ttc z t 41 k kj here f 2 is the finite field with two elements and 2 4 ck c k is an elementary abelian 2 group which we are viewing as a vector space o v e r f 2 given a quadratic field k one can compute r k by computing the rank over f2 of a certain matrix of legendre symbols cf 11 now assume k is imaginary quadratic so k q 1 mm where m is a square free positive integer for each positive integer t each nonnegative integer e and each positive real number x we define

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

a case study in model reduction of linear time varying systems in this paper the balanced truncation procedure is applied to time varying linear systems both in continuous and in discrete time the methods are applied to a linear approximation of a diesel exhaust catalyst model the reduced order systems are obtained by using certain projections instead of direct balancing an approximate zero order hold discretization of continuous time systems is described and a new a priori approximation error bound for balanced truncation in the discrete time case is obtained the case study shows that there are several advantages to work in discrete time it gives simpler implementation with fewer computations

on the existence of fields governing the 2 invariants of the classgroup of as varies this paper formulates general conjectures relating the structure of the 2 classgroup c2 dp associated to q fdp to the splitting of the ideal p in certain algebraic number fields here d i 2 mod 4 is a fixed integer and p varies over primes the conjectures assert that there exists an algebraic number field qj d such that the artin symbol q2 d q p determines the first j 2 invariants of the group c2 dp i e it determines c2 dp c2 dp 2j these conjectures imply that the set of primes p for which c2 dp has a given set of 2 invariants has a natural density which is a rational number existing results prove the conjectures wheneverj i or 2 and also for an infinite set of d withj 3 the smallest open case isj 3 d 21 this paper presents evidence concerning these conjectures for d 4 8 and 21 numerical evidence is given that q23 21 exists and that natural densities which are rational numbers exist for the sets of primes with 2 h dp for d 4 and 8 for i j 7 a search for the hypothetical field 04 4 ruled out the simplest candidate fields 04 4 is not a normal extension of q of degree 16 ramifying only at 2

on resonances and the applicability of galerkin s truncation method for an axially moving string with time varying velocity abstract in this paper an initial boundary value problem for a linear homogeneous equation describing an axially moving string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity with a small fluctuation amplitude the two timescales perturbation method and the laplace transform method have been employed to the equation of motion in search of infinite mode approximate solutions all resonance cases are investigated in detail it will be shown that galerkin s truncation method cannot be applied to this problem in all cases to obtain approximations valid on long timescales

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

vibration analysis of the continuous beam subjected to a moving mass abstract the dynamic behavior of the multi span continuous beam traversed by a moving mass at a constant velocity is investigated in which it is assumed that each span of the continuous beam obeys uniform euler bernoulli beam theory the solution to this system is simply obtained by using both eigenfunction expansion or the modal analysis method and the direct integration method in combination the effects of the inertia and the moving velocity of the load on the dynamic response of the continuous beam are evaluated for three kinds of continuous beams having uniform span length

on the 4 rank of class groups of quadratic number fields we prove that the 4 rank of class groups of quadratic number fields behaves as predicted in an extension due to gerth of the cohen lenstra heuristics

dynamic stiffness matrix development and free vibration analysis of a moving beam abstract the dynamic stiffness matrix of a moving bernoulli euler beam is developed and used to investigate its free flexural vibration characteristics in order to develop the dynamic stiffness matrix it is necessary to derive and solve the governing differential equation of motion of the moving beam in closed analytical form the solution is then used to obtain the general expressions for both responses and loads boundary conditions are applied to determine the constants in the general solution leading to the formation of the frequency dependent dynamic stiffness matrix of the moving beam relating the amplitudes of the harmonically varying loads to those of the corresponding responses the application of the resulting dynamic stiffness matrix using the wittrick williams algorithm is demonstrated by some illustrative examples numerical results for both simply supported and fixed fixed end conditions of the beam are discussed and wherever possible some are compared with those available in the literature

a space time discontinuous galerkin method for the elastic wave equation abstract in this work we present a new high order space time discretization method based on a discontinuous galerkin paradigm for the second order visco elastodynamics equation after introducing the method we show that the resulting space time discontinuous galerkin formulation is well posed stable and retains optimal rate of convergence with respect to the discretization parameters namely the mesh size and the polynomial approximation degree a set of two and three dimensional numerical experiments confirms the theoretical bounds

adaptive dynamic output feedback neural network control of uncertain mimo nonlinear systems with prescribed performance an adaptive dynamic output feedback neural network controller for a class of multi input multi output affine in the control uncertain nonlinear systems is designed capable of guaranteeing prescribed performance bounds on the system s output as well as boundedness of all other closed loop signals it is proved that simply guaranteeing a boundedness property for the states of a specifically defined augmented closed loop system is necessary and sufficient to solve the problem under consideration the proposed dynamic controller is of switching type however its continuity is guaranteed thus alleviating any issues related to the existence and uniqueness of solutions simulations on a planar two link articulated manipulator illustrate the approach

mixed time finite elements for vibration response analysis this paper presents a mixed time finite element method for vibration response analysis the underlying variational formulation is developed from the principle of virtual work conventional spatial discretization techniques are adopted time discretization is implemented by using mixed time finite elements the proposed formulation not only forms a unified variational basis for spatial and temporal discretization it also derives many other robust time step integration algorithms unconditionally stable and high order accurate algorithms with variable numerical dissipation can be constructed systematically moreover the proposed formulations can be used to solve linear as well as non linear problems the accuracy and stability of the derived algorithms are presented

further remarks on potentially global stabilizability given a control system with a nonlinear drift term it is proved that a linear like criterion for almost global stabilizability can be stated at least for control systems of the form x f x bu where f is a polynomial but not necessarily homogeneous vector field these stability criteria also allow for the control of the size of the region of attraction

triangular and tetrahedral space time finite elements in vibration analysis recently several methods of time integration of the equations of motion have been proposed many of them result in square mass damping and stiffness matrices the space time finite element method is an extension of the fem familiar to most engineers over the time domain a special approach enables the use of triangular tetrahedral and hyper tetrahedral elements in time and space by special division of the space time layer the triangular matrix of coefficients in the system of equations can be obtained a simple algorithm enables the storage of non zero coefficients only dynamic solution requires a small amount of the memory compared to other methods and ensures considerable reduction of arithmetic operations the method presented is also efficient in solving both linear and non linear problems matrices for a beam and plane stress strain element are derived exemplary problems solved by the method described have proved the effectiveness of the application of triangular and tetrahedral space time elements in vibration analysis

dynamic behavior and modal control of beams under moving mass abstract the constitutive equation of an euler bernoulli beam under the excitation of moving mass is considered the dynamics of the uncontrolled system is governed by a linear self adjoint partial differential equation a dirac delta function is used to describe the position of the moving mass along the beam and its inertial effects an approximate formulation to the problem is obtained by limiting the inertial effect of the moving mass merely to the vertical component of acceleration having defined a critical velocity in terms of the fundamental period and span of the beam it is shown that for smaller velocities the approximate and exact approaches to the problem almost coincide since the defined critical velocity is fairly large compared to those in practical cases the approximate approach can effectively be used for a wide range of problems there is however a slight variation in critical velocity depending on the weight of the moving mass on the other hand it is shown that the effect of higher vibrational modes is not negligible for certain velocity ranges finally a linear classical optimal control algorithm with a time varying gain matrix with displacement velocity feedback is used to control the response of the beam the efficiency of the control algorithm in suppressing the response of the system under the effect of moving mass with different number of controlled modes and actuators is investigated

a tent pitching scheme motivated by friedrichs theory certain friedrichs systems can be posed on hilbert spaces normed with a graph norm functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet motivated by this continuity property an explicit space time finite element scheme of the tent pitching type with spaces that conform to the continuity property is designed numerical results for a model one dimensional wave propagation problem are presented

on asymptotics of the solution of the moving oscillator problem asymptotic behavior of the solution of the moving oscillator problem is examined for large and small values of the spring stiffness for the general case of non zero beam initial conditions in the limiting case of infinite spring stiffness it is shown that the moving oscillator problem for a simply supported beam is not equivalent in a strict sense to the moving mass problem the two problems are shown to be equivalent in terms of the beam displacements but are not equivalent in terms of stresses the higher order derivatives of the two solutions differ in the general case the force acting on the beam from the oscillator is shown to contain a high frequency component which does not vanish and can even grow when the spring coefficient tends to infinity the magnitude of this force and its dependence on the oscillator parameters can be estimated by considering the asymptotics of the solution for the initial stage of the oscillator motion it is shown that for the case of a simply supported beam the magnitude of the high frequency force depends linearly on the oscillator eigenfrequency and velocity the deficiency of the moving mass model is principally that it fails to predict stresses in the supporting structure for small values of the spring stiffness the moving oscillator problem is shown to be equivalent to the moving force problem the discussion is amply illustrated by results of numerical experiments

stochastic nonlinear stabilization ii inverse optimality after considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper in this second part we address the classical question of when is a stabilizing in probability controller optimal and show that for every system with a stochastic control lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional then we return to the problem from part i and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin

new improved series expansion for solving the moving oscillator problem a new method able to evaluate the dynamic stress response of an elastic beam subject to moving oscillators is presented the proposed procedure improves the convergence and accuracy of the conventional eigenfunction series expansion of beam response taking into account the gravitational inertial and damping effects due to the moving oscillators the improvement of the conventional solution is obtained by means of an extension to continuous systems of the dynamic correction method originally proposed for discretized structures the proposed method is able to account for the truncated higher order eigenfunctions by adding a pseudo static term to the conventional series expansion numerical results are presented to demonstrate the capability of the method to accurately determine the discontinuity and jump in bending moment and shear force distributions respectively

output feedback lyapunov based predictive control of stochastic nonlinear systems this paper considers the problem of output feedback control of stochastic nonlinear systems a predictive controller is designed for which stability and feasibility in a probabilistic sense are guaranteed from an explicitly characterized region of attraction the controller s performance is characterized by its risk of allowing destabilizing system behavior since the controller design relies on certain convergence properties of the state observer a compatible stochastic high gain type observer design is also presented finally simulation results illustrating the efficacy of the design are presented

dwell time controllers for stochastic systems with switching markov chain we study the problem of feedback stabilization of a family of nonlinear stochastic systems with switching mechanism modeled by a markov chain we introduce a novel notion of stability under switching which guarantees a given probability that the trajectories of the system hit some target set in finite time and remain thereinafter our main contribution is to prove that if the expectation of the time between two consecutive switching dwell time is sufficiently large then the system is stable under switching with guaranteed probability we illustrate this methodology by constructing measurement feedback controllers for a wide class of stochastic nonlinear systems

homological stability for hurwitz spaces and the cohen lenstra conjecture over function fields we prove a homological stabilization theorem for hurwitz spaces moduli spaces of branched covers of the complex projective line this has the following arithmetic consequence let 2 be prime and a a nite abelian group then there exists q q a such that for q greater than q a positive fraction of quadratic extensions of fq t have the part of their class group isomorphic to a

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

space time approach to numerical analysis of a string with a moving mass inertial loading of strings beams and plates by mass travelling with near critical velocity has been a long debate typically a moving mass is replaced by an equivalent force or an oscillator with rigid spring that is in permanent contact with the structure such an approach leads to iterative solutions or imposition of artificial constraints in both cases rigid constraints result in serious computational problems a direct mass matrix modification method frequently implemented in the finite element approach gave reasonable results only in the range of relatively low velocities in this paper we present the space time approach to the problem the interaction of the moving mass supporting structure is described in a local coordinate system of the space time finite element domain the resulting characteristic matrices include inertia coriolis and centrifugal forces a simple modification of matrices in the discrete equations of motion allows us to gain accurate analysis of a wide range of velocities up to the velocity of the wave speed numerical examples prove the simplicity and efficiency of the method the presented approach can be easily implemented in the classic finite element algorithms copyright 2008 john wiley sons ltd

nn based adaptive tracking control of uncertain nonlinear systems disturbed by unknown covariance noise a class of uncertain nonlinear systems that are additionally driven by unknown covariance noise is considered based on the backstepping technique adaptive neural control schemes are developed to solve the output tracking control problem of such systems as it is proven by stability analysis the proposed controller guarantees that all the error variables are bounded with desired probability in a compact set while the tracking error is mean square semiglobally uniformly ultimately bounded m sguub the tracking performance and the effectiveness of the proposed design are evaluated by simulation results

solution of linear elastodynamics problems with space time finite elements on structured and unstructured meshes abstract a new implicit approach for the solution of linear elastodynamics problems on structured and unstructured meshes with space time finite elements is suggested new weak formulations are based on time continuous tcg and discontinuous tdg galerkin methods it was shown that for structured meshes the new tcg method has a higher order of accuracy by a factor of two than that of the standard tcg method at the same number of degrees of freedom the accuracy of the new tcg method is one order higher than the accuracy of the standard tdg method the introduction of new weighting functions for the weak formulations of the tcg and tdg methods allows control of the high frequency behavior without degradation of accuracy of the methods a variable number of elements in the time direction as well as a variable order of polynomial time approximations of finite elements for time slabs allows the implementation of a coupled space time adaptive procedure using structured or unstructured meshes numerical examples for 1 d problems demonstrate the effectiveness of the technique

variable time step method with coordinate transformation abstract the variable time step methods for solving moving boundary problems are presented by transforming the variable space domain this results in dissociating the mode of advancement of the boundary from the size of the space mesh that is a small movement of the moving boundary may be chosen for computing the time interval while the space domain is subdivided into larger space meshes as a consequence an enormous amount of saving in computer time may be achieved by using the proposed method two sample problems are selected for the illustration of the method

p ell torsion points in finite abelian groups and combinatorial identities abstract the main aim of this article is to compute all the moments of the number of p l torsion elements in some type of finite abelian groups the averages involved in these moments are those defined for the cohen lenstra heuristics for class groups and their adaptation for tate shafarevich groups in particular we prove that the heuristic model for tate shafarevich groups is compatible with the recent conjecture of poonen and rains about the moments of the orders of p selmer groups of elliptic curves for our purpose we are led to define certain polynomials indexed by integer partitions and to study them in a combinatorial way moreover from our probabilistic model we derive combinatorial identities some of which appearing to be new the others being related to the theory of symmetric functions in some sense our method therefore gives for these identities a somehow natural algebraic context

a differential geometric approach to nonlinear filtering the projection filter this paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters using the differential geometric approach to statistics the projection filter is defined rigorously in the case of exponential families a convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation finally simulation results are discussed for the cubic sensor problem

vibrations of a mindlin plate subjected to a pair of inertial loads moving in opposite directions abstract a mindlin plate subjected to a pair of inertial loads traveling at a constant high speed in opposite directions along arbitrary trajectory straight or curved is presented the masses represent vehicles passing a bridge or track plates a numerical solution is obtained using the space time finite element method since it allows a clear and simple derivation of the characteristic matrices of the time stepping procedure the transition from one spatial finite element to another must be energetically consistent in the case of the moving inertial load the classical time integration schemes are methodologically difficult since we consider the dirac delta term with a moving argument the proposed numerical approach provides the correct definition of force equilibrium in the time interval the given approach closes the problem of the numerical analysis of vibration of a structure subjected to inertial loads moving arbitrarily with acceleration the results obtained for a massless and an inertial load traveling over a mindlin plate at various speeds are compared with benchmark results obtained for a kirchhoff plate the pair of inertial forces traveling in opposite directions causes displacements and stresses more than twice as large as their corresponding quantities observed for the passage of a single mass

a study of the stability of subcycling algorithms in structural dynamics algorithms for explicit integration of structural dynamics problems with multiple time steps subcycling are investigated only one such algorithm due to smolinski and sleith has proved to be stable in a classical sense a simplified version of this algorithm that retains its stability is presented however as with the original version it can be shown to sacrifice accuracy to achieve stability another algorithm in use is shown to be only statistically stable in that a probability of stability can be assigned if appropriate time step limits are observed this probability improves rapidly with the number of degrees of freedom in a finite element model the stability problems are shown to be a property of the central difference method itself which is modified to give the subcycling algorithm a related problem is shown to arise when a constraint equation in time is introduced into a time continuous space time finite element model

counting dihedral and quaternionic extensions we give asymptotic formulas for the number of biquadratic extensions of that admit a quadratic extension which is a galois extension of with a prescribed galois group for example with a galois group isomorphic to the quaternionic group our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the siegel walfisz theorem and the double oscillations theorem

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

the size of selmer groups for the congruent number problem where np is the number of solutions of the congruence y x d2x mod p then ld s has an analytic continuation as an entire function on the complex plane the conjecture of birch and swinnerton dyer then states in particular that the rank r d of ed is equal to the order r d of ld s at s 1 this being the so called analytic rank while we cannot at present find r d in all cases we can at least determine whether or not ld 1 0 and hence conjecturally whether or not r d 0 moreover one has a functional equation for ld s which relates its values at s and 2 s via a sign change ed 1 one may deduce that 1 r d ed it would then follow from the conjecture of birch and swinnerton dyer that the rank is positive whenever ed 1 according to the calculations of birch and stephens 2 one has

semi active control of 1d continuum vibrations under a travelling load abstract the paper presents a method for computing the response of a 1d elastic continuum supported by a set of semi active viscous dampers and induced by a load travelling over it the magnitude of the moving force has been assumed to be constant by neglect of the inertia forces full analytical solution is based on the power series method and is given in an arbitrary time interval the time marching scheme allows us to continue a solution in successive layers with initial conditions taken from the end of previous stages the semi active open loop control strategy is proposed shapes of damping functions are defined as a form of piecewise constant function the control strategy is suboptimal and it outperforms the passive case numerical results are presented for the cases of a string and a bernoulli euler beam

a correction method for the analysis of continuous linear one dimensional systems under moving loads a new correction procedure for dynamic analysis of linear proportionally damped continuous systems under traveling concentrated loads is proposed both cases of non parametric moving forces and parametric moving mass loads are considered improvement in the evaluation of the dynamic response is obtained by separating the contribution of the low frequency lf modes from that of the high frequency hf modes the former is calculated as usual by classical modal analysis while the latter is taken into account using a new series expansion of the corresponding particular solution the advantage of the suggested method is immediately shown in the calculation of the stress distribution since it is able to capture the stress discontinuities due to the nature of the applied loads themselves numerical results are presented to discuss the convergence of the proposed series and to show the accuracy of the calculated response compared to the classical series expansion solution

notes on the stability of non rectangular space time finite elements the method of space time finite elements enables the simple solution of quite new problems it is possible to assume the arbitrary partition of the structure area in each moment of integration of the motion equation instability is caused by a too large time step and too great changes of joint locations in successive time steps a changeable spatial partition is useful in contact dynamic problems in the case of a travelling support generally in problems with movable edges in this paper a stability problem is described and some investigations for chosen types of non rectangular space time finite elements are carried out linear and surface elements which in time space gain an additional time dimension are presented some numerical examples prove the efficiency of the described method under determined limitations

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

revisiting the moving force problem abstract the problem of the vibration of a beam subject to a travelling force is considered the purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force it is shown that for given boundary conditions there exists a unique response velocity dependence function a technique to determine this function is suggested which is based on the assumption that the maximum beam response can be adequately approximated by means of the first beam mode to illustrate this the maximum response function is calculated analytically for a simply supported ss beam and constructed numerically for a clamped clamped beam the effect of the higher modes on the maximum response is investigated and the relative error of the one mode approximation for a ss beam is constructed the estimates obtained substantiate the assumption about adequacy of the one mode approximation in a wide range of velocities in particular the relative error in the neighborhood of the velocity that results in the largest response is less than one percent

stability and accuracy of difference schemes for hyperbolic problems abstract bounds for the error order and error constant of full and semidiscretizations of hyperbolic problems are given in order to be able to compare fulldiscretizations a scaling is introduced this scaling reflects the amount of work needed to perform one time step using the semidiscretization associated with the fulldiscretization lower bounds for these scaled error constants are given these results are derived using the order star technique

stabilization in probability of nonlinear stochastic systems with guaranteed cost we deal with nonlinear dynamical systems consisting of a linear nominal part plus model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense and a given cost functional is minimized we give a lyapunov based separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive algorithms for solving the state feedback and filtering problems with arbitrarily large region of attraction for a wide class of nonlinear systems which at least include feedback linearizable systems

dynamic condensation with synthesis of substructure eigenproperties abstract for structures divided into substructures which are defined by their eigenproperties a combination of the node synthesis and condensation techniques is presented to obtain a first few important eigenproperties of the combined system accurately the accuracy of the calculated modal properties can be increased by iteratively solving an improved and condensed eigenvalue problem if desired the higher modal properties can also be obtained by solving a complementry eigenvalue problem associated with the higher modes the availability of the substructure modes in this approach also provides a very convenient and efficient means of selecting the most appropriate kept degrees of freedom in the condensed eigenvalue problem to expediate the convergence to the correct eigenproperties the methods for coupling of the substructure eigenproperties obtained with different boundary conditions at the interface are described several examples are presented to demonstrate the application of the approach

on three modal synthesis variants abstract a unified formulation of fixed free and loaded interface variants of modal synthesis is presented a formal proof of the exactness of all three variants in the absence of modal truncation is established the sensitivity of the truncation error to the different interface conditions is studied

modelling of vibrating systems using time domain finite element method in this paper several dynamic systems are modelled using the time domain finite element method galerkin s weak principle is used to model the general second order mechanical system and is applied to the dynamics of the simple pendulum problems that arise during the approximation of the final momentum are also investigated furthermore additional dynamic analysis methods are suggested for hybrid co ordinate systems that have both slew and flexible modes the proposed methods are based on both extended hamilton s principle and galerkin s weak principle the matrix wave equation is propagated in a space domain satisfying the geometric natural boundary conditions as a result the flexible motion can be obtained and this was compatible with the applied control input a numerical example is used to demonstrate the effectiveness of the proposed modelling methods for the hybrid co ordinate systems

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

the spinor genus of the integral trace let k be a number field of degree at least 3 in this article we show that the genus of the integral trace form of k contains only one spinor genus additionally we show that exactly 43 resp 29 resp 58 of quadratic resp real quadratic resp imaginary quadratic fields have the same property introduction let k be a number field the rational quadratic form x 7 trk q x has been extensively studied by several authors see for example ba bale c p ep ga mau mire and s for arithmetic purposes a finer invariant of a number field is its integral trace form i e the integral quadratic form obtained by restricting trk q x to the maximal order in k recent applications of the integral trace form can be found in the work of bhargava and shnidman see bhsh where they count cubic orders using the shape an invariant closely related to the integral trace form some other applications of the integral trace on cubic fields can be found in man and man2 given a non degenerate integral quadratic form q it is of great interest to study the number of spinor classes on its genus this is explained by the famous result of eichler eich which says that for an indefinite form q of dimension of at least 3 the spinor genus and the isometry class coincide in this article we analyze the spinor genus of the integral trace form of a number field our main theorem is the following theorem cf theorem 2 12 let k be a non quadratic number field then the genus of the integral trace form of k contains only one proper spinor genus in the case of quadratic fields it is not necessary true that the genus and the proper spinor genus of the integral trace coincide however they agree and differ

the square free sieve and the rank of elliptic curves let e be an elliptic curve over q a celebrated theorem of mordell asserts that e q the abelian group of rational points of e is finitely generated by the rank of e we mean the rank of e q thus the rank of e is positive if and only if e possesses an infinity of rational points relatively few general qualitative assertions can be made about the rank as e varies how large can the rank get although we expect that there are elliptic curves over q with arbitrarily high ranks this is presently unknown what is the average size of the rank recently brumer and mcguinness have reported on their study of 310 716 elliptic curves of prime conductor less than 108 where they have found that 20 06 of those curves have even rank 2 cf bm also see forthcoming work of brumer where subject to a number of standard conjectures he shows that 2 3 is an upper bound for the average rank for all elliptic curves over q ordered in terms of their faltings height what is the behavior of the rank over the family of twists of a given elliptic curve here one has three natural kinds of families of twists 1 quadratic twists one can take any elliptic curve and systematically twist it by all quadratic characters this is the type of family of elliptic curves we are concerned with in this paper specifically if e is an elliptic curve over q given by the weierstrass equation y2 x a x b and d is any squarefree integer the quadratic twist of e by d ed is given by the equation

dynamics of a string moving with time varying speed the paper is dedicated to mathematical analysis of the idealized model of a string moving at a variable speed resonance case is studied and it is shown that an infinite system of equations cannot be reduced some exact solutions are obtained

time finite element methods for structural dynamics summary time finite element methods are developed for the equations of structural dynamics the approach employs the time discontinuous galerkin method and incorporates stabilizing terms having least squares form these enable a general convergence theorem to be proved in a norm stronger than the energy norm results are presented from finite difference analyses of the time discontinuous galerkin and least squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics these results show that for particular interpolations the time finite element method exhibits improved accuracy and stability

absolute versus relative formulations of the moving oscillator problem in the general framework of the bridge vehicle dynamic interaction the so called moving oscillator problem is revisited in order to provide a deeper insight into some analytical and physical aspects not specifically analyzed in previous investigations without lack of generality the case of a stream of moving oscillators crossing a simply supported beam with arbitrary time law is considered the formulations in terms of both absolute and relative displacements of the moving oscillators are critically reviewed and compared and alternative sets of differential equations with time dependent coefficients are derived the study enlightens both theoretically and numerically that impulsive contributions to the dynamic response appear in the relative displacement formulation at the time instants in which each vehicle enters or exits the bridge it is demonstrated that such contributions somehow hidden in the absolute displacement formulation may have a significant influence on the vibration of the moving oscillators and thus cannot be a priori neglected in the analysis it is also shown that the analytical and computational difficulties associated with these additional impulses make preferable the use of the absolute displacement formulation far from being restricted to the case of simply supported beams these findings are valid for any type of bridge structure which induces a discontinuity in the slope of the road profile experienced by the vehicles

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

robust output feedback control of nonlinear stochastic systems using neural networks we present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems the plant dynamics is represented as a nominal linear system plus nonlinearities in turn these nonlinearities are decomposed into a part obtained as the best approximation given by neural networks plus a remaining part which is treated as uncertainties modeling approximation errors and neglected dynamics the weights of the neural network are tuned adaptively by a lyapunov design the proposed controller is obtained through robust optimal design and combines together parameter projection control saturation and high gain observers high performances are obtained in terms of large errors tolerance as shown through simulations

energy dissipative time finite elements for classical mechanics abstract based upon the temporal discretisation of hamilton s canonical equations by means of the continuous galerkin method a petrov galerkin time finite element formulation is presented to analyse non linear mechanical systems for long time integration with the presence of dissipation the time stepping scheme features a correct estimation of physical dissipative energy for mechanical systems with weak dissipation this enables to introduce a moderate numerical dissipation to damp out undesired spurious high frequency modes in a controllable manner numerical examples are performed to demonstrate that the proposed scheme allows us to obtain a correct amount by which the energy changes over the integration run

finite elements in space and time for dynamic contact problems dynamic obstacle and signorini problems are discretized by continuous and discontinuous finite elements in space and time the resulting discrete problems are attributed to a standard implicit time stepping scheme through relaxation of impact phenomena and suitable numerical integration the method can cope with dynamic contact problems which is shown by an analysis of a model problem moreover numerical examples demonstrate that it is actually able to approximate the solution of dynamic contact problems which are not fully covered by the theory copyright 2008 john wiley sons ltd

on the negative pell equation we give asymptotic upper and lower bounds for the number of squarefree d 0 d x such that the equation x 2 dy 2 1 is solvable these estimates as usual can equivalently be interpreted in terms of real quadratic fields with a fundamental unit with norm 1 and give strong evidence in the direction of a conjecture due to p stevenhagen