control design of uncertain quantum systems with fuzzy estimators an approach of control design using fuzzy estimators fes is proposed for quantum systems with uncertainties two types of quantum control problems are considered 1 control of a pure state quantum system in the presence of uncertainties and 2 control design of quantum systems with initial mixed states and uncertainties for the first type of tasks a partial feedback control scheme with an fe is presented to design controllers in this scheme an fe is trained to estimate the quantum state for feedback control of a quantum system and controlled projective measurement is used to assist in controlling the system for the second type of quantum control tasks a probabilistic fuzzy estimator pfe is trained to estimate the quantum state for control design of a quantum system with an initial mixed state and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state two examples of two spin 1 2 systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach

orbits of quantum states and geometry of bloch vectors for n level systems physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than 2 to shed some light on the complicated structure of the set of quantum states we consider a stratification with strata given by unitary orbit manifolds which can be identified with flag manifolds the results are applied to study the geometry of the coherence vector for n level quantum systems it is shown that the unitary orbits can be naturally identified with spheres in only for n 2 in higher dimensions the coherence vector only defines a non surjective embedding into a closed ball a detailed analysis of the three level case is presented finally a refined stratification in terms of symplectic orbits is considered

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

t t 1 transformation is not loosely bernoulli the t t problem open since 1971 is to demonstrate that the t t transformation a naturally arising k transformation is not bernoulli it is shown here not even to be loosely bernoulli

free vibration analysis of functionally graded plates using the element free kp ritz method a free vibration analysis of metal and ceramic functionally graded plates that uses the element free kp ritz method is presented the material properties of the plates are assumed to vary continuously through their thickness according to a power law distribution of the volume fractions of the plate constituents the first order shear deformation plate theory is employed to account for the transverse shear strain and rotary inertia and mesh free kernel particle functions are used to approximate the two dimensional displacement fields the eigen equation is obtained by applying the ritz procedure to the energy functional of the system convergence studies are performed to examine the stability of the proposed method and comparisons of the solutions derived with those reported in the literature are provided to verify its accuracy four types of functionally graded rectangular and skew plates al al2o3 al zro2 ti 6al 4v aluminum oxide and sus304 si3n4 are included in the study and the effects of the volume fraction boundary conditions and length to thickness ratio on their frequency characteristics are discussed in detail

a hybrid energy approach for vibrational modelling of laminated trapezoidal plates with point supports abstract an investigation on the free flexural vibration of symmetric angle ply thin trapezoidal plates continuous over arbitrarily distributed point supports is reported a hybrid energy approach which combines the pb 2 rayleigh ritz method with the lagrangian multiplier method is proposed for the modelling of the aforementioned plate problem the pb 2 rayleigh ritz method uses a set of ritz functions generated from the product of a two dimensional polynomial and the equations of boundaries each raised to the power of 0 1 or 2 corresponding to a free simply supported or clamped edge respectively the geometric boundary conditions associated with the point supports are satisfied through the use of lagrangian multipliers in this paper some new solutions for the natural frequencies of several laminated trapezoidal plates with different stacking sequences and location of point supports are presented the first known mode shapes by means of contour plots for such laminated plates are also included

ergodic properties of color records abstract in a series of papers culminating in the dissertation of the second author under the direction of p w kasteleyn several rigorous results have been obtained concerning the color sequence seen by a random walker on a stochastically black white colored lattice and this under the sole assumption that the coloring is stationary ergodic and independent of the walking in this article we investigate the ergodic properties of the color record process and their implications for the behavior of the sequence nk k 0 of successive times needed for the walker to go from the kth to the k 1 st black point as an example of the type of results obtained we show that if a certain induced color record process is strongly mixing in the ergodic theoretic sense then the average nk tends to the inverse of the density of black points as k tends to infinity and similarly that the distribution of nk tends to a limit that can be explicitly calculated in terms of the distribution of n0 for a certain class of stochastic colorings and random walks we are able to verify that the induced color record process is indeed strongly mixing our main goal however is to clarify the nature of the ergodic properties and thereby provide a tool for future use in the study of color records

three dimensional vibration analysis of cantilevered and completely free isosceles triangular plates the free vibration of cantilevered and completely free isosceles triangular plates based on exact three dimensional elasticity theory is investigated the actual plate domain is first mapped onto a basic cubic domain then the ritz method is applied to derive the eigenfrequency equation from the strain energy and the kinetic energy of the plate a set of chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometry boundary conditions of the plate is developed as the admissible functions of each displacement component the convergence and comparison studies show that rather accurate results can be obtained by using this approach the effects of thickness to width ratio and apex angle on eigenfrequencies of the plates are studied in detail sets of valuable results are presented which may serve as the benchmark values for future numerical techniques in thick plate vibration analysis data for the completely free isosceles triangular plates are presented for the first time

formulation of mindlin engesser model for stiffened plate vibration in this paper a mindlin engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners the theoretical derivation incorporates the mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates and the engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect in the method of solution the resulting energy functionals are minimized using the ritz procedure with a set of admissible two dimensional functions expressed in the form of simple polynomials the key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods with the aim of demonstrating the applicability and versatility of the method numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented several findings and conclusions regarding the method have been highlighted and discussed

the duistermaat heckman integration formula on flag manifolds an exposition is given of various geometrical properties of flag manifolds and of the duistermaat heckman integration formula as applied to flag manifolds

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

geometrically nonlinear analysis of functionally graded plates using the element free kp ritz method abstract the nonlinear response of functionally graded ceramic metal plates fgps under mechanical and thermal loads is investigated using the mesh free kp ritz method the nonlinear formulation is based on the first order shear deformation plate theory and the von karman strains which deal with small strains and moderate rotations the material properties of fgps are assumed to be graded through the thickness direction according to a power law distribution of the volume fraction of the constituents the approximation of the displacement field is expressed in terms of a set of mesh free kernel particle functions the bending stiffness of the plates is evaluated using a stabilized conforming nodal integration method and the membrane and shear stiffnesses are computed using direct nodal integration to eliminate shear locking the nonlinear behavior of the deflection and axial stress is studied for fgps under thermal and mechanical loading and the influences of the volume fraction exponent boundary condition and material properties on the nonlinear response of fgps are examined

stabilizing controllers for bilinear systems the problem of finding stabilizing feedback controllers for continuous bilinear systems where the controls act additively and multiplicatively simultaneously is treated the applicability of the quadratic control law of jacobson 5 and others is extended to the case when the a matrix has arbitary eigenvalues under certain conditions a class of bilinear systems common among biochemical flow systems is defined the dyadic bilinear systems a control scheme the so called division controller for dyadic bilinear systems is suggested the practicality of the control schemes is demonstrated on the problem of controlling the neutron level in a fission reactor

sliding mode control of two level quantum systems this paper proposes a robust control method based on sliding mode design for two level quantum systems with bounded uncertainties an eigenstate of the two level quantum system is identified as a sliding mode the objective is to design a control law to steer the system s state into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system hamiltonian we propose a controller design method using the lyapunov methodology and periodic projective measurements in particular we give conditions for designing such a control law which can guarantee the desired robustness in the presence of the uncertainties the sliding mode control method has potential applications to quantum information processing with uncertainties

engineering stable discrete time quantum dynamics via a canonical qr decomposition we analyze the asymptotic behavior of discrete time markovian quantum systems with respect to a subspace of interest global asymptotic stability of subspaces is relevant to quantum information processing in particular for initializing the system in pure states or subspace codes we provide a linear algebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace we then construct a design algorithm for discrete time feedback control that allows to stabilize a target subspace proving that if the control problem is feasible then the algorithm returns an effective control choice in order to prove this result a canonical qr matrix decomposition is derived and also used to establish the control scheme potential for the simulation of open system dynamics

non smooth lyapunov function based global stabilization for quantum filters this paper addresses the global stabilization problem for a class of quantum filters via non smooth lyapunov functions due to the intrinsic symmetric topology of filter state space the smooth controls synthesized via the classical lyapunov stochastic stability theory fail to obtain the global stabilizability because of the existence of the so called antipodal eigenstates as such for the first time we introduce a non smooth lyapunov like theory for generic stochastic nonlinear systems which includes a continuous lyapunov like theorem and a discontinuous lyapunov like theorem for stability in probability applying the non smooth lyapunov like theory switching control and continuous control in saturation form are constructed for the quantum filters with consideration of the sliding motion of filter state the non smooth property enables these controls to deal with the symmetric topology of filter state space and to solve the problem of global stabilization for quantum filters the eigenstate transferring is obtained as a special result distinguishing these non smooth lyapunov based controls from classical control approaches for quantum filters the effectiveness of the non smooth lyapunov based controls is illustrated through the control design for the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the controls

variations on a theme by mark kac mark kac s theorem on the mean recurrence time in a stationary stochastic process in discrete time with discrete states is taken as the starting point for a series of variations most of which are formulated in terms of 0 1 processes whereas the original theorem deals with the mean recurrence time of a given state under the condition that the state is realized at time 0 this condition is dropped in part of the variations two others refer to the variance of the recurrence time and two to the poincare cycle of a dynamical system most variations consist in inequalities and formal identities for the mean first arrival time and subsequent recurrence times for the given state

bang bang control design for quantum state transfer based on hyperspherical coordinates and optimal time energy control we present a constructive control scheme for solving quantum state engineering problems based on the parameterization of the state vector in terms of complex hyperspherical coordinates unlike many control schemes based on factorization of unitary operators the scheme gives explicit expressions for all generalized euler angles in terms of the hyperspherical coordinates of the initial and final states the factorization when applicable has added benefits that phase rotations can be combined and performed concurrently the control procedure can be realized using simple bang bang or square wavefunction controls optimal time energy control is considered to find the optimal control amplitude the extension of the scheme to implement arbitrary unitary operators is also discussed

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

quantum measurement based feedback control a nonsmooth time delay control approach this paper addresses the problem of measurement based feedback control for quantum systems in which the time to compute the filter based control input is taken into account by considering the input delay it starts with a new lyapunov lasalle like theorem for delay dependent stochastic stability of a class of time delay stochastic nonlinear systems nonsmooth time delay control is then constructed to compensate for the control computation time which is known but arbitrarily long while globally stabilizing the quantum filters almost surely the nonsmooth property enables the control to deal with the symmetric topology of filter state space the effectiveness of the proposed control is illustrated through the global stabilization of the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the proposed control

a ritz vibration analysis of doubly curved rectangular shallow shells using a refined first order theory integral expressions for strain and kinetic energies in vibration analysis of shear deformable doubly curved shallow shells are presented although the formulation follows the first order shear deformation theory the consideration of lame parameters for the transverse shear strain through shell thickness which have been hitherto neglected by other researchers shows linear distribution functions instead of constant values if the lame parameters were dropped finite higher order two dimensional orthogonal polynomials pb 2 functions previously used in thin shell analyses 3 6 have been generalized from three to five degrees to account for the additional rotation fields of a moderately thick shell these global shape functions satisfy the kinematic boundary conditions at the outset the excellent performance and versatility of the computational methodology of the pb 2 ritz method are illustrated in representative numerical simulations the resultant matrix size is far smaller than other discretization methods and yet accurate solutions can be obtained the validity of the results is verified through direct comparisons the discrepancy of various formulations with and without the lame parameters is presented and discussed

controllability of quantum mechanical systems by root space decomposition of su n the controllability property of the unitary propagator of an n level quantum mechanical system subject to a single control field is described using the structure theory of semisimple lie algebras sufficient conditions are provided for the vector fields in a generic configuration as well as in a few degenerate cases

controllability of quantum systems with switching control this article focuses on wavefunction controllability of a class of quantum systems with switching control first we present a specific quantum system which is not wavefunction controllable under the action of any one of two controllers with different fixed structures however we prove that the system is wavefunction controllable if the control input is allowed to switch between the two controllers then we present a sufficient condition for wavefunction controllability of a class of quantum systems with switching control and briefly discuss the problem of control design for such quantum control systems finally two illustrative examples are presented to demonstrate a possible control design process for the proposed method

generalized differential quadrature method for the free vibration of truncated conical panels abstract this paper presents an improved generalized differential quadrature gdq method for the investigation of the effects of boundary conditions on the free vibration characteristics of truncated conical panels the truncated conical panel is an important geometrical shape in the fields of aerospace marine and structural engineering however despite this importance few works in free vibration analysis have dealt with this particular geometry in this work the vibration characteristics of clamped and simply supported truncated conical shells are obtained for various circumferential wave numbers further the effects of the vertex and subtended angles on the frequency parameters are also examined in detail due to limited published results in the open literature results for a range of cases are compared with those generated from the commercial finite element solver mcneal schwendler corporation nastran and excellent agreement is observed

a topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon we show that a continuous dynamical system on a state space that has the structure of a vector bundle on a compact manifold possesses no globally asymptotically stable equilibrium this result is directly applicable to mechanical systems having rotational degrees of freedom in particular the result applies to the attitude motion of a rigid body in light of this result we explain how attitude stabilizing controllers obtained using local coordinates lead to unwinding instead of global asymptotic stability

ergodic and bernoulli properties of analytic maps of complex projective space we examine the measurable ergodic theory of analytic maps f of complex projective space we focus on two different classes of maps ueda maps of p n and rational maps of the sphere with parabolic orbifold and julia set equal to the entire sphere we construct measures which are invariant ergodic weak or strong mixing exact or automorphically bernoulli with respect to these maps we discuss topological pressure and measures of maximal entropy h f h top f log deg f we find analytic maps of p 1 and p 2 which are one sided bernoulli of maximal entropy including examples where the maximal entropy measure lies in the smooth measure class further we prove that for any integer d 1 there exists a rational map of the sphere which is one sided bernoulli of entropy log d with respect to a smooth measure

analysis of effectiveness of lyapunov control for non generic quantum states a lyapunov based control design for natural trajectory tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable using dynamical systems tools we show almost global asymptotic stability for stationary target states subject to certain conditions on the hamiltonians and discuss effectiveness of the design when these conditions are not satisfied for pseudo pure target states the effectiveness of the design is studied further for both stationary and non stationary states using alternative tools

effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells abstract a thorough computational investigation is presented into the effects of initial twist and thickness variation on the vibratory characteristics of cantilevered pretwisted thin shallow conical shells with generally varying thickness an energy approach with the ritz minimization procedure is employed to arrive at a governing eigenvalue equation the admissiblepb 2shape functions which comprise sets of mathematically complete two dimensional orthogonal polynomials and a basic function are introduced to account for the boundary constraints and to approximate the three dimensional displacements of the conical shell the effects of angle of twist thickness variation and geometric parameters on the vibration response are presented in a comprehensive parametric study which provides useful new design data selected vibration mode shapes are also included to enhance the existing literature it is found that an increase in the angle of twist does not necessarily increase the torsional stiffness on the contrary the fundamental frequencies is reduced in the present analysis it is also observed that non zero angle of twist and non uniform chordwise thickness variation cause the absent of vibration mode symmetry

asymptotic properties of feedback solutions for a class of quantum control problems control of quantum systems described by the schrodinger equation is considered feedback control laws are developed for orbit tracking via controlled hamiltonians and their asymptotic properties are analyzed numerical integration via time splitting is also investigated and used to demonstrate the feasibility of the proposed feedback laws

on the use of pb 2 rayleigh ritz method for free flexural vibration of triangular plates with curved internal supports this paper presents a set of comprehensive and accurate results for the free flexural vibration of triangular plates of arbitrary boundary conditions with without curved internal supports these results are presented for ten distinct cases involving the combinations of free simply supported or clamped edge conditions in the present study a simple and straightforward pb 2 rayleigh ritz method is employed to determine the first few natural frequencies for the triangular plates with a wide range of aspect ratios i e a b 2 5 1 2 1 2 3 and 2 a set of pb 2 ritz functions consisting of the product of a two dimensional polynomial function and a basic function is used the basic function is defined by the product of 1 equations of the prescribed continuous piecewise boundary each raised to the power of 0 1 or 2 corresponding to a free simply supported or clamped edge and 2 equations of the internal supports the members of the generated set of functions satisfy automaticaly all the kinematic boundary conditions of the plate at the outset the present results for some cases are compared with available published values from the open literature

the improved complex variable element free galerkin method for two dimensional schrodinger equation abstract a numerical study of two dimensional schrodinger equation is carried out using the improved complex variable element free galerkin icvefg method the icvefg method involves employment of the improved complex variable moving least squares icvmls in the element free galerkin efg procedure for numerical approximation the icvmls is used to construct trial functions for the two dimensional schrodinger equation in the form of one dimensional basis function that effectively reduces the number of unknown coefficients in this study the applicability of the icvefg method is examined through a number of numerical example problems convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases the stability and accuracy of the icvefg method are validated by comparing the computed results with the exact solutions

modeling and control of quantum systems an introduction the scope of this work is to provide a self contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems as well as a brief survey on the main approaches to control synthesis while part of the existing theory especially in the open loop setting stems directly from classical control theory most notably geometric control and optimal control a number of tools specifically tailored for quantum systems have been developed since the 1980s in order to take into account their distinctive features the probabilistic nature of atomic scale physical systems the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback design problems the relevant dynamical models for both closed and open quantum systems are presented along with the main results on their controllability and stability a brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies

mixing properties for random walk in random scenery consider the lattice z d d geq 1 together with a stochastic black white coloring of its points and on it a random walk that is independent of the coloring a local scenery perceived at a given time is a pattern of colors seen by the walker in a finite box around his current position under weak assumptions on the probability distributions governing walk and coloring we prove asymptotic independence of local sceneries perceived at times 0 and n in the limit as n rightarrow infty and at times 0 and t k in the limit as k rightarrow infty where t k is the random k th hitting time of a black point an immediate corollary of the latter result is the convergence in distribution of the interarrival times between successive black hits i e of t k 1 t k as k rightarrow infty the limit distribution is expressed in terms of the distribution of the first hitting time t 1 the proof uses coupling arguments and ergodic theory

optimal control of two level quantum systems we study the manipulation of two level quantum systems this research is motivated by the design of quantum mechanical logic gates which perform prescribed logic operations on a two level quantum system a quantum bit we consider the problem of driving the evolution operator to a desired state while minimizing an energy type cost mathematically this problem translates into an optimal control problem for systems varying on the lie group of special unitary matrices of dimension two with cost that is quadratic in the control we develop a comprehensive theory of optimal control for two level quantum systems this includes in particular a classification of normal and abnormal extremals and a proof of regularity of the optimal control functions the impact of the results of the paper on nuclear magnetic resonance experiments and quantum computation is discussed

a rayleigh ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions abstract to overcome the lack of a more general method for free vibration analysis of trapezoidal plates a computationally efficient and highly accurate rayleigh ritz approach with the newly developed orthogonal plate functions is proposed to solve these problems with any combination of clamped simply supported and free edge support conditions the deflection of the plate is approximated by a set of two dimensional orthogonal plate functions generated using the gram schmidt procedure which expresses the entire plate domain into two implicitly related variables in the present paper the effects of the fibre orientation on the vibrational behaviour of the plates are considered the numerical results for isotropic and anisotropic trapezoidal plates are presented where possible the numerical results are verified with other existing values in the literature

reconstructing a random scenery observed with random errors along a random walk path we show that an i i d uniformly colored scenery on observed along a random walk path with bounded jumps can still be reconstructed if there are some errors in the observations we assume the random walk is recurrent and can reach every point with positive probability at time k the random walker observes the color at her present location with probability 1 and an error y k with probability the errors y k k 0 are assumed to be stationary and ergodic and independent of scenery and random walk if the number of colors is strictly larger than the number of possible jumps for the random walk and is sufficiently small then almost all sceneries can be almost surely reconstructed up to translations and reflections

switching control of closed quantum systems via the lyapunov method in this paper we consider the state transfer problem for closed quantum systems under a degenerate case where the linearized system around the target state is not controllable it is known that the traditional lyapunov control methods may fail to guarantee the convergence to the target state under the degenerate case hence we propose to use multiple lyapunov functions and design a switching control strategy to achieve more accurate state transfer it is shown that the system can converge to the intersection of invariant sets including the target state the explicit analysis of the convergence is provided to design the switching law moreover the effectiveness of open loop lyapunov control is discussed simulation studies are presented to show the improved control performance

an element free based solution for nonlinear schrodinger equations using the icvmls ritz method an improved complex variable moving least squares ritz icvmls ritz method is proposed for predicting numerical solution of the two dimensional nonlinear schrodinger equation in this element free solution procedure the icvmls approximation is employed to reduce the number of unknown coefficients in the trial function it follows by the ritz procedure to derive the final algebraic equation system through discretizing the constructed energy formulation of the nonlinear schrodinger equation the central differencing scheme and newton s algorithm are adopted to solve the nonlinear equation system numerical experiments are conducted on the final form of the governing equation system to demonstrate the accuracy and efficiency of the element free icvmls ritz method by comparing the computed results with the available analytical solutions

retrieving random media benjamini asked whether the scenery reconstruction methods of matzinger see e g 21 22 20 can be done in polynomial time in this article we give the following answer for a 2 color scenery and simple random walk with holding we prove that a piece of the scenery of length of the order 3 n around the origin can be reconstructed up to a reflection and a small translation with high probability from the first 2 310 n observations with a constant 0 independent of n thus the number of observations needed is polynomial in the length of the piece of scenery which we reconstruct the probability that the reconstruction fails tends to 0 as n

elasticity solutions for free vibrations of annular plates from three dimensional analysis abstract this article examines the vibrational characteristics of annular plates by using the three dimensional elasticity theory it aims to raise the quality of the investigation beyond that provided by the two dimensional plate theories by resorting to a full three dimensional analysis a polynomials ritz model based on sets of orthogonally generated polynomial functions to approximate the spatial displacements of the plates in cylindrical polar coordinates is presented the model is then used to extract the full vibration spectrum of natural frequencies and mode shapes the vibration responses due to the variations of boundary conditions and thickness are investigated frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of the method is validated through appropriate convergence and comparison studies

robust incoherent control of qubit systems via switching and optimisation a robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state this scheme consists of two main steps projective measurement on the initial mixed state and optimal control between two pure states the first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states the second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state the connection between the two steps is accomplished by a switching strategy to accomplish the second step two approaches are presented in detail these approaches are time optimal transition with unbounded control and bang bang control with minimal switches the minimal time and minimal number of switches in these approaches can be calcu

numerical analysis of generalized regularized long wave equation using the element free kp ritz method abstract a numerical analysis of the generalized regularized long wave grlw equation by application of the element free kp ritz method is performed to approximate the displacement field an element free kernel particle estimation is employed and a system of nonlinear discrete equations is achieved by using the ritz minimization procedure to the energy expressions validation of the present numerical solutions with the exact results has been conducted by numerical examples and evidenced a good agreement

buckling of thick skew plates the paper considers the elastic buckling of thick skew plates up to now very little work has been done on this subject and the paper aspires to fill this gap based on the principle of stationary total potential energy and the recently developed pb 2 rayleigh ritz method as a solution procedure buckling solutions for skew plates of various aspect ratios skew angles and boundary conditions are determined the tabulation of these results not available thus far should be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for thick plate analysis

feedback stabilization of isospectral control systems on complex flag manifolds application to quantum ensembles the convex set of density operators of an n level quantum mechanical system foliated as a complex flag manifold where each leaf is identified with the adjoint unitary orbit of the eigenvalues of a density matrix for an isospectral bilinear control system evolving on such an orbit the state feedback stabilization problem admits a natural lyapunov based time varying feedback design a global description of the domain of attraction of the closed loop system can be provided based on a ldquoroot spacerdquo like structure of the cone of density operators the converging conditions are time independent but depend on the topology of the flag manifold it is shown that the closed loop must have a number of equilibria at least equal to the euler characteristic of the manifold thus imposing topological obstructions to global stabilizability

a pb 2 ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform abstract this paper presents a free flexural vibration analysis of shallow cylindrical shells of rectangular planform with arbitrary combinations of free simply supported and clamped boundaries the pb 2 ritz method previously used in the plate analysis by one of the authors is now extended to shallow shell studies the ritz approach along with the in plane and transverse displacements assumed in the form of orthogonal polynomials is used to formulate the problems numerical results for the vibration frequencies for wide ranges of aspect ratio shallowness ratio and thickness ratio are presented several selected contour plots of the mode shapes for six different combinations of boundary conditions are presented as usual the accuracy of the present method is illustrated by convergence tests and comparison with the well established results from the literature

stabilizability of closed orbits abstract the main contribution of this paper is a version of the jurdjevic quinn method for feedback stabilization of closed orbits of autonomous affine control systems

vibration analysis of multi span plates having orthogonal straight edges abstract an accurate numerical technique is developed for flexural vibration of rectangular and l shaped plates continuous over rigid supports with arbitrary number of spans a set of orthogonally generated two dimensional plates function is used in the rayleigh ritz method to determine the natural frequencies of the plate systems several numerical examples are presented and the results obtained where possible are compared with the known solutions in the literature the present method is proven to be extremely versatile in solving a broad class of the aforementioned problems

feedback control of quantum state reduction feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement we formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter we explore the use of stochastic lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability

constructive control of quantum systems using factorization of unitary operators we demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise and decay times or gaussian wavepackets to illustrate the technique it is applied to find control schemes to achieve population transfers for pure state systems complete inversions of the ensemble populations for mixed state systems create arbitrary superposition states and optimize the ensemble average of dynamic observables

analysis of lyapunov method for control of quantum states the natural trajectory tracking problem is studied for generic quantum states represented by density operators a control design based on the hilbert schmidt distance as a lyapunov function is considered the control dynamics is redefined on an extended space where the lasalle invariance principle can be correctly applied even for non stationary target states lasalle s invariance principle is used to derive a general characterization of the invariant set which is shown to always contain the critical points of the lyapunov function critical point analysis of the latter is used to show that for generic states it is a morse function with n isolated critical points including one global minimum one global maximum and n 2 saddles it is also shown however that the actual dynamics of the system is not a gradient flow and therefore a full eigenvalue analysis of the linearized dynamics about the critical points of the dynamical system is necessary to ascertain stability of the critical points this analysis shows that a generic target state is locally asymptotically stable if the linearized system is controllable and the invariant set is regular and in fact convergence to the target state trajectory in this case is almost global in that the stable manifolds of all other critical points form a subset of measure zero of the state space on the other hand if either of these sufficient conditions is not satisfied the target state ceases to be asymptotically stable a center manifold emerges around the target state and the control design ceases to be effective

treatments of over restrained boundaries for doubly connected plates of arbitrary shape in vibration analysis abstract the problem of the free flexural vibrations of plates of doubly connected arbitrary shape is investigated a hybrid energy approach which combines both the advantages of the rayleigh ritz method and the lagrange multiplier method is developed for analysing the aforementioned plate problems the rayleigh ritz method with a set of pb 2 shape functions is used to formulate the plates with classical boundary conditions as a single continuum element while the lagrange multipliers are imposed at discrete points in the inner plate boundaries for instance when the overrestrained boundary has occurred the admissible pb 2 shape function consists of the product of a two dimensional polynomial and a basic function the basic function is defined by the product of the equations of the prescribed piecewise continuous boundary shape each raised to the power of 0 1 or 2 corresponding respectively to a free simply supported or clamped edge this set of functions automatically satisfies all the kinematic boundary conditions of the plate at the outset numerical results for several examples of doubly connected plates of arbitrary shape are presented to demonstrate the applicability and accuracy of the present method

application of two dimensional orthogonal plate function to flexural vibration of skew plates abstract a set of two dimensional orthogonal plate functions is used as an admissible deflection function for the study of the flexural vibration of skew plates by the rayleigh ritz method from a prescribed starting function satisfying the boundary conditions the higher terms in the two dimensional orthogonal plate functions are generated by using the gram schmidt orthogonalization process the method is applied to obtain results for a few particular rhombic plates with different support conditions at various skew angles where possible the numerical results presented are compared with the values obtained by other numerical methods in the literature the results should be of considerable value and practical significance in design applications

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

flexural vibration of shear deformable circular and annular plates on ring supports this paper presents an analysis of free flexural vibration of circular and annular mindlin plates lying on multiple internal concentric ring supports the rayleigh ritz method with an admissible displacement function expressed in terms of a set of simple polynomials is used to obtain the governing eigenvalue equation the natural frequencies of circular and annular mindlin plates with one or two ring supports having inner and outer peripheries with different combinations of free simply supported and clamped conditions are determined a comprehensive set of vibration results is presented and where possible these have been verified with existing solutions published in the open literature no previous theoretical results for thick annular plates supported with internal rings are known to exist thus the study should be useful and valuable to engineers and researchers

notes on sliding mode control of two level quantum systems in dong d and petersen i r 2012 sliding mode control of two level quantum systems automatica 48 725 735 a sliding mode control approach has been proposed for two level quantum systems to deal with bounded uncertainties in the system hamiltonian this paper further extends these results in two directions one extension is to consider the effect of uncertainties during the process of driving the system s state back to the sliding mode domain from outside and we propose two approaches to accomplish this control task the other extension generalizes the previous design approach to consider uncertainties described as perturbations in the free hamiltonian

controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds for isospectral bilinear control systems evolving on the so called complex flag manifolds i e on the orbits of the hermitian matrices under unitary conjugation action it is shown that controllability is almost always verified easy and generic sufficient conditions are provided the result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems in addition we show that systems having different drifts corresponding for example to different larmor frequencies are simultaneously controllable by the same control field

vibration of shallow conical shells with shear flexibility a first order theory a formulation of shear deformation theory implemented numerically for the prediction of vibratory characteristics of shallow conical shell panels is presented the derivation of thickness shear is assumed in a linear approximation the lame parameter for the transverse shear strain component which has previously been neglected is considered this consideration accounts for the replacement of a term in transverse strain distribution through the shell thickness which results in linear transverse shear strain distribution in contrast to the constant distribution hitherto known to researchers in this field the energy integral which incorporates the shear deformation and rotary inertia is minimized to derive the governing eigen matrix equation a set of benchmark frequency solutions is presented for two exemplary conical shells the cantilever and the fully clamped shells some selected mode shapes in terms of mid surface contour plots and three dimensional meshes are also illustrated

analysis of quantum linear systems response to multi photon states the purpose of this paper is to present a mathematical framework for analyzing the response of quantum linear systems driven by multi photon states both the factorizable namely no correlation among the photons in the channel and unfactorizable multi photon states are treated pulse information of a multi photon input state is represented in terms of tensor and the response of quantum linear systems to multi photon input states is characterized by tensor operations analytic forms of output correlation functions and output states are derived the proposed framework is applicable no matter whether the underlying quantum dynamic system is passive or active examples from the physics literature are used to illustrate the results presented

rapid lyapunov control of finite dimensional quantum systems abstract rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process bang bang lyapunov control can speed up the control process but cannot guarantee convergence to a target state this paper proposes two classes of new lyapunov control methods that can achieve rapidly convergent control for quantum states one class is switching lyapunov control where the control law is designed by switching between bang bang lyapunov control and standard lyapunov control the other class is approximate bang bang lyapunov control where we propose two special control functions which are continuously differentiable and yet have a bang bang type property related stability results are given and a construction method for the degrees of freedom in the lyapunov function is presented to guarantee rapid convergence to a target eigenstate being isolated in the invariant set several numerical examples demonstrate that the proposed methods can achieve improved performance for rapid state control of quantum systems

a long time tail for random walk in random scenery consider a simple random walk on d whose sites are colored black or white independently with probabilityq resp 1 q walk and coloring are independent letn k be the number of steps by the walk between itskth and k 1 th visits to a black site i e the length of itskth white run and let k e n k q 1 our main result is a proof that lim k k d 2 k 1 q q d 2 2 d 2 d 2 since it is known thatq 1 k e n 1 n k 1 b e n 1 b e n k 1 b withb the event that the origin is black exhibits a long time tail in the run length autocorrelation function numerical calculations of k 1 k 100 ind 1 2 and 3 show that there is an oscillatory behavior of k for smallk this damps exponentially fast following which the power law sets in fairly rapidly we prove that if the coloring is not independent but is convex in the sense of fkg then the decay of k cannot be faster than

lyapunov control of bilinear schrodinger equations a lyapunov based approach for trajectory tracking of the schrodinger equation is proposed in the finite dimensional case convergence is precisely analyzed connection between the controllability of the linearized system around the reference trajectory and asymptotic tracking is studied when the linearized system is controllable such a feedback ensures almost global asymptotic convergence when the linearized system is not controllable the stability of the closed loop system is not asymptotic to overcome such lack of convergence we propose when the reference trajectory is an eigenstate a modification based on adiabatic invariance simulations illustrate the simplicity and also the interest for trajectory generation

vibration of eccentric ring and line supported circular plates carrying concentrated masses abstract the vibration of circular plates supported by combinations of ring and line supports and which are carrying concentrated masses is investigated for the first time to the author s knowledge by using the newly developed pb 2 rayleigh ritz method a set of ritz functions consisting of the product of the boundary expressions is used as the admissible displacement function this set of pb 2 ritz functions can accurately approximate the mode shapes of these circular plates with any prescribed boundary conditions and interior supports such as eccentric annular and or line supports to validate the present method numerical calculations have been carried out for several simplified plate problems and these are compared with those results available in the literature excellent agreement is achieved in all cases

an improved moving least squares ritz method for two dimensional elasticity problems we propose an improved moving least squares ritz imls ritz method with its element free framework developed for studying two dimensional elasticity problems using the imls approximation for the field variables the discretized governing equations of the problem are derived via the ritz procedure in the imls an orthogonal function system with a weight function is employed as the basis for construction of its displacement field by using the element free imls ritz method solutions of the two dimensional elasticity problems are obtained the applicability of the element free imls ritz method is illustrated through three selected example problems the convergence characteristics of the method are examined by varying the number of nodes and geometric parameters of these examples the accuracy of the method is validated by comparing the computed results with the efg and exact solutions

asymptotically brownian skew products give non loosely bernoulli k automorphisms a quite natural exponential mixing condition on a real valued cocyclef implies that the cocycle is asymptotically approximable by brownian motion to a degree better thant 1 2 this in turn implies that the skew extension by a positive entropy ergodic flow using the cocycle is not loosely bernoulli in complete analogy to kalikow st t 1 argument kal

erratum for feedback stabilization of isospectral control systems on complex flag manifolds application to quantum ensembles nov 07 2019 2028 the results in the above titled paper ibid vol 52 no 11 pp 2019 2028 nov 07 are contradicted slightly by those found in two others cited here the results are explained here