the eigenvalues of second order spectral differentiation matrices the eigenvalues of the pseudospectral second derivative matrix with homogeneous dirichlet boundary conditions are important in many applications of spectral methods this paper investigates some of their properties numerical results show that a certain fraction of the eigenvalues approximate the eigenvalues of the continuous operator very accurately but the errors in the remaining ones are large it is demonstrated that the inaccurate eigenvalues correspond to those eigenfunctions of the continuous operator that cannot be resolved by polynomial interpolation in the spectral grid in particular it is proved that 7r points on average per wavelength are sufficient for successful interpolation of the eigenfunctions of the continuous operator in a chebyshev distribution of nodes and six points per wavelength for a uniform distribution these results are in agreement with the observed fractions of accurate eigenvalues by using the characteristic polynomial a bound on the spectral radius of the differentiation matrix is derived that is accurate to 2 or better the effect of filtering on the eigenvalues is studied numerically

stochastic controllability and minimum energy control of systems with multiple delays in control in recent years various controllability problems for different types of linear dynamical systems have been considered in many publications and monographs

reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics abstract galerkin and stabilized galerkin least squares and galerkin gradient least squares finite element methods for solving problems of time harmonic acoustics are presented and analyzed the error of discretization is related to spurious representation of physical phenomena namely dispersion anisotropy and reflection all of which decrease with mesh refinement the performance of the stabilized methods in terms of dispersion and anisotropy is identical both are superior to the galerkin method relaxing wave resolution requirements further insight into the design of these methods is provided by the analyses the stabilized methods differ in the degree of spurious reflection that is engendered by transitions in mesh size the performance of galerkin gradient least squares deteriorates on non uniform meshes however galerkin least squares maintains its enhanced performance exhibiting low sensitivity to transitions in mesh size thereby reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics guidelines for discretization pertaining to mesh orientation and wave resolution are presented

toward a universal adaptive finite element strategy part 3 design of meshes abstract in this third paper in our series the issue of designing h p meshes which are optimal in some sense is addressed criteria for h p meshes are derived which are based on the idea of minimizing the estimated error over a mesh with a fixed number of degrees of freedom an optimization algorithm is developed based on these criteria and is applied to several model one dimensional and two dimensional elliptic boundary value problems numerical results indicate that the approach can lead to exponential rates of convergence

a comparison of numerical collocation and variational procedures to the hypersingular acoustic integral operator abstract a major difficulty in implementing many of the more innovative acoustic formulations for the solution of submerged three dimensional thin shells of arbitrary geometry in an unbounded fluid medium has been the difficulty of numerically approximating a hypersingular integral operator a variational approach given by hamdi reduces this hypersingularity cauchy singularity to a weak singularity allowing for its accurate numerical approximation recently mariem and hamdi a new boundary finite element method for fluid structure interaction internat j numer methods engrg 24 1987 1251 1267 presented an acoustic formulation for thin shells where the pressure difference across the shell is related to the shell s normal velocity solely in terms of this integral operator despite its advantage of generating a symmetric fluid matrix a double surface integration is required to form this matrix some researchers have endeavoured to develop a collocation method of approximating this highly singular operator in this paper a novel solution to the numerical approximation of this operator is given in the implementation of both the variational and collocation methodologies quadratic quadrilateral elements are used to interpolate for the acoustic and geometric variables results are then presented for thin shell scattering and radiation problems for both closed and non closed thin shells demonstrating the validity and accuracy of both methods

on numerical cubatures of singular surface integrals in boundary element methods we present and analyze methods for the accurate and efficient evaluation of weakly cauchy and hypersingular integrals over piecewise analytic curved surfaces in 3 the class of admissible integrands includes all kernels arising in the numerical solution of elliptic boundary value problems in three dimensional domains by the boundary integral equation method the possibly not absolutely integrable kernels of boundary integral operators in local coordinates are pseudohomogeneous with analytic characteristics depending on the local geometry of the surface at the source point this rules out weighted quadrature approaches with a fixed singular weight for weakly singular integrals it is shown that duffy s triangular coordinates leadalways to a removal of the kernel singularity also asymptotic estimates of the integration error are provided as the size of the boundary element patch tends to zero these are based on the rabinowitz richter estimates in connection with an asymptotic estimate of domains of analyticity in 2 it is further shown that the modified extrapolation approach due to lyness is in the weakly singular case always applicable corresponding error and asymptotic work estimates are presented for the weakly singular as well as for cauchy and hypersingular integrals which e g arise in the study of crack problems we analyze a family of product integration rules in local polar coordinates these rules are hierarchically constructed from finite part integration formulas in radial and gaussian formulas in angular direction again we show how the rabinowitz richter estimates can be applied providing asymptotic error estimates in terms of orders of the boundary element size

eigenvalues of the laplacian in two dimensions the eigenvalue problem for the laplace operator in two dimensions is classical in mathematics and physics nevertheless computational methods for estimating the eigenvalues are still of much current interest particularly in applications to acoustic and electromagnetic waveguides although our primary interest is with the computational methods there are a number of theoretical results on the behavior of the eigenvalues and eigenfunctions that are useful for understanding the methods and in addition are of interest in themselves these results are discussed first and then the various computational methods that have been used to estimate the eigenvalues are reviewed with particular emphasis on methods that give error bounds some of the more powerful techniques available are illustrated by applying them to a model problem

can billiard eigenstates be approximated by superpositions of plane waves the plane wave decomposition method pwdm is one of the most popular strategies for numerical solution of the quantum billiard problem the method is based on the assumption that each eigenstate in a billiard can be approximated by a superposition of plane waves at a given energy from the classical results on the theory of differential operators this can indeed be justified for billiards in convex domains in contrast in the present work we demonstrate that eigenstates of non convex billiards in general cannot be approximated by any solution of the helmholtz equation regular everywhere in r2 in particular by linear combinations of a finite number of plane waves having the same energy from this we infer that pwdm cannot be applied to billiards in non convex domains furthermore it follows from our results that unlike the properties of integrable billiards where each eigenstate can be extended into the billiard exterior as a regular solution of the helmholtz equation the eigenstates of non convex billiards in general do not admit such an extension

hp adaptive finite elements in electromagnetics a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for curvilinear elements is presented the proposed method is illustrated and verified by a series of 2d experiments which include elements with curved boundaries and nonhomogeneous media

fast computation of high frequency dirichlet eigenmodes via spectral flow of the interior neumann to dirichlet map we present a new algorithm for numerical computation of large eigenvalues and associated eigenfunctions of the dirichlet laplacian in a smooth star shaped domain in d d 2 conventional boundary based methods require a root search in eigenfrequency k hence take o n3 effort per eigenpair found where n o kd 1 is the number of unknowns required to discretize the boundary our method is o n faster achieved by linearizing with respect to k the spectrum of a weighted interior neumann to dirichlet ntd operator for the helmholtz equation approximations to the square roots kj of all o n eigenvalues lying in k k where o 1 are found with o n3 effort we prove an error estimate with c independent of k we present a higher order variant with eigenvalue error scaling empirically as o 5 and eigenfunction error as o 3 the former improving upon the scaling method of vergini and saraceno for planar domains d 2 with an assumption of absence of spectral concentration we also prove rigorous error bounds that are close to those numerically observed for d 2 we compute robustly the spectrum of the ntd operator via potential theory nystrom discretization and the cayley transform at high frequencies 400 wavelengths across with eigenfrequency relative error 10 10 we show that the method is 103 times faster than standard ones based upon a root search 2014 wiley periodicals inc

brief paper controllability of boolean control networks with time delays in states this paper investigates the controllability of boolean networks with time invariant delays in states after a brief introduction on converting the logic dynamics to discrete time delay systems the controllability via two kinds of controls is studied one kind of control is generated by boolean control networks another kind of control is free boolean sequences in both cases necessary and sufficient conditions of the controllability of boolean control networks are proved finally examples are given to illustrate the efficiency of the obtained results

the spectrum of the chebyshev collocation operator for the heat equation it is shown that the eigenvalues of the pseudospectral chebyshev second derivative operator with separated boundary conditions are real negative and distinct an application to the full potential equation is also presented

system decomposition with respect to inputs for boolean control networks abstract in this paper the problem of system decomposition with respect to inputs is investigated for boolean control networks bcns first based on the linear representation of bcns some algebraic equivalent conditions for the decomposability are obtained second the concept of perfect equal vertex partition pevp is proposed for bcns a necessary and sufficient graphical condition for the decomposability i e the existence of a pevp is proposed third for calculating a pevp an algorithm called vertex set uniting algorithm vsua is designed finally a biological example is analyzed to show the effectiveness of the proposed method

scattering reflection and impedance of waves in chaotic and disordered systems with absorption we review recent progress in analysing wave scattering in systems with both intrinsic chaos and or disorder and internal losses when the scattering matrix is no longer unitary by mapping the problem onto a nonlinear supersymmetric model we are able to derive closed form analytic expressions for the distribution of reflection probability in a generic disordered system one of the most important properties resulting from such an analysis is statistical independence between the phase and the modulus of the reflection amplitude in every perfectly open channel the developed theory has far reaching consequences for many quantities of interest including local green functions and time delays in particular we point out the role played by absorption as a sensitive indicator of mechanisms behind the anderson localization transition we also provide a random matrix based analysis of s matrix and impedance correlations for various symmetry classes as well as the distribution of transmitted power for systems with broken time reversal invariance completing previous works on the subject the results can be applied in particular to the experimentally accessible impedance and reflection in a microwave or an ultrasonic cavity attached to a system of antennas

controllability of measure driven evolution systems with nonlocal conditions this paper investigates complete controllability of semilinear measure driven differential systems with nonlocal conditions without assuming the compactness of the evolution system related to the linear part of the measure system some sufficient conditions for controllability are established by using the measure of noncompactness and the monch fixed point theorem the results obtained here improve and generalize many known results

an algorithm for the evaluation of multidimensional direct and inverse discrete chebyshev transforms abstract a method is presented for the efficient computation of n d n dimensional imbricated sums of direct and inverse discrete chebyshev transforms the algorithm consists essentially in the generalization of well known onedimensional procedures which are fitted together in order to perform the pre and post processing of the chebyshev coefficients array

a priori error estimations of hp finite element approximations for hierarchical models of plate and shell like structures a priori error estimates of hp finite element approximations for hierarchical models of the thin elastic plate and shell like structures are derived the error in the approximations of a hierarchical model consists of the modelling error due to assumptions on displacement or stress fields and the finite element approximation error of discretizations of such a model also non uniformity with respect to the thickness owing to numerical locking is included in the present error estimates numerical results are given supporting the theoretical results

brief paper complete controllability of impulsive stochastic integro differential systems this paper is concerned with the controllability of impulsive stochastic integro differential systems sufficient conditions of complete controllability for impulsive stochastic integro differential systems are obtained by using schaefer s fixed point theorem a numerical example is provided to show the effectiveness of the proposed results

on hp error estimation in the bem for a three dimensional helmholtz exterior problem the purpose of the paper is to give an a priori convergence estimate for the hp adaptive boundary element method the method is used to solve an exterior helmholtz boundary value problem with the robin s boundary condition in the three dimensional space the mathematical model describes an acoustic wave scattering problem on a bounded elastic solid where time harmonic process is assumed the estimate consists of three parts which correspond to influence of three errors caused by interpolation of functions geometry and an incident wave

brief paper controllability of probabilistic boolean control networks this paper deals with the controllability of probabilistic boolean control networks first a survey on the semi tensor product approach to probabilistic boolean networks is given second the controllability of probabilistic boolean control networks via two kinds inputs is studied finally examples are given to show the efficiency of the obtained results

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

modeling of electromagnetic absorption scattering problems using hp adaptive finite elements a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for affine elements is presented the proposed method is illustrated and verified with a series of 2d experiments including elements with curved boundaries and nonhomogeneous media

controllability and observability of boolean control networks the controllability and observability of boolean control networks are investigated after a brief review on converting a logic dynamics to a discrete time linear dynamics with a transition matrix some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix based on the discrete time dynamics the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely then the problem of observability is also solved by giving necessary and sufficient conditions

consolidating boundary methods for finding the eigenstates of billiards the plane wave decomposition method a widely used means of numerically finding eigenstates of the helmholtz equation in billiard systems is described as a variant of the mathematically well established boundary integral method bim a new unified framework encompassing the two methods is discussed furthermore a third numerical method which we call the gauge freedom method is derived from the bim equations this opens the way to further improvements in eigenstate search techniques

first principles model of time dependent variations in transmission through a fluctuating scattering environment fading is the time dependent variation in transmitted signal strength through a complex medium due to interference or temporally evolving multipath scattering in this paper we use random matrix theory rmt to establish a first principles model for fading including both universal and nonuniversal effects this model provides a more general understanding of the most common statistical models rayleigh fading and rice fading and provides a detailed physical basis for their parameters we also report experimental tests on two ray chaotic microwave cavities the results show that our rmt model agrees with the rayleigh and rice models in the high loss regime but there are strong deviations in low loss systems where the rmt approach describes the data well

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

a gpu parallelized spectral method for elliptic equations in rectangular domains we design and implement a polynomial based spectral method on graphic processing units gpus the key to success lies in the seamless integration of the matrix diagonalization technique and the new generation cuda tools the method is applicable to elliptic equations in rectangular domains with general boundary condition we show remarkable speedups of up to 15 times in the 2 d case and more than 35 times in the 3 d case

classical wave experiments on chaotic scattering we review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems scattering theory has to be applied for a quantitative interpretation of the measurements most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation in all studied examples a quantitative agreement between experiment and theory is achieved to this end it is necessary however to take absorption and imperfect coupling into account concepts that were ignored in most previous theoretical investigations classical phase space signatures of scattering are being examined in a small number of experiments

solution of 3d laplace and helmholtz equations in exterior domains using hp infinite elements abstract this work is devoted to a convergence study for infinite element discretizations for laplace and helmholtz equations in exterior domains the proposed approximation applies to separable geometries only combining an hp fe discretization on the boundary of the domain with a spectral like representation resulting from the separation of variables in the radial direction the presentation includes a convergence proof for the laplace equation and a stability analysis for the variational formulation of the helmholtz equation in weighted sobolev spaces the theoretical investigations are verified and illustrated with numerical examples for the exterior spherical domain

a minimum time control for boolean control networks with impulsive disturbances this paper investigates a mayer type optimal control and minimum time control of a boolean control network bcn with impulsive disturbances using the semi tensor product the bcn with impulsive disturbances is converted into algebraic discrete time impulsive dynamic systems and several necessary conditions for optimality are derived then we consider the problem of steering a bcn with impulsive disturbances from a given initial state to a desired state in minimal time and a necessary condition stated in the form of maximum principle is obtained for a control to be time optimal it shows that the impulsive disturbances play an important role in the optimal control problem for bcns at last a biological example is given to illustrate the effectiveness and advantage of the obtained results

on some recent adventures into improved finite element cfd methods for convective transport abstract the quest continues for computational fluid dynamics cfd algorithms that are accurate and efficient for convection dominated applications including shocks travelling fronts and wall layers the boundary value optimal galerkin weak statement invariably requires manipulation either in the test space or in an augmented form for the conservation law system to handle the disruptive character introduced by the discretized first order convection term an incredible variety of methodologies have been derived and examined to address this issue in particular seeking achievement of accurate and monotone discrete approximate solutions in an efficient implementation the utk cfd research group continues its search on examining the breadth of approaches leading to development of a consistent encompassing theoretical statement exhibiting quality performance included herein are adventures into generalized taylor series lax wendroff methods characteristic euler flux resolutions sub grid embedded high degree lagrange bases with static condensation and assembled stencil fourier analysis optimization for finite element weak statement implementations for appropriate model problems including steady convection diffusion and pure unsteady convection and benchmark navier stokes definitions recent advances have lead to candidate accurate monotone methods with linear basis efficiency this contribution highlights the theoretical developments and presents quantitative documentation of achievable high quality solutions

boolean dynamics of networks with scale free topology the dynamics of boolean networks with scale free topology are studied the existence of a phase transition from ordered to chaotic dynamics governed by the value of the scale free exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories the phase diagram shows that the phase transition occurs for values of the scale free exponent in the open interval 2 2 5 since the boolean networks under study are directed graphs the scale free topology of the input connections and that of the output connections are studied separately ultimately these two topologies are shown to be equivalent a numerical study of the attractor structure of the configuration space reveals that this structure is similar in both networks with scale free topologies and networks with homogeneous random topologies however an important result of this work is that the fine tuning usually required to achieve stability in the dynamics of networks with homogeneous random topologies is no longer necessary when the network topology is scale free finally based on the results presented in this work it is hypothesized that the scale free topology favors the evolution and adaptation of network functioning from a biological perspective

input state incidence matrix of boolean control networks and its applications the input state incidence matrix of a control boolean network is proposed it is shown that this matrix contains complete information of the input state mapping using it an easily verifiable necessary and sufficient condition for the controllability of a boolean control network is obtained the corresponding control which drives a point to a given reachable point is designed moreover certain topological properties such as the fixed points and cycles of a boolean control network are investigated then as another application a sufficient condition for the observability is presented finally the results are extended to mix valued logical control systems

experimental investigation of wigner s reaction matrix for irregular graphs with absorption we use tetrahedral microwave networks consisting of coaxial cables and attenuators connected by t joints to make an experimental study of wigner s reaction k matrix for irregular graphs in the presence of absorption from measurements of the scattering matrix s for each realization of the microwave network we obtain distributions of the imaginary and real parts of k our experimental results are in good agreement with theoretical predictions

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

brief paper boolean derivative calculation with application to fault detection of combinational circuits via the semi tensor product method using the semi tensor product method this paper investigates the boolean derivative calculation with application to fault detection of combinational circuits and presents a number of new results first a new set of formulas is obtained to calculate the boolean derivative by the semi tensor product method then the obtained new results are applied to detecting the multiple faults of combinational circuits and a new detection method is proposed finally two illustrative examples are studied by using the results obtained in this paper the study of illustrative examples shows that the new detection method can be used for detection of more than two faults effectively

optimal control of logical control networks this paper considers the infinite horizon optimal control of logical control networks including boolean control networks as a special case using the framework of game theory the optimal control problem is formulated in the sight of the algebraic form of a logical control network its cycles can be calculated algebraically then the optimal control is revealed over a certain cycle when the games using memory 1 which means the players only consider previous steps action at each step are considered the higher order logical control network is introduced and its algebraic form is also presented which corresponds to a conventional logical control network i e 1 then it is proved that the optimization technique developed for conventional logical control networks is also applicable to this memory case

plane wave quantization for polygonal billiards there is theoretical evidence indicating that generic polygons do not admit eigenfunctions that are superpositions of plane waves however we find that a plane wave quantization for a family of polygonal billiards gives results in very good agreement with theoretical predictions indeed the fraction of missing states decreases as the number of sides is increased we provide a resolution of this contradiction while theory says that no plane wave eigenfunctions are possible for polygonal boundaries it is not applicable to the curvilinear boundaries approximating these polygons this is analogous to the classical mechanics of polygonal billiards where according to continuum mathematics there is no chaos yet discrete mathematics finds it in the quantum treatment considered here according to continuum mathematics there can be no plane wave eigenfunctions yet discrete mathematics finds them

range dependence of the response of a spherical head model the head related transfer function hrtf varies with range as well as with azimuth and elevation to better understand its close range behavior a theoretical and experimental investigation of the hrtf for an ideal rigid sphere was performed an algorithm was developed for computing the variation in sound pressure at the surface of the sphere as a function of direction and range to the sound source the impulse response was also measured experimentally the results may be summarized as follows first the experimental measurements were in close agreement with the theoretical solution second the variation of low frequency interaural level difference with range is significant for ranges smaller than about five times the sphere radius third the impulse response reveals the source of the ripples observed in the magnitude response and provides direct evidence that the interaural time difference is not a strong function of range fourth the time delay is well approximated by well known ray tracing formula due to woodworth and schlosberg finally except for this time delay the hrtf for the ideal sphere appears to be minimum phase permitting exact recovery of the impulse response from the magnitude response in the frequency domain

asymptotic convergence in finite and boundary element methods part 2 the lbb constant for rigid and elastic scattering problems abstract the paper is a continuation of 1 and contains the evaluation of the exact lbb constant in terms of the wave number for typical problems all with spherical geometry in elastic scattering solutions to the problem of scattering of a plane wave on an elastic spherical shell for different wave numbers illustrate the dramatic effect of the magnitude of the lbb constant on the convergence

universal and nonuniversal properties of wave chaotic scattering systems prediction of the statistics of scattering in typical wave chaotic systems requires combining system specific information with universal aspects of chaotic scattering as described by random matrix theory this rapid communication shows that the average impedance matrix which characterizes such system specific properties can be semiclassically calculated in terms of ray trajectories between ports theoretical predictions are compared with experimental results for a microwave billiard demonstrating that the theory successfully uncovered universal statistics of wave chaotic scattering systems

relaxation schemes for spectral multigrid methods the effectiveness of relaxation schemes for solving the systems of algebraic equations which arise from spectral discretizations of elliptic equations is examined iterative methods are an attractive alternative to direct methods because fourier transform techniques enable the discrete matrix vector products to be computed almost as efficiently as for corresponding but sparse finite difference discretizations preconditioning is found to be essential for acceptable rates of convergence preconditioners based on second order finite difference methods are used a comparison is made of the performance of different relaxation methods on model problems with a variety of conditions specified around the boundary the investigations show that iterations based on incomplete lu decompositions provide the most efficient methods for solving these algebraic systems

complete controllability of nonlinear stochastic impulsive functional systems abstract this paper is concerned with the controllability of a kind of nonlinear stochastic impulsive functional systems sufficient conditions for the complete controllability of the nonlinear stochastic impulsive functional systems are obtained by using schauder fixed point theorem a numerical example is given to illustrate the effectiveness of the theoretical results

computation of the helmholtz eigenvalues in a class of chaotic cavities using the multipole expansion technique in this paper we present a numerical computation of the energy levels and the corresponding wave functions in a microwave resonator using the multipole expansion technique the approach permits closed form fast and robust solutions of the helmholtz equation and the schrodinger equation for two dimensional systems in an important class of wave chaos problem in particular wave functions inside the billiard are expressed in terms of a simple expansion of hankel functions the implementation of the approach is described and the classical bowtie cavity is considered as a case study to demonstrate the versatility and efficiency of the method to validate the accuracy the field distribution and the eigenvalues calculated using this approach are compared to the solution obtained by boundary integral method the case when the cavity contains objects perfect electric conductors and or dielectrics is also presented and discussed

reachability of higher order logical control networks via matrix method this paper investigates the reachability of higher order logical control networks first with semi tensor product method the matrix expression of a higher order logical control network is given then a partitioned matrix is constructed which intuitively shows the input state mapping information with this matrix some conditions are obtained for the reachability of higher order logical control networks finally an algorithm is designed to find control sequences that drive a given initial state to a given destination state

quantising a generic family of billiards with analytic boundaries a generic family of plane billiards has been discovered recently the shape of the boundary is given by the quadratic conformal image of the unit circle and is thus real analytic for small deformations of the unit disc the billiard is a typical kam system but becomes ergodic or even mixing when the curvature of the boundary vanishes at some point the kolmogorov entropy has been calculated and it increases with the deformation of the boundary the author studies aspects of the quantum chaos for this billiard he solves numerically the eigenvalue problem for the laplace operator with dirichlet s boundary condition he examines the spectrum and inspects the avoided crossings at which mixing of nearby states occurs the variation of the nodal structure and of the localisation properties of the eigenfunctions is studied in analysing the level spacing distribution he finds a continuous transition from the poisson distribution towards the wigner distribution the exponent in the level repulsion law varies continuously along with a generic perturbation for small perturbations it seems to be proportional to the square root of the perturbation parameter

chebyshev 3 d spectral and 2 d pseudospectral solvers for the helmholtz equation two chebyshev solvers are presented for the linear helmholtz equation the first algorithm is a 3 d direct spectral solver based on a diagonalization technique whilst the second performs an iterative pseudospectral 2 d calculation with finite difference preconditioning both techniques handle general nonhomogeneous boundary conditions computing times and accuracies of the two methods are compared

modelling and strategy optimisation for a kind of networked evolutionary games with memories under the bankruptcy mechanism abstractthis paper investigates the evolutionary dynamic and strategy optimisation for a kind of networked evolutionary games whose strategy updating rules incorporate bankruptcy mechanism and the situation that each player s bankruptcy is due to the previous continuous low profits gaining from the game is considered first by using semi tensor product of matrices method the evolutionary dynamic of this kind of games is expressed as a higher order logical dynamic system and then converted into its algebraic form based on which the evolutionary dynamic of the given games can be discussed second the strategy optimisation problem is investigated and some free type control sequences are designed to maximise the total payoff of the whole game finally an illustrative example is given to show that our new results are very effective

stability and stabilization of boolean networks with impulsive effects abstract this paper investigates the stability and stabilization of boolean networks with impulsive effects after giving a survey on semi tensor product of matrices we convert a boolean network with impulsive effects into impulsive discrete time dynamics then some necessary and sufficient conditions are given for the stability and stabilization of boolean networks with impulsive effects finally examples are provided to illustrate the efficiency of the obtained results

kalman decomposition for boolean control networks the kalman decomposition problem for boolean control networks bcns is solved completely a necessary and sufficient condition described by vertex partitions of digraphs is proposed for the kalman decomposition and an algorithm is designed to compute the logical coordinate transformation that results in the kalman decomposition finally two examples are presented one example illustrates the procedure of realizing the kalman decomposition the other one reveals that not all the bcns can be transformed into the kalman decomposition form this is an essential property different from that of the traditional linear control systems

relevance of chaos in numerical solutions of quantum billiards in this paper we have tested several general numerical methods in solving the quantum billiards such as the boundary integral method bim and the plane wave decomposition method pwdm we performed extensive numerical investigations of these two methods in a variety of quantum billiards integrable systens circles rectangles and segments of circular annulus kolmogorov armold moser kam systems robnik billiards and fully chaotic systems ergodic such as bunimovich stadium sinai billiard and cardiod billiard we have analyzed the scaling of the average absolute value of the systematic error delta e of the eigenenergy in units of the mean level spacing with the density of discretization b which is number of numerical nodes on the boundary within one de broglie wavelength and its relationship with the geometry and the classical dynamics in contradistinction to the bim we find that in the pwdm the classical chaos is definitely relevant for the numerical accuracy at a fixed density of discretization b we present evidence that it is not only the ergodicity that matters but also the lyapunov exponents and kolmogorov entropy we believe that this phenomenon is one manifestation of quantum chaos

adaptive integration techniques for almost singular functions in the boundary element method abstract three numerical adaptive integration schemes for almost singular functions occurring in the boundary element method which use subdivision of a domain or moving of nodes are discussed some numerical examples show efficiency of the methods

stochastic stability of markovian jumping genetic regulatory networks with mixed time delays abstract in this paper the stability analysis problem is investigated for a class of markovian jumping genetic regulatory networks grns with mixed time delays discrete time delays and distributed time delays and stochastic perturbations the main purpose of the addressed stability analysis problem is to establish some easy to verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid and protein is asymptotically stable by utilizing a more general lyapunov krasovskii functional based on the idea of delay decomposing and the lmi linear matrix inequality technique we derive sufficient delay dependent conditions ensuring the asymptotically stability of the grns with mixed time delays and noise perturbations in terms of lmi finally simulation examples are exploited to illustrate the effectiveness of the developed theoretical results

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

model construction of boolean network via observed data in this paper a set of data is assumed to be obtained from an experiment that satisfies a boolean dynamic process for instance the dataset can be obtained from the diagnosis of describing the diffusion process of cancer cells with the observed datasets several methods to construct the dynamic models for such boolean networks are proposed instead of building the logical dynamics of a boolean network directly its algebraic form is constructed first and then is converted back to the logical form firstly a general construction technique is proposed to reduce the size of required data the model with the known network graph is considered motivated by this the least in degree model is constructed that can reduce the size of required data set tremendously next the uniform network is investigated the number of required data points for identification of such networks is independent of the size of the network finally some principles are proposed for dealing with data with errors

global robust stability and stabilization of boolean network with disturbances abstract based on semi tensor product of matrices global robust stability and stabilization of boolean network bn with disturbances are investigated firstly the definition of global robust stability for bn with disturbances is presented by using the algebraic state space representation of disturbed bn some necessary and sufficient criteria are obtained to ensure the global robust stability with respect to w r t a fixed point or w r t a limit cycle in contrast if a given disturbed bn is not globally robust stable w r t a fixed point or w r t a limit cycle system can achieve stability by a matrix transformation technique however it is a difficult task to find such a suitable matrix transformation in this paper a pinning state feedback control design is proposed to find a suitable transformation the obtained results are well illustrated by numerical example

controllability of higher order boolean control networks using the semi tensor product method this paper investigates the controllability of a th order boolean control network after a brief introduction on semi tensor product of matrices to th order boolean control networks the controllability issue is studied first a systematic procedure to reconstruct the logical dynamic of a th order boolean control network from its network transition matrix is presented for design purpose then the controllability via two types of controls is considered necessary and sufficient conditions are provided for each case the application of input state incidence matrix to the controllability of th order boolean control networks is studied finally as an application examples are given to illustrate the effectiveness of the obtained results

diabolical points in the spectra of triangles accidental degeneracies between energy levels e j and e j 1 of a real hamiltonian can occur generically in a family of hamiltonians labelled by at least two parameters x y energy level surfaces in e x y space have locally a double cone diabolo connection and we refer to the degeneracies themselves as diabolical points we studied the family of systems in which a particle moves freely within hard walled triangles vibrations of triangular membranes with x and y labelling two of the angles using an efficient green function technique to compute the levels we found several diabolical points for low lying levels as well as some symmetry degeneracies the lowest diabolical point occurred for levels 5 and 6 of the triangle 130 57 30 73 18 70 the conical structure was confirmed by noting that the normal derivative u of the wavefunction at a boundary point changed sign during a small circuit of the diabolical point the form of the variation of u around a circuit and the changing pattern of nodal lines of agreed with theoretical expectations an estimate of the total number of degeneracies n d j involving levels 1 through j based on the energy scaling of cone angles and the level spacing distribution gave n d j j 2 5 and our limited data support this prediction analytical theory confirmed that for thin triangles where our computational method is slow there are no degeneracies in the energy range studied

global stability and stabilization of switched boolean network with impulsive effects the present paper investigates the global stability and stabilization of switched boolean network with impulsive effects by using the semi tensor product the algebraic form of the switched boolean network with impulsive effects is obtained then sufficient and necessary condition is presented for the global stability of the switched boolean network with impulsive effects furthermore sufficient and necessary conditions are provided for the stabilization of the switched boolean network with impulsive effects under two types of controls finally examples are presented to illustrate the main results

poloidal toroidal decomposition in a finite cylinder the navier stokes equations in a finite cylinder are written in terms of poloidal and toroidal potentials in order to impose incompressibility regularity of the solutions is ensured in several ways first the potentials are represented using a spectral basis which is analytic at the cylindrical axis second the non physical discontinuous boundary conditions at the cylindrical corners are smoothed using a polynomial approximation to a steep exponential profile third the nonlinear term is evaluated in such a way as to eliminate singularities the resulting pseudo spectral code is tested using exact polynomial solutions and the spectral convergence of the coefficients is demonstrated our solutions are shown to agree with exact polynomial solutions and with previous calculations of axisymmetric vortex breakdown and of onset of non axisymmetric helical spirals parallelization by azimuthal wavenumber is shown to be highly effective

statistics of quantum transport in weakly nonideal chaotic cavities we consider statistics of electronic transport in chaotic cavities where time reversal symmetry is broken and one of the leads is weakly nonideal that is it contains tunnel barriers characterized by tunneling probabilities i using symmetric function expansions and a generalized selberg integral we develop a systematic perturbation theory in 1 i valid for an arbitrary number of channels and obtain explicit formulas up to second order for the average and variance of the conductance and for the average shot noise higher moments of the conductance are considered to leading order

universal statistics of the scattering coefficient of chaotic microwave cavities we consider the statistics of the scattering coefficient s of a chaotic microwave cavity coupled to a single port we remove the nonuniversal effects of the coupling from the experimental s data using the radiation impedance obtained directly from the experiments we thus obtain the normalized scattering coefficient whose probability density function pdf is predicted to be universal in that it depends only on the loss quality factor of the cavity we compare experimental pdfs of the normalized scattering coefficients with those obtained from random matrix theory rmt and find excellent agreement the results apply to scattering measurements on any wave chaotic system

a linear representation of dynamics of boolean networks a new matrix product called semi tensor product of matrices is reviewed using it a matrix expression of logic is proposed where a logical variable is expressed as a vector a logical function is expressed as a multiple linear mapping under this framework a boolean network equation is converted into an equivalent algebraic form as a conventional discrete time linear system analyzing the transition matrix of the linear system formulas are obtained to show a the number of fixed points b the numbers of cycles of different lengths c transient period for all points to enter the set of attractors and d basin of each attractor the corresponding algorithms are developed and used to some examples

a pseudospectral method for solution of the three dimensional incompressible navier stokes equations abstract a new chebyshev pseudospectral technique based on the projection method that was previously applied by the authors to the solution of two dimensional incompressible navier stokes equations in primitive variables for nonperiodic boundary conditions is extended to solve the three dimensional navier stokes equations the crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain on the boundaries as well as in the interior the key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition the method was tested on a two dimensional driven cavity flow and the results were compared with those of the most accurate finite difference calculation the three dimensional driven cavity flow was then calculated at the same reynolds numbers as the two dimensional cases i e re 100 400 and 1000 in the calculated results three dimensional boundary effects were observed in all cases and became more apparent with increasing reynolds number

output controllability and optimal output control of state dependent switched boolean control networks in the present paper we investigate the output controllability and optimal output control problems of a state dependent switched boolean control network by using the semi tensor product the algebraic form of the system is obtained then output controllability problems of the system are discussed and some necessary and sufficient conditions are given next the mayer type optimal output control issue is considered and an algorithm is provided to find out the control sequence at last an example is given to show the effectiveness of the main results

application of hp adaptive be fe methods to elastic scattering abstract the investigation focuses on the development of hp adaptive methods for simulation of acoustical scattering problems the present formulation is based on steady state linear elasticity equations coupled with the burton miller integral equation representing the behavior of a surrounding acoustical medium the highlights of the proposed approach include a mathematically consistent variational formulation of the problem an hp adaptive fe be approximation based on standard galerkin methods an element by element solver a residual based a posteriori error estimate an hp adaptive strategy particular attention is given to asymptotic convergence and to a comparison of theory and numerical simulations

hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions abstract a weakly singular form of the hypersingular boundary integral equation bie traction equation for 3 d elastic wave problems is developed in this paper all integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements regular quadrature and collocation procedures used for conventional bies are sufficient for the discretization of the original hypersingular bie this weakly singular form of the hypersingular bie is applied to the composite bie formulation which uses a linear combination of the conventional bie and the hypersingular bie to remove the fictitious eigenfrequencies existing in the conventional bie formulation for elastic wave problems numerical examples employing different types of boundary elements clearly demonstrate the effectiveness and efficiency of the developed formulation

on the convergence of the p version of the boundary element galerkin method abstract the authors consider various physical problems which may be formulated in terms of integral equations of the first kind including the two dimensional screen neumann and dirichlet problems in acoustics and crack problems in elasticity sharp regularity results for the solutions are available for these problems proven is the convergence of the p version for some galerkin boundary element schemes based on the integral equation formulations it is shown that the rate of convergence obtained by our method is twice that for the usual h version

solution of elastic scattering problems in linear acoustics using h p boundary element method abstract the work is a continuation of 1 a simplified 3d model problem reduced from the general class of elastic scattering problems is analyzed focusing attention on such practical details of the 3d implementation as a triangles based h p approximation and corresponding data structure integration of singular integrals and its effect on theoretically optimal rates of convergence a posteriori error estimation and sample adaptive strategies

exact a posteriori error analysis of the least squares finite element method1this work was supported by nsc under grant nsc87 2115 m 009 005 taiwan 1 a residual type a posteriori error estimator is presented for the least squares finite element method the estimator is proved to equal the exact error in a norm induced by some least squares functional the error indicator of each element is equal to the exact error norm restricted to the element as well in other words the estimator is perfectly effective and reliable for error control and for adaptive mesh refinement the exactness property requires virtually no assumptions on the regularity of the solution and on the finite element order in the approximation or in the estimation the least squares method is in a very general setting that applies to various linear boundary value problems such as the elliptic systems of first order and of even order and the mixed type partial differential equations numerical results are given to demonstrate the exactness

strategy optimization for static games based on stp method abstract in this paper we consider the choice behavior of players in a static game and discuss solutions to static games of complete information problem via semi tensor product stp method some properties of the dominant behaviors are obtained based on which choosing the dominant strategies deleting the dominated strategies are used to optimize the strategy sets so as to obtain solutions to the considered game examples are given to show the effectiveness of the results

extension of the variational theory of complex rays to shells for medium frequency vibrations a new approach to the calculation of vibrations of weakly damped elastic structures in the medium frequency range called the variational theory of complex rays vtcr is being developed here the extension of this theory to shells of relatively small curvature is considered numerical examples of structures made of plates and shells demonstrate the capabilities of the vtcr

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

recent progress on application of hp adaptive be fe methods to elastic scattering summary several new issues related to the projcct described in references 1 3 are reported the presented problems include i sensitivity of p convergence results to geometric parametrizations and an idea of a new mesh generation for lip approximations 2 a posteriori error estimation for the coupled problem 3 a better understanding of the meaning of the asymptotic convergence a few typical numerical examples conclude the presentation

stability and l_1 gain analysis of boolean networks with markovian jump parameters this paper presents some results on stability and l 1 gain analysis of boolean networks with markovian jump parameters a necessary and sufficient condition for global stability of the concerned boolean networks is given in terms of linear programming by utilizing the semi tensor product of matrices and some properties of linear positive systems then the definition of lyapunov function for stochastic boolean networks is presented and lyapunov theorem is derived moreover an l 1 gain problem for stochastic boolean networks with external disturbances is formulated and solved by a sufficient condition examples are shown to illustrate the effectiveness of the obtained results

solution of elastic scattering problems in linear acoustics using h p boundary element methods abstract a simplified model problem reduced from the general class of elastic scattering problems is analyzed both classical helmholtz and hypersingular formulations are discussed and a general h p boundary element method based on the burton miller combination of both approaches is formulated a simple l 2 residual a posteriori error estimate is discussed as a basis of adaptive h or p refinements