on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

fractal measures of first passage time of a simple random walk abstract we consider random walks starting at the site i 1 on a one dimensional lattice segment with an absorbing boundary at i 0 and a reflecting boundary at i l we find that the typical value of first passage time fpt is independent of system size l while the mean value diverges linearly with l the qth moment of the fpt diverges with system size as l2q 1 for q 1 2 for a finite but large l the fpt distribution has an 1 t tail cut off by an exponential of the form exp t l2 however if l is set equal to infinity the distribution has an algebraic tail given by t 1 2 we find that the generalised dimensions d q have a nontrivial dependence on q this shows that the fpt distribution is a multifractal we also calculate the singularity spectrum f

quasi hyperbolic semigroups abstract we introduce the notion of quasi hyperbolic operators and c 0 semigroups examples include the push forward operator associated with a quasi anosov diffeomorphism or flow a quasi hyperbolic operator can be characterised by a simple spectral property or as the restriction of a hyperbolic operator to an invariant subspace there is a corresponding spectral property for the generator of a c 0 semigroup and it characterises quasi hyperbolicity on hilbert spaces but not on other banach spaces we exhibit some weaker properties which are implied by the spectral property

ultradiffusion on the fractal branching koch curves ultradiffusion is defined on a family of fractal branching koch curves by an exact renormalization decimation transformation the anomalous long time behaviour of the autocorrelation function is obtained for the particular hierarchy the authors find a non universal crossover c1 m 1 2m and a universal one c2 1 2 as the effective temperature c is increased where m is the maximum ramification number of the fractal they also find that for large m the dynamic behaviour of ultradiffusion on the fractal is independent of the effective temperature c

initiation of damage in the kauffman model an alternate method is presented for initiating damage to the kauffman model a numerical study suggests that this modification increases the efficiency of generating damage clusters without changing their fractal properties

rational rotation numbers for maps of the circle we consider families of maps of the circle of degree 1 which are homeomorphisms but not diffeomorphisms that is maps like x to x t frac c 2 pi sin 2 pi x bmod 1 withc 1 we prove that the set of parameter values corresponding to irrational rotation numbers has lebesgue measure 0 in other words the intervals on which frequency locking occurs fill up the set of full measure

the parametric solutions of eigenstructure assignment for controllable and uncontrollable singular systems the previous results about the parametric solutions of eigenstructure assignment for singular systems applied by pure proportional or proportional plus derivative state feedback can only apply to controllable systems it is because the parametric solutions of the right generalized eigenvectors corresponding to the infinite and uncontrollable finite eigenvalues have still not been found in this paper the parametric solutions of the right generalized eigenvectors for finite controllable or uncontrollable eigenvalues and infinite controllable or uncontrollable eigenvalues when the system is applied by pure proportional or proportional plus derivative state feedback are given hence the parametric solution of eigenstructure assignment can be used to design the state feedback of both the controllable and uncontrollable systems the condition for detecting the regularity of the resulting system is also given

a re examination of the quantum theory of optical cavities with moving mirrors the quantization of linearly polarized light in an ideal optical cavity with moving boundaries is re examined the mathematical results of the earlier study by moore are obtained using more conventional techniques in contrast to moore it is shown that the theory does possess a hamiltonian and a schrodinger picture when any suitable lagrangian coordinate system is chosen it is demonstrated that the quantum as well as the classical physics is independent of the choice of lagrangian coordinate system

geometric structure and feedback in singular systems the output nulling a e r b invariant subspaces are defined for singular systems rigorously justifying the name and demonstrating that special cases of these geometric objects are the familiar subspace of admissible conditions and the supremal a e r b invariant subspace a novel singular system structure algorithm is used to compute them by numerically efficient means their importance for describing the possible closed loop geometric structure in terms of the open loop geometric structure is shown an approach to spectrum assignment in singular systems that is based on a generalized lyapunov equation is introduced the equation is used to compute feedback gains to place poles and assign various closed loop invariant subspaces while guaranteeing closed loop regularity

emergent properties in random complex automata abstract studies of large randomly assembled binary boolean node automata have demonstrated that such systems can spontaneously exhibit enormously ordered dynamical behavior an important approach to characterizing these behaviors has consisted of studying ensembles of automata ensemble specifications have been based on 1 choice of boolean function regulating each node in the automaton 2 random or biased mappings of the 2 n automata states into themselves 3 the numbers of inputs k per node this article briefly reviews these approaches reports new results on the expected behavior of threshold automata and automata with a particular class of biased mappings in addition it discusses emergent highly ordered dynamical behavior in random automata rich in a specific class of canalizing boolean functions due to the crystallization of powerful subautomata called forcing structures the ordered behaviors may be of importance in biological evolution in physics and in the design of adaptive automata

multifractality and the kauffman model the author simulates the spread of an initial damage in the kauffman cellular automata at its critical point on the square lattice he calculates various moments of the probability that a site has been damaged n times and checks for multifractality in the critical exponents for different ensembles specifically he finds no evidence for multifractality when the moments of the probabilities are evaluated with lattice size l but multifractal behaviour occurs when the moments are monitored as a function of time t

critical circle maps near bifurcation we estimate harmonic scalings in the parameter space of a one parameter family of critical circle maps these estimates lead to the conclusion that the hausdorff dimension of the complement of the frequency locking set is less than 1 but not less than 1 3 moreover the rotation number is a holder continuous function of the parameter

periodic and quasi periodic solutions of nonlinear wave equations via kam theory in this paper the nonlinear wave equation u u u xx v x u x t varepsilon u 3 x t 0 is studied it is shown that for a large class of potentials v x one can use kam methods to construct periodic and quasi periodic solutions in time for this equation

generalized diffusion equation for anisotropic anomalous diffusion motivated by studies of comblike structures we present a generalization of the classical diffusion equation to model anisotropic anomalous diffusion we assume that the diffusive flux is given by a diffusion tensor acting on the gradient of the probability density where each component of the diffusion tensor can have its own scaling law we also assume scaling laws that have an explicit power law dependence on space and time solutions of the proposed generalized diffusion equation are consistent with previously derived asymptotic results for the probability density on comblike structures

multifractal nature of diffusion on hierarchical structures the authors study the moments of the first passage time t of random walks on hierarchical structures using the exact enumeration method they find that the different moments scale with the size of the system with an infinite hierarchy of exponents characterising a multifractal behaviour

a numerical study of the likelihood of phase locking abstract we report the results of numerical computation of the size of the set of s for which the hemeomorphism of the circle f k x x k 2 sin 2 x mod 1 is phased locked for values of k ranging from 0 1 to 1 the results suggest that for moderate values of k phase locking is unlikely except for small periods but that for k 1 almost all s give phase locking with large periods accounting for a surprisingly large portion of the total

eigenstructure assignment by decentralized output feedback a complete parametric approach the problem of eigenstructure assignment in multivariable linear systems by decentralized output feedback is considered by using a complete parametric solution of a generalized sylvester matrix equation parametric representations of both the left and right closed loop eigenvectors and generalized eigenvectors as well as the feedback gains with respect to the closed loop eigenvalues and two series of partially free parameter vectors are established the obtained result does not require any conditions on the closed loop eigenvalues and generalizes some previous results in this area an example shows the effect of the proposed approach

finite difference solution of a nonlinear klein gordon equation with an external source in this paper we consider the darboux problem for a 1 1 dimensional cubic nonlinear klein gordon equation with an external source stable finite difference scheme is constructed on a four point stencil which does not require additional iterations for passing from one level to another it is proved that the finite difference scheme converges with the rate o h 2 when the exact solution belongs to the sobolev space w 2 2

on c2 diffeomorphisms of the circle which are of type iii1 for every irrational number 0 1 which is not of constant type we construct ac 2 diffeomorphism of the circle with rotation number which is of type iii1 this diffeomorphism can be chosen arbitrarily close to the rotationr our methods also allow us to construct for every liouville number 0 1 ac diffeomorphism of the circle with rotation number which is of type iii1

multifractal nature of the first passage time for biased diffusion on percolation clusters abstract we study diffusion on percolation clusters in the presence of a constant bias field e acting in the three dimensional euclidean space specifically we are interested in scaling behavior of the distribution function of the first passage times moments of that distribution function with respect to time variable exhibit a typical multifractal mf behavior for an arbitrary bias field e including the value e 0

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

a new solution to the generalized sylvester matrix equation av evf bw abstract this note deals with the problem of solving the generalized sylvester matrix equation av evf bw with f being an arbitrary matrix and provides complete general parametric expressions for the matrices v and w satisfying this equation the primary feature of this solution is that the matrix f does not need to be in any canonical form and may be even unknown a priori the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems in control systems theory

eigenstructure assignment in descriptor systems coordinate free conditions are given for pole assignment by feedback in linear descriptor singular systems which guarantee closed loop regularity these conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback

scaling of the first passage time and the survival probability on exact and quasi exact self similar structures the authors calculate the asymptotic behaviour of the moments of the first passage time and survival probability for random walks on an exactly self similar tree and on a quasi self similar comb by applying an exact decimation approach to the master equations for the hierarchical comb a transition from ordinary to anomalous diffusion occurs at r 2 where r is the ratio of teeth length in successive iterations of the structure in the anomalous regime r 2 the positive integer moments of the first passage time tq scale as ltau q with tau q 1 2q 1 ln r ln 2 where l is the linear distance from input to output the asymptotic behaviour of the survival probability is studied using both scaling theory and by a direct solution of the master equations they find that the characteristic time t in the asymptotic exponential decay of the survival probability exp t t scales as t approximately ltau with tau ln r2 ln 2 i e tau is distinct from tau 1 however substantial corrections to this asymptotic form for tau exist and these are needed to account for the recent simulation data of havlin and matan 1988

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

differentiability at the tip of arnold tongues for diophantine rotations numerical studies and renormalization group explanations we study numerically the regularity of arnold tongues corresponding to diophantine rotation numbers of circle maps at the edge of validity of kam theorem this serves as a good test for the numerical stability of two different algorithms we find empirically that arnold tongues are only finitely differentiable at the tip we also find several scaling properties of the sobolev norms of the conjugacy near the breakdown we also provide a renormalization group explanation of the regularity at the tip and the scaling behaviors of the sobolev regularity we also uncover empirically some other patterns which require explanation

parametric eigenstructure assignment in second order descriptor linear systems this note considers eigenstructure assignment in second order descriptor linear systems via proportional plus derivative feedback it is shown that the problem is closely related with a type of so called second order sylvester matrix equations through establishing two general parametric solutions to this type of matrix equations two complete parametric methods for the proposed eigenstructure assignment problem are presented both methods give simple complete parametric expressions for the feedback gains and the closed loop eigenvector matrices the first one mainly depends on a series of singular value decompositions and is thus numerically simple and reliable the second one utilizes the right factorization of the system and allows the closed loop eigenvalues to be set undetermined and sought via certain optimization procedures an example shows the effect of the proposed approaches

solution to the second order sylvester matrix equation mvf sup 2 dvf kv bw this note provides a complete general parametric solution v w to the generalized second order sylvester matrix equation mvf sup 2 dvf kv bw with f being an arbitrary square matrix the primary feature of this solution is that the matrix f does not need to be in any canonical form or may be even unknown a priori the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems involving second order dynamical systems

long time behavior and energy growth for electromagnetic waves reflected by a moving boundary the author studies the phenomenon of a wave reflected back and forth between two parallel perfectly conducting plates one of which is oscillating normally to itself by making a careful analysis of the reflected space time characteristics he establishes a representation formula for the solutions of maxwell s equations in terms of the initial data this representation formula together with properties of iterated maps of an interval yield a precise asymptotic description as t to infinity of the solutions the main result is that if there is a finite number of reflected characteristics which are periodic then the energy of all solutions grows without bound as t to infinity irrespective of the initial data

construction of quasi periodic solutions of state dependent delay differential equations by the parameterization method ii analytic case abstract we construct analytic quasi periodic solutions of a state dependent delay differential equation with quasi periodically forcing we show that if we consider a family of problems that depends on one dimensional parameters with some non degeneracy conditions there is a positive measure set of parameters for which the system admits analytic quasi periodic solutions the main difficulty to be overcome is the appearance of small divisors and this is the reason why we need to exclude parameters our main result is proved by a nash moser fast convergent method and is formulated in the a posteriori format of numerical analysis that is given an approximate solution of a functional equation which satisfies some non degeneracy conditions we can find a true solution close to it this is in sharp contrast with the finite regularity theory developed in 18 we conjecture that the exclusion of parameters is a real phenomenon and not a technical difficulty more precisely for generic families of perturbations the quasi periodic solutions are only finitely differentiable in open sets in the complement of parameters set

torus maps and the problem of a one dimensional optical resonator with a quasiperiodically moving wall abstract we study the problem of the asymptotic behavior of the electromagnetic field in an optical resonator one of whose walls is at rest and the other is moving quasiperiodically with d 2 incommensurate frequencies we show that this problem can be reduced to a problem about the behavior of the iterates of a map of the d dimensional torus that preserves a foliation by irrational straight lines in particular the jacobian of this map has d 1 eigenvalues equal to 1 we present rigorous and numerical results about several dynamical features of such maps we also show how these dynamical features translate into properties for the field in the cavity in particular we show that when the torus map satisfies a kam theorem which happens for a cantor set of positive measure of parameters the energy of the electromagnetic field remains bounded when the torus map is in a resonant region which happens in open sets of parameters inside the gaps of the previous cantor set the energy grows exponentially

on the solution to the sylvester matrix equation av bw evf a simple direct complete and explicit parametric solution of the generalized sylvester matrix equation av bw evf is proposed for matrix f in the jordan form with arbitrary eigenvalues using the smith canonical form of the matrix a se b the obtained solution is in a clear neat form and may have important applications in descriptor linear system theory

solution to matrix equation av bw evf and eigenstructure assignment for descriptor systems a simple complete analytical restriction free parametric solution with complete and explicit freedom of matrix equation av bw evf is presented based on the presented solution of this equation an approach for eigenstructure assignment for continuous descriptor system ex ax bu via descriptor variable feedback u kx is proposed parametric forms of the gain matrix and the eigenvectors associated with the assigned finite closed loop eigenvalues are given the approach is shown to be better than that of fahmy and o reilly 1989 int j contr 49 129 143 in the sense that it not only possesses the functions of the approach of fahmy and o reilly 1989 int j contr 49 129 143 but also has the following three advantages 1 it eliminates the requirements on the assigned finite closed loop poles 2 it provides more design parameters and 3 it needs less computational work

an example of pure stability for the wave equation with moving boundary abstract this paper studies the behavior of the energy of the wave equation solution in a finite moving domain 0

length of state cycles of random boolean networks an analytic study in this paper we consider the mean length of transients and the length of state cycles in random boolean networks we present an approximate calculation of these quantities as a function of the size and connectivity of the network where using an annealed approximation we derive a recursive formula for the length of steps of the system using the mean step length and an effective momentary state space we calculate an approximate formula for the probability distribution function pdf of the length of state cycles and transients we compare this pdf with analytical results in special cases and with simulations by the monte carlo procedure

scaling properties of diffusion on comb like structures the authors study the scaling properties of the probability density of random walks on comb like structures they find that in contrast to the first passage time in which several exponents are needed to characterise their distribution the probability density can be described by a single exponent

anderson localization for the 1 d discrete schrodinger operator with two frequency potential we prove the complete exponential localization of eigenfunctions for the 1 d discrete schrodinger operators with quasi periodic potentials having two basic frequencies it is shown also that for such operators there is no forbidden zones in the spectrum unlike the operators with one basic frequency

high order multi symplectic schemes for the nonlinear klein gordon equation in this paper we construct multi symplectic schemes with any order of accuracy for the nonlinear klein gordon equation by concatenating the symplectic schemes for odes some existing schemes such as the preissman scheme and the leap frog scheme and new multi symplectic schemes are constructed we also show that the composition method which plays a crucial role in finding the high order symplectic integrators for the odes can also be applied to construct high order multi symplectic schemes for pdes extension of the concatenating method to more than one space dimension is also discussed numerical experiments are presented to show the order and the efficiency of the constructed multi symplectic schemes

the spectrum of a hyperbolic evolution operator abstract we study the time t map u which maps initial data u 0 u 1 to the solution and its derivative u t u t t of the homogeneous wave equation in a domain with time t periodic boundary the spectrum of u and the type of the spectrum are completely analyzed the spectrum is the unit circle if a certain rotation number is irrational it is a full annulus if this rotation number is rational and a weak additional assumption is satisfied

nonlinear resistor fractal networks topological distances singly connected bonds and fluctuations the authors consider a fractal network of nonlinear resistors with the voltage v behaving as a power of the current i mod v mod r mod i mod alpha the resistance between two points at a distance l is r l varies as lzeta alpha they prove that zeta 0 describes the scaling of the topological chemical distance while zeta infinity describes that of the number of singly connected red bonds for random resistors they also consider the width of the resistance distribution delta r varies as l zeta 2 alpha values for zeta and zeta 2 are explicitly derived for two model fractals and delta r r is found to grow with l for the sierpinski gasket and alpha 1 612 the relevance of the results to percolation clusters is discussed

three coupled oscillators mode locking global bifurcations and toroidal chaos abstract many systems exhibit behaviour which can be described by three coupled oscillators provided the coupling is not too strong such systems can be modelled by maps of the two torus to itself in this paper we describe and explain those aspects of the bifurcation diagram for two parameter families of torus maps that involve change of mode locking type we introduce the concepts of partial and full mode locking for the coupled oscillators these notions correspond to the presence of one or two rational relations between the frequencies respectively numerical investigation of a particular family of torus maps reveals an intricate web of global bifurcations in order to explain the results we first show that we can approximate maps in the neighbourhood of a rational translation to arbitrary order by the time 1 map of a flow on the torus then we analyse those condimension 1 and 2 bifurcations for flows on the torus which change the set of frequency ratios we find a large variety of bifurcation diagrams in particular many involving homotopically non trivial saddle connections next we ask how the picture changes when the time 1 maps of a family of flows are perturbed to a general family of diffeomorphisms we find toroidal chaos in the neighbourhood of all these bifurcations meaning that there exist orbits which perform a pseudo random sequence of rotations in different directions around the torus the corresponding behaviour for the coupled oscillators is that the frequency ratios perform a random walk finally we show how all these ingredients can be put together to give global scenarios for bifurcation for families of torus maps which we believe to be of general applicability to physical systems with three weakly coupled modes of oscillation

theory of circle maps and the problem of one dimensional optical resonator with a periodically moving wall we consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions notably well known results in the theory of circle maps which we review briefly imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially even if these intervals are dense for typical motions of the reflecting boundary in the complement there is a positive measure set of parameters where the energy remains bounded

dynamic and energetic analyses of a string slider non linear coupling system by variable grid finite difference in this paper a string slider non linear coupling system with time dependent boundary condition is considered one partial differential equation pde describing the transverse small amplitude vibration of the string non linearly coupled with one ordinary differential equation ode describing the horizontal displacement of the slider are derived by hamilton s principle this is a moving boundary problem since the unknown position of the slider has to be determined as a part of the solutions a transformation of the variable that converts the original non stationary boundary conditions to a set of fixed boundary conditions is proposed to avoid the increased complication and loss of accuracy associated with unequal space intervals near the moving boundary the finite difference method with variable grid is employed to show the numerical results of the coupling effect between the string and slider finally some periodic motions of the moving boundary are assigned to show the divergence of the string vibrations

kronecker maps and sylvester polynomial matrix equations the concepts of kronecker maps and sylvester polynomial matrix equations are proposed some properties of the kronecker maps are deduced it is shown that many kinds of matrix equations can be formulated into the so called sylvester polynomial matrix equations with the help of the kronecker maps general explicit solutions of the sylvester polynomial matrix equations are established when the polynomial matrices possess f primeness for the nonsquare case the proposed solutions can offer all the degrees of freedom represented by a free parameter matrix

attractors on an n torus quasiperiodicity versus chaos the occurrence of quasiperiodic motions in nonconservative dynamical systems is of great fundamental importance however current understanding concerning the question of how prevalent such motions should be is incomplete with this in mind the types of attractors which can exist for flows on an n torus are studied numerically for n 3 and 4 specifically nonlinear perturbations are applied to maps representing n frequency quasiperiodic attractors these perturbations can cause the original n frequency quasiperiodic attractors to bifurcate to other types of attractors our results show that for small and moderate nonlinearity the frequency of occurrence of quasiperiodic motions is as follows n frequency quasiperiodic attractors are the most common followed by n 1 frequency quasiperiodic attractors followed by periodic attractors however as the nonlinearity is further increased n frequency quasiperiodicity becomes less common ceasing to occur when the map becomes noninvertible chaotic attractors are very rare for n 3 for small to moderate nonlinearity but are somewhat more common for n 4 examination of the types of chaotic attractors that occur for n 3 reveals a rich variety of structure and dynamics in particular we see that there are chaotic attractors which apparently fill the entire n torus i e limit sets of orbits on these attractors are the entire torus furthermore these are the most common types of chaotic attractors at moderate nonlinearities

a reduced order observer for descriptor systems abstract in this paper a reducer order observer is analyzed for so called generalized state space or descriptor systems based on the staircase form for generalized state space models a recursive algorithm is presented to construct a reduced order observer for a given observable descriptor system in the algorithm only the eigenfrequencies of the observer have to be specified

distributions and moments of structural properties for percolation clusters we study numerically and by scaling methods the distributions and moments of several structural properties of percolation clusters in two and three dimensions the clusters are generated at criticality and properties such as the distribution of the mass as a function of linear size or chemical distance are studied our results suggest that the hierarchy of moments can be represented by a single gap exponent using a scaling approach we obtain analytical forms for the different distribution functions which agree very well with the numerical data

solution to generalized sylvester matrix equations an explicit solution to the generalized sylvester matrix equation ax by exf is established this solution is expressed in terms of the r controllability matrix of e a b a generalized symmetric operator matrix and an observability matrix moreover based on this solution solutions to some other matrix equations are also derived the results may provide great convenience for the analysis and synthesis problems related to these equations

a geometric approach to eigenstructure assignment for singular systems moore s well known result on the feedback assignment of eigenstructure in linear state space systems 5 was generalized to descriptor systems in 9 in this note we make some useful extensions to fill out the theory to begin with we do not assume controllability of the plant it is shown that the maximum number of finite closed loop eigenvalues is equal to dim el where l is the supremal a e r b invariant subspace in order to relate the possible closed loop structure to the open loop plant structure we define a set of indexes for descriptor systems which are in many respects similar to the controllability indexes of state space systems in terms of these controllability indexes we give a systematic approach to selecting the closed loop eigenvectors a major contribution of this note is the fact that it is geometric in nature and hence avoids any decomposition of the system matrices into a special form e g weierstrass form 1 the geometric setting introduced here should constitute a basis for further research in generalizing the well known results in geometric system theory disturbance decoupling input output decoupling etc to singular systems

solutions to matrix equations x axb cy r and x axb cy r abstract the present work proposed an alternative approach to find the closed form solutions of the nonhomogeneous yakubovich matrix equation x a x b c y r based on the derived closed form solution to the nonhomogeneous yakubovich matrix equation the solutions to the nonhomogeneous yakubovich quaternion j conjugate matrix equation x a x b c y r are obtained by the use of the real representation of a quaternion matrix the existing complex representation method requires the coefficient matrix a to be a block diagonal matrix over complex field in contrast in this publication we allow a quaternion matrix of any dimension as an application eigenstructure assignment problem for descriptor linear systems is considered

search for multifractality in damage spreading for kauffman cellular automata the authors check how an initial disturbance called the damage spreads through a square lattice of kauffman cellular automata at their critical point they determine the moments of the probability that a site has been damaged n times and check for multifractality in the fractal dimensions or critical exponents of these moments of the damage probability

scaling of the first passage time of biased diffusion on hierarchical comb structures biased diffusion on hierarchical comb structures is studied within an exact renormalisation group scheme the scaling exponents of the moments of the first passage time for random walks are obtained it is found that the scaling properties of the diffusion depend only on the direction of bias in a particular case the presence of bias may give rise to a new multifractality

the structure of mode locked regions in quasi periodically forced circle maps using a mixture of analytic and numerical techniques we show that the mode locked regions of quasi periodically forced arnold circle maps form complicated sets in parameter space these sets are characterized by pinched off regions where the width of the mode locked region becomes very small by considering general quasi periodically forced circle maps we show that this pinching occurs in a broad class of such maps having a simple symmetry 2000 elsevier science b v all rights reserved

sympletic finite difference approximations of the nonlinear klein gordon equation we analyze three finite difference approximations of the nonlinear klein gordon equation and show that they are directly related to symplectic mappings two of the schemes the perring skyrme and ablowitz kruskal ladik are long established and the third is a new higher order accurate scheme we test the schemes on traveling wave and periodic breather problems over long time intervals and compare their accuracy and computational costs with those of symplectic and nonsymplectic method of lines approximations and a nonsymplectic energy conserving method

solutions to the matrix equation ax exf by an explicit solution to the generalized sylvester matrix equation ax exf by with the matrix f being a companion matrix is given this solution is represented in terms of the r controllability matrix of e a b generalized symmetric operator and a hankel matrix moreover several equivalent forms of this solution are presented the obtained results may provide great convenience for many analysis and design problems a numerical example is used to illustrate the effectiveness of the proposed approach

damage spreading and multifractality in the travelling salesman problem the authors study numerically the spreading of damage in the euclidean travelling salesman problem there is a critical temperature tc approximately 0 20 0 25 below which damage does not spread they search for multifractal behaviour in the moments of the damage probability distribution multifractality is found in the frozen phase when the moments are monitored as a function of time if they are evaluated with the number of cities multifractal behaviour occurs in the chaotic phase

application of the symplectic finite difference time domain scheme to electromagnetic simulation an explicit fourth order finite difference time domain fdtd scheme using the symplectic integrator is applied to electromagnetic simulation a feasible numerical implementation of the symplectic fdtd sfdtd scheme is specified in particular new strategies for the air dielectric interface treatment and the near to far field nff transformation are presented by using the sfdtd scheme both the radiation and the scattering of three dimensional objects are computed furthermore the energy conserving characteristic hold for the sfdtd scheme is verified under long term simulation numerical results suggest that the sfdtd scheme is more efficient than the traditional fdtd method and other high order methods and can save computational resources

parametric eigenstructure assignment for continuous time descriptor systems abstract eigenstructure assignment for continuous time descriptor systems ex t ax t bu t via descriptor variable feedback control u t kx t is treated a new parametric form for the gain matrix k which assigns rank e arbitrary finite eigenvalues to the closed loop system is developed this form embraces two sets of design parameter vectors characterizing respectively the assignable eigenvectors associated with the finite eigenvalues and a necessary and sufficient condition for closed loop system regularity in addition a certain submatrix of k turns out to be totally free whenever nullity e exceeds rank b unlike earlier methods the eigenvectors associated with the infinite eigenvalues are dispensed with in the solution algorithm

an explicit solution to the matrix equation ax xf by a complete general and explicit solution to the generalized sylvester matrix equation ax xf by with the matrix f in a companion form is proposed the solution is in an extremely neat form represented by a symmetric operator matrix a hankel matrix and the controllability matrix of the matrix pair a b furthermore several equivalent forms of this solution are also presented based on these presented results explicit solutions to the normal sylvester equation and the well known lyapunov matrix equation are also established the results provide great convenience to the analysis of the solution to the equation and can perform important functions in many analysis and design problems in control systems theory as a demonstration a simple and effective approach for parametric pole assignment is proposed

exponential growth for the wave equation with compact time periodic positive potential we prove the existence of smooth positive potentials v t x periodic in time and with compact support in x for which the cauchy problem for the wave equation u tt xu cv t x ud 0 has solutions with exponentially growing global and local energy moreover we show that there are resonances 2 c

robust eigenstructure assignment via dynamical compensators abstract based on a proposed complete parametric approach for eigenstructure assignment in multivariable linear systems via dynamical compensators insightful parametrizations of the closed loop eigenvalues sensitivities to the perturbed elements in the open loop system matrices are obtained and an effective algorithm for eigenvalue assignment with minimum sensitivity in multivariable linear systems via dynamical compensators is then proposed the algorithm does not contain going back procedures and allows the closed loop eigenvalues to be conveniently optimized within desired regions a numerical example demonstrates its effect simplicity and numerical property

on transversal oscillations of a vertically translating string with small time harmonic length variations abstract in this paper the free transverse vibrations of a vertically moving string with a harmonically time varying length are studied the string length variations are assumed to be small by using the multiple timescales perturbation method in conjunction with a fourier series approach we determine the resonance frequencies and derive the non secularity conditions in the form of an infinite dimensional system of coupled ordinary differential equations this system describes the long time behavior of the amplitudes of the oscillations then the eigenvalues of the obtained system are studied by the galerkin truncation method and applicability of this method is discussed apart from this the dynamic stability of the solution is investigated by an energy analysis additionally resonance detuning is considered