anti collusion fingerprinting for multimedia digital fingerprinting is a technique for identifying users who use multimedia content for unintended purposes such as redistribution these fingerprints are typically embedded into the content using watermarking techniques that are designed to be robust to a variety of attacks a cost effective attack against such digital fingerprints is collusion where several differently marked copies of the same content are combined to disrupt the underlying fingerprints we investigate the problem of designing fingerprints that can withstand collusion and allow for the identification of colluders we begin by introducing the collusion problem for additive embedding we then study the effect that averaging collusion has on orthogonal modulation we introduce a tree structured detection algorithm for identifying the fingerprints associated with k colluders that requires o klog n k correlations for a group of n users we next develop a fingerprinting scheme based on code modulation that does not require as many basis signals as orthogonal modulation we propose a new class of codes called anti collusion codes accs which have the property that the composition of any subset of k or fewer codevectors is unique using this property we can therefore identify groups of k or fewer colluders we present a construction of binary valued acc under the logical and operation that uses the theory of combinatorial designs and is suitable for both the on off keying and antipodal form of binary code modulation in order to accommodate n users our code construction requires only o spl radic n orthogonal signals for a given number of colluders we introduce three different detection strategies that can be used with our acc for identifying a suspect set of colluders we demonstrate the performance of our acc for fingerprinting multimedia and identifying colluders through experiments using gaussian signals and real images

exact boundary controllability of vibrating non classical euler bernoulli micro scale beams abstract this study investigates the exact controllability problem for a vibrating non classical euler bernoulli micro beam whose governing partial differential equation pde of motion is derived based on the non classical continuum mechanics in this paper it is proved that via boundary controls it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time this control objective is achieved based on the pde model of the system which causes that spillover instabilities do not occur

tempered stable levy motion and transient super diffusion the space fractional diffusion equation models anomalous super diffusion its solutions are transition densities of a stable levy motion representing the accumulation of power law jumps the tempered stable levy motion uses exponential tempering to cool these jumps a tempered fractional diffusion equation governs the transition densities which progress from super diffusive early time to diffusive late time behavior this article provides finite difference and particle tracking methods for solving the tempered fractional diffusion equation with drift a temporal and spatial second order crank nicolson method is developed based on a finite difference formula for tempered fractional derivatives a new exponential rejection method for simulating tempered levy stables is presented to facilitate particle tracking codes

exponential stabilisation of a simple tree shaped network of timoshenko beams system the stabilisation problem of a forked triple system of timoshenko beams which is a simple tree shaped network is considered in this article suppose that the root of the fork is clamped at the interior node of the fork the displacement and rotational angle of the beams are continuous the shearing force and bending moments of the beams satisfy the transmission conditions the feedback controllers are designed at the exterior tips to stabilise this system then the closed loop system is proved to be well posed by the eigenfrequency analysis together with the asymptotic technique the system is shown to satisfy the spectrum determined growth condition finally this closed loop system is proved to be exponentially stable furthermore a simulation is given to support these results

on the stabilization of a flexible beam with a tip mass we study the stability of a flexible beam that is clamped at one end and free at the other a mass is also attached to the free end of the beam to stabilize this system we apply a boundary control force at the free end of the beam we prove that the closed loop system is well posed and is exponentially stable we then analyze the spectrum of the system for a special case and prove that the spectrum determines the exponential decay rate for the considered case

heavy tailed log hydraulic conductivity distributions imply heavy tailed log velocity distributions 1 equations of contaminant transport describing non gaussian dispersion of solute in heterogeneous porous media have been developed by several authors e g berkowitz and scher 1995 1998 benson 1998 2001 berkowitz et al 2000 and baeumer et al 2005 the equations assume that solute particle movement in time and or space can be described by heavy tailed probability distributions e g levy stable distributions this assumption requires a mechanism for solute particles to move through heterogeneous porous media in a manner that can be approximated with heavy tailed probability distributions this work investigates whether a heavy tailed levy stable distribution of increments in log hydraulic conductivity results in a heavy tailed distribution of increments in log velocity a heavy tailed distribution of increments in log velocity would be a mechanism for solute particle movement in time or space that can be described by a heavy tailed probability distribution a computer algorithm was written to generate realistic hydraulic conductivity fields the algorithm modifies the spectral synthesis method for generating fractional brownian motion i e saupe 1988 and brewer and wheatcraft 1994 and produces self similar hydraulic conductivity fields with a heavy tailed levy stable distribution of increments in log hydraulic conductivity a monte carlo approach was adopted in which 100 hydraulic conductivity fields were generated for each of the following values of 0 8 1 1 1 4 and 1 7 the usgs finite difference groundwater code modflow was used to calculate the velocity fields and the increments in longitudinal log hydraulic conductivity and log velocity from the fields were analyzed to determine whether they were consistent with a heavy tailed levy stable probability density function pdf after determining that the distributions of increments in log hydraulic conductivity and log velocity were consistent with a levy stable pdf the tail parameters describing each pair of hydraulic conductivity and velocity fields were estimated with the nolan 1997 maximum likelihood estimator the relationship between the two tail parameters was then determined there are three conclusions of this research first mandelbrot and pp plots confirm that levy stable distributions of increments in log hydraulic conductivity give rise to levy stable distributions of increments in log velocity second the tail parameter for the increments in log velocity is typically smaller indicating a heavier probability tail than the corresponding tail parameter for the increments in log hydraulic conductivity third there is a positive statistical relation between the two tail parameters

the expansion of a semigroup and a riesz basis criterion problems on the expansion of a semigroup and a criterion for being a riesz basis are discussed in the present paper suppose that a is the generator of a c0 semigroup on a hilbert space and a 1 a 2 a with 2 a is consisted of isolated eigenvalues distributed in a vertical strip it is proved that if 2 a is separated and for each 2 a the dimension of its root subspace is uniformly bounded then the generalized eigenvectors associated with 2 a form an l basis under different conditions on the riesz projection the expansion of a semigroup is studied in particular a simple criterion for the generalized eigenvectors forming a riesz basis is given as an application a heat exchanger problem with boundary feedback is investigated it is proved that the heat exchanger system is a riesz system in a suitable state hilbert space

a mass balance based numerical method for the fractional advection dispersion equation theory and application 1 the inherent heterogeneity of many geophysical systems often gives rise to fast and slow pathways to water and chemical movement and one approach to model solute transport through such media is the continuous time random walk ctrw one special asymptotic case of the ctrw is the fractional advection dispersion equation fade which has proven to be a promising alternative to model anomalous dispersion and has been increasingly used in hydrology to model chemical transport in both surface and subsurface water most practical problems in hydrology have complicated initial and boundary conditions and need to be solved numerically but the numerical solution of the fade is not trivial in this paper we present a finite volume approach to solve the fade where the spatial derivative of the dispersion term is fractional we also give methods to solve different boundary conditions often encountered in practical applications the linear system resulting from the temporal spatial discretization is solved using a semi implicit scheme the numerical method is derived on the basis of mass balance and its accuracy is tested against analytical solutions the method is then applied to simulate tracer movement in a stream and a near saturated hillslope in a naturally structured upland podzol field in northeast scotland

properties of a class of c0 semigroups on banach spaces and their applications abstract in this paper we investigate some properties of a class of c 0 semigroups on banach spaces suppose that the spectrum of the infinitesimal generator is discrete and there are only finitely many eigenvalues in each vertical strip we show that such semigroups can be expanded by their generalized eigenvectors under certain conditions as a consequence we assert that the semigroups with these conditions are eventually differentiable provided that the system of generalized eigenvectors is complete as an example we apply our results to a one dimensional wave control system

the damped string problem revisited abstract we revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it employing methods familiar from supersymmetric quantum mechanics we also derive completeness and riesz basis results with parentheses for the associated root functions under less smoothness assumptions on the coefficients than usual using operator theoretic methods rather than detailed eigenvalue and root function asymptotics only

riesz basis property of serially connected timoshenko beams in this paper we study the riesz basis property of serially connected timoshenko beams with joint and boundary feedback controls suppose that the left end of the whole beam is clamped and the right end is free at intermediate nodes the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous the collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system we prove that the operator determined by the closed loop system has compact resolvent and generates a c 0 semigroup in an appropriate hilbert space we also show that there is a sequence of the generalized eigenvectors of the operator that forms a riesz basis with parentheses hence the spectrum determined growth condition holds therefore if the imaginary axis is not an asymptote of the spectrum then the closed loop system is exponentially stable finally we give a conclusion remark to explain that our result can be applied not

normalized truncated levy walks applied to the study of financial indices abstract this work is devoted to the study of the statistical properties of financial indices from developed and emergent markets we performed a new analysis of the behavior of several financial indices by using a normalized truncated levy walk model we conclude that the truncated levy distribution describes perfectly the evolution of the financial indices near a crash for both well developed and emergent markets

on controllability of a rotating string we consider the problem of controllability of a rotating string we say that a set of initial data of the string is controllable if for any initial data of this set by suitable manipulation of the exterior force the string goes to rest the main result of the paper is a description of controllable sets of initial data the equation is not strongly hyperbolic to get exact controllability of such equation in the sharp time interval we use control functions from sobolev spaces with noninteger indices to prove our results we apply the method of moments that has been widely used in control theory of distributed parameter systems since the classical papers of h o fattorini and d l russell we use recent results about exponential bases in sobolev spaces with noninteger indices

levy flights in a steep potential well levy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial monomodal to a terminal bimodal distribution occurs chechkin et al phys rev e 67 010102 r 2003 in this paper we present a detailed study of levy flights in potentials of the type u x x c with c 2 apart from the bifurcation into bimodality we find the interesting result that for c 4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial condition and the building up of the two emerging side peaks which are characteristic for the stationary state thus for certain system parameters there exists a transient trimodal distribution of the levy flight these properties of levy flights in external potentials of the power law type can be represented by certain phase diagrams we also present details about the proof of multimodality and the numerical procedures to establish the probability distribution of the process

on controllability of a non homogeneous elastic string with memory abstract we are motivated by the problem of control for a non homogeneous elastic string with memory we reduce the problem of controllability to a non standard moment problem the solution of the latter problem is based on an auxiliary riesz basis property result for a family of functions quadratically close to the nonharmonic exponentials this result requires the detailed analysis of an integro differential equation and is of interest in itself for function theory controllability of the string implies observability of a dual system

exponential bases in sobolev spaces in control and observation problems for the wave equation the fourier method in control systems reduces the study of controllability observability to the study of related exponential families in this paper we present examples of such systems specifically those for which we can prove that the related exponential families form a riesz basis in corresponding appropriately defined sobolev spaces this makes it possible to choose natural pairs of spaces the state space observability space and the control space state space depending on whether an observation or a control problem is studied respectively so that the observation and control operators are isomorphisms

space fractional advection diffusion and reflective boundary condition anomalous diffusive transport arises in a large diversity of disordered media stochastic formulations in terms of continuous time random walks ctrws with transition probability densities showing space and or time diverging moments were developed to account for anomalous behaviors a broad class of ctrws was shown to correspond on the macroscopic scale to advection diffusion equations involving derivatives of noninteger order in particular ctrws with l evy distribution of jumps and finite mean waiting time lead to a space fractional equation that accounts for superdiffusion and involves a nonlocal integral differential operator within this framework we analyze the evolution of particles performing symmetric l evy flights with respect to a fluid moving at uniform speed v the particles are restricted to a semi infinite domain limited by a reflective barrier we show that the introduction of the boundary condition induces a modification in the kernel of the nonlocal operator thus the macroscopic space fractional advection diffusion equation obtained is different from that in an infinite medium

exponentially damped levy flights multiscaling and exchange rates abstract we employ our previously suggested exponentially damped levy flight physica a 326 2003 544 to study the multiscaling properties of 30 daily exchange rates against the us dollar together with a fictitious euro dollar rate physica a 286 2000 353 though multiscaling is not theoretically seen in either stable levy processes or abruptly truncated levy flights it is even characteristic of smoothly truncated levy flights phys lett a 266 2000 282 eur phys j b 4 1998 143 we have already defined a class of quasi stable processes in connection with the finding that single scaling is pervasive among the dollar price of foreign currencies physica a 323 2003 601 here we show that the same goes as far as multiscaling is concerned our novel findings incidentally reinforce the case for real world relevance of the levy flights for modeling financial prices

sampling and interpolation problems for vector valued signals in the paley wiener spaces a new approach to sampling interpolation problem for vector valued signals is proposed for a function signal f from the paley wiener space pw pi bbc n of entire vector valued functions the sampling data are defined as the inner products langf lambdan alphan rang of f lambdan and vectors alphan it is proved that alphan lambdan is a sampling and interpolating sequence for pw pi bbc n if and only if the family alphanei lambdan t forms a riesz basis in l 2 pi pi bbc n this relation allows to characterize all sampling and interpolating sequences in terms of a generating matrix function to produce a wide class of matrix functions generating sampling and interpolating sequences we consider the matrix sturm liouville problems and apply the boundary control theory for hyperbolic dynamical systems this approach allows to construct both asymptotically uniform and nonuniform sampling and interpolating sequences

uncoupled continuous time random walks solution and limiting behavior of the master equation a detailed study is presented for a large class of uncoupled continuous time random walks ctrws the master equation is solved for the mittag leffler survival probability the properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed finally some common objections found in the literature are thoroughly reviewed

the boundary control approach to the titchmarsh weyl m function i the response operator and the a amplitude we link the boundary control theory and the titchmarsh weyl theory this provides a natural interpretation of the a amplitude due to simon and yields a new efficient method to evaluate the titchmarsh weyl m function associated with the schrodinger operator h x 2 q x on l 2 0 with dirichlet boundary condition at x 0

wavelets and the angle between past and future the main result the riesz projectionp or equivalently hilbert transformt is bounded in the weighted spacel2 w wherewis a matrix valued weight if and only ifsupi 1 i iw 1 2 1 i iw 1 1 2 wheresupremumis taken over all intervalsi motivation for this problem comes from stationary processes riesz projection is bounded means the angle between past and future of a stationary process with spectral measurewis nonzero in the scalar case the result is the well known hunt muckenhoupt wheeden theorem the main step in our proof is to show that a vector haar system forms an unconditional basis inl2 w as a byproduct of our approach we get some new results about bases of wavelets in weighted spaces in both scalar and vector valued cases

a chebyshev pseudospectral method to solve the space time tempered fractional diffusion equation a chebyshev pseudospectral method to solve the space time tempered fractional diffusion equation

generalized fractional diffusion equations for accelerating subdiffusion and truncated levy flights fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time for processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order such equations were introduced in a v chechkin r gorenflo and i sokolov phys rev e 66 046129 2002 for the description of the processes getting more anomalous in the course of time decelerating subdiffusion and accelerating superdiffusion here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time which we call respectively accelerating subdiffusion and decelerating superdiffusion for the former process by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time for the latter process we demonstrate by a particular example how the power law truncated levy stable distribution evolves in time to the distribution with power law asymptotics and gaussian shape in the central part the special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics

simultaneous control problems for systems of elastic strings and beams abstract controllability problems for n strings or beams controlled from a common endpoint are studied we give necessary and sufficient conditions for simultaneous spectral and approximate controllability and describe the space of simultaneously reachable states as a function of the position of the endpoint for each type of controllability result the sharp controllability time is obtained the proofs are based on new results in nonharmonic fourier series which describe riesz bases of exponential divided differences

fluid limit of the continuous time random walk with general levy jump distribution functions the continuous time random walk ctrw is a natural generalization of the brownian random walk that allows the incorporation of waiting time distributions psi t and general jump distribution functions eta x there are two well known fluid limits of this model in the uncoupled case for exponential decaying waiting times and gaussian jump distribution functions the fluid limit leads to the diffusion equation on the other hand for algebraic decaying waiting times psi approximately t 1 beta and algebraic decaying jump distributions eta approximately x 1 alpha corresponding to levy stable processes the fluid limit leads to the fractional diffusion equation of order alpha in space and order beta in time however these are two special cases of a wider class of models here we consider the ctrw for the most general levy stochastic processes in the levy khintchine representation for the jump distribution function and obtain an integrodifferential equation describing the dynamics in the fluid limit the resulting equation contains as special cases the regular and the fractional diffusion equations as an application we consider the case of ctrws with exponentially truncated levy jump distribution functions in this case the fluid limit leads to a transport equation with exponentially truncated fractional derivatives which describes the interplay between memory long jumps and truncation effects in the intermediate asymptotic regime the dynamics exhibits a transition from superdiffusion to subdiffusion with the crossover time scaling as tauc approximately lambda alpha beta where 1 lambda is the truncation length scale the asymptotic behavior of the propagator green s function of the truncated fractional equation exhibits a transition from algebraic decay for t tauc

expansion of solution in terms of generalized eigenfunctions for a hyperbolic system with static boundary condition this paper studies a linear hyperbolic system with static boundary condition that was first studied in neves et al j funct anal 67 1986 320 344 it is shown that the spectrum of the system consists of zeros of a sine type function and the generalized eigenfunctions of the system constitute a riesz basis with parentheses for the root subspace the state space thereby decomposes into topological direct sum of root subspace and another invariant subspace in which the associated semigroup is superstable that is to say the semigroup is identical to zero after a finite time period

hydraulic conductivity velocity and the order of the fractional dispersion derivative in a highly heterogeneous system 1 a one dimensional fractional order advection dispersion equation accurately models the movement of the core of the tritium plume at the highly heterogeneous made site an a priori estimate of the parameters in that equation including the order of the fractional dispersion derivative was based on the assumption that the observed power law heavy tail of the hydraulic conductivity k field would create a similarly distributed velocity field monte carlo simulations were performed to test this hypothesis results from the monte carlo analysis show that heavy tailed k fields do give rise to heavy tailed velocity fields however the exponent of the power law the tail parameter describing these two distributions is not necessarily the same the tail parameter that characterizes a velocity distribution is not solely dependent on the tail parameter that characterizes the k distribution the k field must also have long range dependence so that water may flow through relatively continuous high k channels

analytic approach to the problem of convergence of truncated levy flights towards the gaussian stochastic process an analytic expression for characteristic function defining a truncated l evy flight is derived it is shown that the characteristic function yields results in agreement with recent simulations of truncated l evy flights by mantegna and stanley phys rev lett 73 2946 1994 with the analytic expression for the characteristic function the convergence of the l evy process towards the gaussian is demonstrated without simulations in the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures

moments for tempered fractional advection diffusion equations this paper develops moment formulas for exponentially tempered fractional advection diffusion equations tfades that transition from anomalous to asymptotic diffusion limits over time exact analytical expressions or series representations for spatial moments up to the fourth order are derived by integral transform or asymptotic expansion approach a fully lagrangian solver cross verified by an implicit eulerian approach is also developed to calculate numerically the complete evolution of moments for the tfades with complex initial and boundary conditions moment analysis identifies the diffusion equation that attracts the tempered anomalous diffusion in the long time limit fitting of moments measured at two end members of alluvial systems checks the applicability of moment analysis in understanding real diffusion

bifurcation bimodality and finite variance in confined levy flights we investigate the statistical behavior of levy flights confined in a symmetric quartic potential well u x proportional variant x 4 at stationarity the probability density function features a distinct bimodal shape and decays with power law tails which are steep enough to give rise to a finite variance in contrast to free levy flights from a delta initial condition a bifurcation of the unimodal state is observed at t c 0 the nonlinear oscillator with potential u x ax 2 2 bx 4 4 a b 0 shows a crossover from unimodal to bimodal behavior at stationarity depending on the ratio a b

exact controllability and stabilization of a vibrating string with an interior point mass in this article we examine the problems of boundary control and stabilization for a one dimensional wave equation with interior point masses we show that singularities in waves are smoothed one order as they cross a point mass thus in the case of one interior point mass with e g l 2 dirichlet control at the left end the most general reachable space from 0 that one can expect is l 2 times h 1 to the left of the mass and h 1 times l 2 to the right of the mass we show that this is in fact the optimal result modulo certain compatibility conditions several related results for both control and stabilization of such systems are also given

an integrability condition on the resolvent for hyperbolicity of the semigroup abstract in this paper we present necessary and sufficient conditions on the resolvent of the generator of a strongly continuous semigroup in order that the corresponding semigroup is hyperbolic the proof is based on a new characterization of the growth bound in terms of the resolvent as an application we discuss three examples

fractal mobile immobile solute transport 1 a fractal mobile immobile model for solute transport assumes power law waiting times in the immobile zone leading to a fractional time derivative in the model equations the equations are equivalent to previous models of mobile immobile transport with power law memory functions and are the limiting equations that govern continuous time random walks with heavy tailed random waiting times the solution is gained by performing an integral transform on the solution of any boundary value problem for transport in the absence of an immobile phase in this regard the output from a multidimensional numerical model can be transformed to include the effect of a fractal immobile phase the solutions capture the anomalous behavior of tracer plumes in heterogeneous aquifers including power law breakthrough curves at late time and power law decline in the measured mobile mass the made site mobile tritium mass decline is consistent with a fractional time derivative of order 0 33 while haggerty et al s 2002 stream tracer test is well modeled by a fractional time derivative of order 0 3

fractional diffusion equation for a power law truncated levy process abstract truncated levy flights are stochastic processes which display a crossover from a heavy tailed levy behavior to a faster decaying probability distribution function pdf putting less weight on long flights overcomes the divergence of the levy distribution second moment we introduce a fractional generalization of the diffusion equation whose solution defines a process in which a levy flight of exponent is truncated by a power law of exponent 5 a closed form for the characteristic function of the process is derived the pdf of the displacement slowly converges to a gaussian in its central part showing however a power law far tail possible applications are discussed

on fractional tempered stable processes and their governing differential equations we derive the governing equation of the tempered stable subordinator hereafter tss which generalizes the space fractional differential equation satisfied by the law of the stable subordinator itself this equation is expressed in terms of the shifted fractional derivative of order 0 1 coinciding with the stability parameter we then generalize this equation by introducing a time fractional derivative of order 0 1 resp 1 1 and we prove that it is satisfied by the law of a tss time changed by the inverse of a stable subordinator resp by the stable subordinator itself the corresponding processes can therefore be called fractional ts processes finally we provide fractional extensions of the relativistic stable processes which we define as a brownian motion with a random time argument represented by independent fractional ts processes of order resp 1

crossover between levy and gaussian regimes in first passage processes we propose an approach to the problem of the first passage time our method is applicable not only to the wiener process but also to the non gaussian l evy flights or to more complicated stochastic processes whose distributions are stable to show the usefulness of the method we particularly focus on the first passage time problems in the truncated l evy flights the so called kobol processes from koponen boyarchenko and levendorskii in which the arbitrarily large tail of the l evy distribution is cut off we find that the asymptotic scaling law of the first passage time t distribution changes from t ensuremath ensuremath alpha 1 ensuremath alpha law non gaussian l evy regime to t ensuremath 3 2 law gaussian regime at the crossover point this result means that an ultraslow convergence from the non gaussian l evy regime to the gaussian regime is observed not only in the distribution of the real time step for the truncated l evy flight but also in the first passage time distribution of the flight the nature of the crossover in the scaling laws and the scaling relation on the crossover point with respect to the effective cutoff length of the l evy distribution are discussed

oscillation criteria for second order forced elliptic differential equations with mixed nonlinearities in the case of oscillatory potentials we establish some oscillation criteria for the second order forced elliptic differential equation with mixed nonlinearities div a x y c x y e x when n 1 our results extend those of kong q kong interval criteria for oscillation of second order linear ordinary differential equations j math anal appl 229 1999 258 270 for certain second order linear ordinary differential equations sun and meng y g sun f w meng interval criteria for oscillation of second order differential equations with mixed nonlinearities appl math comput 2007 doi 10 10 1016 j amc 2007 08 042 for certain second order differential equations with mixed nonlinearities yang q yang interval oscillation criteria for a second order nonlinear ordinary differential equations with oscillatory potential appl math comput 135 2003 49 64 for a forced second order superlinear ordinary differential equation when n 2 our theorems are more general and improve the oscillation criteria of zhuang r k zhuang annual oscillation criteria for second order nonlinear elliptic differential equations j comput anal math 2007 doi 10 1016 j cam 2007 06 031 for a forced second order undamped elliptic differential equation

on the connection between exponential bases and certain related sequences in l2 π π a sequence of vectors fn in a separable hilbert space h is a frame if there are positive constants a b such that a f 2 n f fn 2 b f 2 for all f h and fn is a riesz sequence if it is a riesz basis in the closure of the space spanned by the vectors fn the latter of the following two questions has been raised by khrushchev nikolskii and pavlov can every frame of complex exponentials ei nx in l2 be made into a riesz basis by removing from ei nx a suitable collection of the functions ei nx can every riesz sequence ei nx in l2 be made into a riesz basis by adjoining to ei nx a suitable collection of exponentials ei nx ei nx we show that this is indeed so for all frames and riesz sequences ei nx studied so far and we prove that we can always solve both problems in a certain weak sense however our main conclusion is that the answer to both questions is no

efficient algorithms for chemical threshold testing problems we consider a generalization of the classical group testing problem let us be given a sample contaminated with a chemical substance we want to estimate the unknown concentration c of this substance in the sample there is a threshold indicator which can detect whether the concentration is at least a known threshold we consider both the case when the threshold indicator does not affect the tested units and the more difficult case when the threshold indicator destroys the tested units for both cases we present a family of efficient algorithms each of which achieves a good approximation of c using a small number of tests and of auxiliary resources each member of the family provides a different tradeoff between the number of tests and the use of other resources involved by the algorithm previously known algorithms for this problem use more tests than most of our algorithms do

on competitive group testing in many fault detection problems the goal is to identify defective items from a set of items with a minimum number of tests each test is on a subset of items which tells whether the subset contains a defective item or not the concept of competitive algorithm has been developed to relate the properties of the group testing algorithms that assume that the number of defective items d is known to those without any a priori knowledge on d a new concept of strongly competitive algorithm is defined that relates different characteristics of these two classes of algorithms and present an interesting relationship between the two concepts competitive and strongly competitive a strongly competitive algorithm is also presented

exponential stability of uniform euler bernoulli beams with non collocated boundary controllers a b s t r a c t we study the stability of a robot system composed of two euler bernoulli beams with noncollocated controllers by the detailed spectral analysis we prove that the asymptotical spectra of the system are distributed in the complex left half plane and there is a sequence of the generalized eigenfunctions that forms a riesz basis in the energy space since there exist at most finitely many spectral points of the system in the right half plane to obtain the exponential stability we show that one can choose suitable feedback gains such that all eigenvalues of the system are located in the left half plane hence the riesz basis property ensures that the system is exponentially stable finally we give some simulation for spectra of the system

on using random walks to solve the space fractional advection dispersion equations the solution of space fractional advection dispersion equations fade by random walks depends on the analogy between the fade and the forward equation for the associated markov process the forward equation which provides a lagrangian description of particles moving under specific markov processes is derived here by the adjoint method the fade however provides an eulerian description of solute fluxes there are two forms of the fade based on fractional flux ff ade and fractional divergence fd ade the ff ade is derived by taking the integer order mass conservation of non local diffusive flux while the fd ade is derived by taking the fractional order mass conservation of local diffusive flux the analogy between the fade and the forward equation depends on which form of the fade is used and on the spatial variability of the dispersion coefficient d in the fade if d does not vary in space then the fades can be solved by tracking particles following a markov process with a simple drift and an stable levy noise with index that corresponds to the fractional order of the fade if d varies smoothly in space and the solute concentration at the upstream boundary remains zero the fd ade can be solved by simulating a markov process with a simple drift an stable levy noise and an additional term with the dispersion gradient and an additional levy noise of order 1 however a non markov process might be needed to solve the ff ade with a space dependent d except for specific d such as a linear function of space

high order numerical approximation formulas for riemann liouville riesz tempered fractional derivatives construction and application i abstract in this paper we develop a new numerical algorithm for solving the riesz tempered space fractional diffusion equation the stability and convergence of the numerical scheme are discussed via the technique of matrix analysis finally numerical experiments are performed to confirm the effectiveness of our numerical algorithm

riesz basis property and exponential stability of controlled euler bernoulli beam equations with variable coefficients this paper studies the basis property and the stability of a distributed system described by a nonuniform euler bernoulli beam equation under linear boundary feedback control it is shown that there is a sequence of generalized eigenfunctions of the system which forms a riesz basis for the state hilbert space the asymptotic distribution of eigenvalues the spectrum determined growth condition and the exponential stability are concluded the results are applied to a nonuniform beam equation with viscous damping of variable coefficient as a generalization of existing results for the uniform beam

continuous time random walks simulation of continuous trajectories continuous time random walks have been developed as a straightforward generalization of classical random walk processes some ten years ago fogedby introduced a continuous representation of these processes by means of a set of langevin equations h c fogedby phys rev e 50 1657 1994 the present work is devoted to a detailed discussion of fogedby s model and presents its application for the robust numerical generation of sample paths of continuous time random walk processes

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

fundamental solution of the tempered fractional diffusion equation in this paper we consider the space time fractional diffusion equation dt u x t k dx u x t 0 x r t 0 with the tempered riemann liouville derivative of order 0 1 in space and the caputo derivative of order 0 1 in time the fundamental solution which turns out to be a spatial probability density function is given in computable series form as well as in integral representation the spatial moments of the probability density function are determined explicitly for an arbitrary order n 0 moreover green s function of the untempered neutral fractional diffusion equation is analyzed in view of absolute and relative extreme points at the end of this article we point out a remarkably and important integral representation for accurate evaluation of the m wright mainardi function m x of order 0 1 and arguments x r0

exponentially damped levy flights abstract since real processes seem to departure from standard levy distributions modifications to the latter have been suggested in literature these include abruptly truncated phys rev lett 73 1994 2946 smoothly truncated phys rev e 52 1995 1197 phys lett a 266 2000 282 and gradually truncated levy flights physica a 268 1999 231 physica a 275 2000 531 we put forward what we call an exponentially damped levy flight which encompasses the previous cases in the presence of increasing and positive feedbacks our distribution is assumed to deviate from the levy in both a smooth and gradual fashion we estimate the truncation parameters by nonlinear least squares to optimally fit the distribution tails that is a novel approach for estimating parameters and of the levy the method is illustrated with daily data on exchange rates for 15 countries against the us dollar our results show that the exponentially damped levy flight fits the data well when increasing and positive deviations are present