a novel approach to an impulsive feedback control with and without memory involvement abstract the present work studies the effect of an impulsive perturbation to classical and fractional classes of initial value problems scattering properties of the time sequences corresponding to the impulses are studied in the both integer and non integer order cases it is shown that the sign changing property of the perturbation function determines the mentioned scattering property of the kick times

chaos synchronization of the fractional lu system abstract chaos synchronization of the fractional lu system is theoretically and numerically studied by two methods the suitable conditions for achieving synchronization of this fractional differential system are derived by using the laplace transform theory numerical simulations coincide with the theoretical analysis

lyapunov functions for riemann liouville like fractional difference equations abstract discrete memory effects are introduced by fractional difference operators asymptotic stabilities of nonlinear fractional difference equations are investigated in this paper a linear scalar fractional difference equality is utilized lyapunov second direct method is proposed for nonlinear discrete fractional systems asymptotic stability conditions are provided and some examples are given

buckling of a conical thin shell with variable thickness under a dynamic loading this study considers the buckling of an elastic truncated conical shell having a meridional thickness expressed by an arbitrary function subject to a uniform external pressure which is a power function of time at first the fundamental relations and donnell type dynamic buckling equation of an elastic conical shell with variable thickness have been obtained then employing galerkin s method those equations have been reduced to a time dependent differential equation with variable coefficients finally applying the ritz type variational method the critical static and dynamic loads the corresponding wave numbers dynamic factor and critical stress impulse have been found analytically using the results thus obtained the effects of the thickness variations with a power or an exponential function the variation of the semi vertex angle and the variation of the power of time in the external pressure expression are studied through pertinent computations it is observed that these factors have appreciable effects on the critical parameters of the problem in the heading

numerical solution of the space fractional fokker planck equation the traditional second order fokker planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of brownian motion densities of stable type have been used to describe the probability distribution of these motions the resulting governing equation of these motions is similar to the traditional fokker planck equation except that the order of the highest derivative is fractional in this paper a space fractional fokker planck equation sffpe with instantaneous source is considered a numerical scheme for solving sffpe is presented using the riemann liouville and grunwald letnikov definitions of fractional derivatives the sffpe is transformed into a system of ordinary differential equations ode then the ode system is solved by a method of lines numerical results for sffpe with a constant diffusion coefficient are evaluated for comparison with the known analytical solution the numerical approximation of sffpe with a time dependent diffusion coefficient is also used to simulate levy motion with stable densities we will show that the numerical method of sffpe is able to more accurately model these heavy tailed motions

chaos synchronization of fractional chaotic maps based on the stability condition abstract in the fractional calculus one of the main challenges is to find suitable models which are properly described by discrete derivatives with memory fractional logistic map and fractional lorenz maps of riemann liouville type are proposed in this paper the general chaotic behaviors are investigated in comparison with the caputo one chaos synchronization is designed according to the stability results the numerical results show the method s effectiveness and fractional chaotic map s potential role for secure communication

on stability of nonlinear nonautonomous discrete fractional caputo systems abstract conditions to establish mittag leffler stability of solutions for nonlinear nonautonomous discrete caputo like fractional systems just from the linear associated system is shown mittag leffler stability for linear systems is tackled pointing out properties the matrix must satisfy additionally features on solutions for linear systems are included in order to establish the equivalence between uniform asymptotical stability and exponential stability converse like lyapunov theorem is developed and a particular result to show mittag leffler stability from a condition on a linear part of the full system is worked

recovery of singularities for formally determined inverse problems in this paper we considered several formally determined problems in two dimensions there are no global identifiability results for these problems however we can recover an important feature of these functions namely their singularities more precisely we prove that one can determine the location and strength of singularities of anl compactly supported potential by knowing the associated scattering amplitude at a fixed energy also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium

recovering singularities of a potential from singularities of scattering data in this paper we show that the leading singularities of certain potentials can be determined from the leading singularities of the backscattering as well as other determined sets of scattering data the potentials in question are conormal with respect to smooth surfaces of arbitrary dimension the restrictions on their orders allow for unbounded potentials in all dimension greater than or equal to three

fractional differential mask a fractional differential based approach for multiscale texture enhancement in this paper we intend to implement a class of fractional differential masks with high precision thanks to two commonly used definitions of fractional differential for what are known as grumwald letnikov and riemann liouville we propose six fractional differential masks and present the structures and parameters of each mask respectively on the direction of negative x coordinate positive x coordinate negative y coordinate positive y coordinate left downward diagonal left upward diagonal right downward diagonal and right upward diagonal moreover by theoretical and experimental analyzing we demonstrate the second is the best performance fractional differential mask of the proposed six ones finally we discuss further the capability of multiscale fractional differential masks for texture enhancement experiments show that for rich grained digital image the capability of nonlinearly enhancing complex texture details in smooth area by fractional differential based approach appears obvious better than by traditional integral based algorithms

dynamic buckling of cylindrical shells subject to an axial impact in a symplectic system this paper discusses the dynamic pre buckling of finite cylindrical shells in the propagation and reflection of axial stress waves by introducing the hamiltonian system into dynamic buckling of structures the problem can be described mathematically in a symplectic space the solutions of hamiltonian dual equations shown in canonical variables are obtained the problem is reduced to the determination of eigenvalues and eigensolutions with the former indicating critical buckling loads and the latter buckling modes numerical example presented shows phenomena of axisymmetric and non axisymmetric dynamic buckling subject to impacts of axial load

computing finite rotations of shells by an asymptotic numerical method abstract we present an asymptotic numerical algorithm for the computation of elastic shells with large rotations the theoretical formulation involves a three field hu washizu functional which allows us to put the problem into a quadratic framework the spatial discretization is based on geometrically exact element recently presented by buchter et al buchter et al three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept int j numer methods engrg 37 1994 2551 1568 several classical benchmarks are discussed to define the best strategy and to assess the validity and the efficiency of the present method as compared to more classical iterative algorithms

influence of localized imperfections on the buckling of cylindrical shells under axial compression the influence of localized imperfections on the buckling of a long cylindrical shell under axial compression is analysed by using a double scale analysis including interaction modes this leads to a system of coupled complex non linear differential equations with discontinuous derivatives we propose analytical formulas to predict the reduction of the critical buckling load

random vibration analysis of axially compressed cylindrical shells under turbulent boundary layer in a symplectic system a random vibration analysis of an axially compressed cylindrical shell under a turbulent boundary layer tbl is presented in the symplectic duality system by expressing the cross power spectral density psd of the tbl as a fourier series in the axial and circumferential directions the problem of structures excited by a random distributed pressure due to the tbl is reduced to solving the harmonic response function which is the response of structures to a spatial and temporal harmonic pressure of unit magnitude the governing differential equations of the axially compressed cylindrical shell are derived in the symplectic duality system and then a symplectic eigenproblem is formed by using the method of separation of variables expanding the excitation vector and unknown state vector in symplectic space decoupled governing equations are derived and then the analytical solution can be obtained in contrast to the modal decomposition method mdm the present method is formulated in the symplectic duality system and does not need modal truncation and hence the computations are of high precision and efficiency in numerical examples harmonic response functions for the axially compressed cylindrical shell are studied and a comparison is made with the mdm to verify the present method then the random responses of the shell to the tbl are obtained by the present method and the convergence problems induced by fourier series expansion are discussed finally influences of the axial compression on random responses are investigated

the synchronization of fractional order rossler hyperchaotic systems abstract the synchronization of fractional order hyperchaotic systems is studied using the rossler system as an example based on the laplace transformation theory sufficient conditions for global synchronization of the systems are given analytically also the variational iteration method is implemented to give the approximate solution for the fractional order error system of the two identical hyperchaotic systems which is in good agreement with the approximate solution using the classical laplace transformation method numerical methods and simulations on the master slave systems are presented to verify the results obtained

on saint venant s principle in pin jointed frameworks numerical experiments performed by hoff 50 years ago on the application of saint venant s principle to frameworks are extended and his conclusions qualified guided by these results a general treatment is formulated employing a state variable approach this leads directly to an eigenvalue problem in which the decay rates are the eigenvalues of the cell transfer matrix unity eigenvalues correspond to the transmitting modes of rigid body displacement and the stress resultants of tension bending moment shearing force and twisting moment consideration of the associated eigenvectors and principal vectors gives exact values for the equivalent continuum beam properties of the framework such as equivalent cross sectional area poisson s ratio second moment of area shear coefficient and torsion constant

chaotic vibration bifurcation stabilization and synchronization control for fractional discrete time systems abstract the main intention of this paper is to investigate the dynamics of fractional cubic map and fractional holmes map from four perspectives chaos bifurcation stabilization and synchronization via jacobian matrix algorithm we estimate the largest lyapunov exponents of fractional maps to examine the existence of chaos in accordance with the observation of chaotic vibration affected by fractional difference order in addition with the help of the novel asymptotic stability criterion for linear incommensurate fractional difference systems the effective control laws of stabilization and synchronization for fractional chaotic maps are achieved respectively besides experimental investigations and numerical simulations are implemented to further verify the effectiveness of the proposed results

on riemann and caputo fractional differences in this paper we define left and right caputo fractional sums and differences study some of their properties and then relate them to riemann liouville ones studied before by miller k s and ross b atici f m and eloe p w abdeljawad t and baleanu d and a few others also the discrete version of the q operator is used to relate the left and right caputo fractional differences a caputo fractional difference equation is solved the solution proposes discrete versions of mittag leffler functions

on chaos in the fractional order grassi miller map and its control abstract in this paper we propose and examine the fractional form corresponding to the grassi miller integer order discrete time system we show experimental phase portraits and bifurcation diagrams to highlight the ranges of parameters and fractional orders over which chaos is observed in addition we propose two distinct control schemes for the proposed fractional map the first controller stabilizes the states and forces them towards zero asymptotically the second controller aims to synchronize a pair of maps with non identical parameters throughout the paper numerical results are presented to verify the analytic results

on state space elastostatics within a plane stress sectorial domain the wedge and the curved beam the plane stress sectorial domain is analysed according to a state space formulation of the linear theory of elasticity when loading is applied to the straight radial edges flanks with the circular arcs free of traction one has the curved beam when loading is applied to the circular arcs with the flanks free of traction one has the elastic wedge a complete treatment of just one problem the elastic wedge say requires two state space formulations the first describes radial evolution for the transmission of the stress resultants force and moment while the second describes circumferential evolution for determination of the rates of decay of self equilibrated loading on the circular arcs as anticipated by saint venant s principle these two formulations can be employed subsequently for the curved beam where now radial evolution is employed for the saint venant decay problem and circumferential evolution for the transmission modes power law radial dependence is employed for the wedge and is quite adequate except for treatment of the so called wedge paradox for this and the curved beam the formulations are modified so that ln r takes the place of the radial coordinate r the analysis is characterised by a preponderance of repeating eigenvalues for the transmission modes and the state space formulation allows a systematic approach for determination of the eigen and principal vectors the so called wedge paradox is related to accidental eigenvalue degeneracy for a particular angle and its resolution involves a principal vector describing the bending moment coupled to a decay eigenvector restrictions on repeating eigenvalues and possible jordan canonical forms are developed finally symplectic orthogonality relationships are derived from the reciprocal theorem

hamiltonian system based saint venant solutions for multi layered composite plane anisotropic plates this paper presents hamiltonian system based saint venant solutions for the problem of multi layered composite plane anisotropic plates a mixed energy variational principle is proposed and dual equations are derived in the symplectic space the schemes of separation of variables and eigenfunction expansion instead of the traditional semi inverse method are implemented and compatibility conditions at interfaces are formulated by dual variables by expending eigenfunctions in the subspace with zero eigenvalue an analytical solution of a cantilever composite plate is presented to illustrate the proposed approach

a semi analytical buckling analysis of imperfect cylindrical shells under axial compression abstract in the framework of the cellular bifurcation theory we investigate the effect of distributed and or localized imperfections on the buckling of long cylindrical shells under axial compression using a double scale perturbative approach including modes interaction we establish that the evolution of amplitudes of instability patterns is governed by a non homogeneous second order system of three non linear complex equations the localized imperfections are included by employing jump conditions for their amplitude and permitting discontinuous derivatives by solving these amplitude equations we show the influence of distributed and or localized imperfections on the reduction of the critical load to assess the validity of the present method our results are compared to those given by two finite element codes

the saint venant problem and principle in elasticity abstract the traditional semi inverse solution method of the saint venant problem and the saint venant principle which were described in the euclidian space under the lagrange system formulation are updated to be solved in the symplectic space under the conservative hamiltonian system thus the saint venant problem and the saint venant principle have been unified by the direct method it is proved in the present paper that all the saint venant solutions can be obtained directly via the zero eigenvalue solutions and all their jordan normal forms of the corresponding hamiltonian operator matrix and the saint venant principle corresponds to neglect of all the non zero eigenvalue solutions in which the non zero eigenvalue gives the decay rate

synchronization of chaotic fractional order systems via active sliding mode controller abstract in this paper we propose a controller based on active sliding mode theory to synchronize chaotic fractional order systems in master slave structure master and slave systems may be identical or different based on stability theorems in the fractional calculus analysis of stability is performed for the proposed method finally three numerical simulations synchronizing fractional order lu lu systems synchronizing fractional order chen chen systems and synchronizing fractional order lu chen systems are presented to show the effectiveness of the proposed controller the simulations are implemented using two different numerical methods to solve the fractional differential equations

a discrete fractional order cournot duopoly game abstract this paper focuses on associating the cournot duopoly problem with long memory effects first of all we generate a discrete fractional order cournot duopoly game by introducing the caputo fractional order difference calculus to the classical duopoly theory in the fractional order game participants can make their decisions by taking full advantage of their historical information then we discuss both nash equilibria and local stability of the game by employing the linear approximation theory at last we numerically validate the main results by using bifurcation diagrams phase portraits the largest lyapunov exponent and the 0 1 test algorithms

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

asymptotic numerical methods and pade approximants for non linear elastic structures in this paper we apply asymptotic numerical methods for computing non linear equilibrium paths of elastic beam plate and shell structures the non linear branches are sought in the form of asymptotic expansions and they are determined by solving numerically fem several linear problems with a single stiffness matrix a large number of terms of the series can be easily computed by using recurrence formulas in comparison with a more classical step by step procedure the method is rapid and automatic we show with some examples that the choice of the expansion s parameter and the use of pade approximants play an important role in the determination of the size of the domain of convergence

chaos synchronization of the chua system with a fractional order chaos synchronization of two identical chua systems with the same fractional order is studied by utilizing the pecora carroll pc method the active passive decomposition pad method the one way coupling method and the bidirectional coupling one the sufficient conditions for achieving synchronization between these two systems are derived via the laplace transformation theory numerical simulations show the effectiveness of the theoretical analyses

a fractional model with parallel fractional maxwell elements for amorphous thermoplastics abstract we develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics the fractional model is composed of two parallel fractional maxwell elements the first fractional maxwell model is used to describe the glass transition while the second component is aimed at describing the viscous flow we further derive the analytical solutions for the stress relaxation modulus and complex modulus through laplace transform we then demonstrate the model is able to describe the master curves of the stress relaxation modulus storage modulus and loss modulus which all show two distinct transition regions the obtained parameters show that the modulus of the two fractional maxwell elements differs in 2 3 orders of magnitude while the relaxation time differs in 7 9 orders of magnitude finally we apply the model to describe the stress response of constant strain rate tests the model together with the parameters obtained from fitting the master curve of stress relaxation modulus can accurately predict the temperature and strain rate dependent stress response

recovery of the singularities of a potential from backscattering data in general dimension abstract we prove that in dimension n 2 the main singularities of a complex potential q having a certain a priori regularity are contained in the born approximation q b constructed from backscattering data this is archived using a new explicit formula for the multiple dispersion operators in the fourier transform side we also show that q q b can be up to one derivative more regular than q in the sobolev scale on the other hand we construct counterexamples showing that in general it is not possible to have more than one derivative gain sometimes even strictly less depending on the a priori regularity of q

asymptotic numerical method for buckling analysis of shell structures with large rotations in this paper the buckling and post buckling of elastic structures taking into account large rotations are investigated using an asymptotic numerical method the critical points are detected by two different ways first by a bifurcation indicator second by analysing the poles of a pade approximant the first step of the post buckling branch is computed starting from the bifurcation point and using an extended system the remaining bifurcating branch is followed by the same algorithm as for the fundamental path several examples are tested to show the effectiveness of the proposed method

the axial torsional vibration of pretwisted beams we investigate the coupled axial torsional vibration of pretwisted beams the equations of motion governing the extension torsion and cross sectional warping of pretwisted beams are derived from hamiltons principle and the common assumptions used to simplify the equations are carefully examined through scaling analysis inconsistencies in previous works such as the neglect of spatial and time derivatives of torsion in the lagrangian functional are remedied giving rise to fourth order terms in the equations of motion that are significant for higher harmonics furthermore scaling analysis of the governing equations yields a set of objective criteria for checking the validity of the frequently misused assumption that the warping function under pretwist is locally identical to that of a prismatic beam we show that this simplification is responsible for the common poor prediction of axial resonance frequencies for pretwisted beams

microlocal analysis of scattering data for nested conormal potentials consider the potential scattering problem for the wave equation begin array rcl partial t 2 bigtriangleup q u 0 text in mathbb r n times mathbb r u delta t x cdot omega text for t rho end array 1 where q is a compactly supported potential and omega in s n 1 is fixed here is the value such that supp q subset vert x vert leq rho

a bridging technique to analyze the influence of boundary conditions on instability patterns in this paper we present a new numerical technique that permits to analyse the effect of boundary conditions on the appearance of instability patterns envelope equations of landau ginzburg type are classically used to predict pattern formation but it is not easy to associate boundary conditions for these macroscopic models indeed envelope equations ignore boundary layers that can be important for instance in cases where the instability starts first near the boundary in this work the full model is considered close to the boundary an envelope equation in the core and they are bridged by the arlequin method 1 simulation results are presented for the problem of buckling of long beams lying on a non linear elastic foundation

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

a parametrix for the fundamental solution of the klein gordon equation on asymptotically de sitter spaces abstract in this paper we construct a parametrix for the forward fundamental solution of the wave and klein gordon equations on asymptotically de sitter spaces without caustics we use this parametrix to obtain asymptotic expansions for solutions of u f and to obtain a uniform l p estimate for a family of bump functions traveling to infinity

three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept conventional shell formulations such as 3 or 5 parameter theories or even 6 parameter theories including the thickness change as extra parameter require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness this means that the normal stress in thickness direction has to either vanish or be constant in general these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions the main objective of the present study is to introduce directly a complete 3 d constitutive law without modification therefore a 7 parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects

the inverse backscattering problem in three dimensions this article is a study of the mapping from a potentialq x onr3 to the backscattering amplitude associated with the hamiltonian q x the backscattering amplitude is the restriction of the scattering amplitudea k k es2 s2 toa k we show that in suitable complex banach spaces the map fromq x toa x x x x x is usually a local diffeomorphism hence in contrast to the overdetermined problem of recoveringq from the full scattering amplitude the inverse backscattering problem is well posed