inclusion principle for the rayleigh ritz based substructure synthesis according to this substructure synthesis the motion of every substructure is modeled in terms of quasicomparison functions which are linear combinations of admissible functions capable of satisfying all the boundary conditions

a new steganography method which preserves histogram generalization of lsb histogram based steganalysis methods diagnose abnormalities in the stego histogram lsb and outguess are two steganography methods which preserve the cover histogram completely these methods embed some extra bits to retain the cover histogram however these techniques adversely affect the statistical and perceptual attributes of the cover media lsb was proposed to improve lsb by prohibiting some pixels from changing resulting in the reduction of the extra bits in this paper we improve the lsb method by proposing a technique to distinguish sensitive pixels and protect them from extra bit embedding which causes lower distortion in the co occurrence matrices in addition we extend lsb to preserve the dct coefficients histogram of jpeg images and generalize this method to the case where more than one bit of the cover elements are used the experimental results show that the improved lsb method produces fewer traces in the co occurrence matrices than the lsb method furthermore the histogram based attacks cannot detect stego images produced by the proposed method with or without extra bits embedding therefore the visual quality of the cover can be improved by the elimination of extra bit embedding

rayleigh ritz based substructure synthesis for flexible multibody systems this paper is concerned with the modeling of flexible multibody systems by a rayleigh ritz based substructure synthesis method so that certain advantages can be accrued by using the variational approach to derive the eigenvalue problem as with the classical rayleigh ritz method if the admissible functions used to represent the motion of the substructures are not chosen properly convergence can suffer this paper presents a new substructure synthesis method with superior convergence characteristics achieved by representing the motion by means of a recently developed class of functions namely the class of quasi compari son functions this improved convergence is shown to be related to improved approximation of both the differential equations and the natural boundary conditions the theory is demonstrated by means of a numerical example i introduction t his investigation is concerned with the modeling of flexible multibody systems many structures such as fixedwing aircraft helicopters flexible spacecraft flexible robots etc can be modeled as assemblages of interacting flexible bodies a method proposed by hurty1 2 in the early 1960s and known as component mode synthesis consists of modeling the motion of the individual substructures referred to as components by means of component modes he uses three types of modes to represent the motion of a substructure rigid body modes constraint modes and normal modes to define constraint modes hurty divides the constraints into two classes statically determinate and redundant the constraint modes are equal in number to the number of redundant constraints and are defined by producing a unit displacement on each redundant constraint in turn with all other constraints fixed the normal modes represent the modes of vibration of the components with all constraints fixed an approach by craig and hampton3 differs from that of hurty 1 2 mainly in the selection of the component modes indeed craig and hampton suggest two types of component modes boundary modes providing for displacements and rotations at points along the substructure boundaries and related to the constraint modes of hurty and substructure modes corresponding to completely restrained boundaries the substructures modeled individually in refs 1 3 are made to act together as a single structure by eliminating the redundant generalized coordinates arising from the fact that displacements at points common to two adjacent substructures are included twice in the overall problem formulation once for each substructure the elimination process is based on the use of constraint equations resulting from the enforcement of compatibility conditions which amounts to saying that the displacement of a boundary point shared by two substructures is the same in another approach to the problem proposed by

an adaptive secret image sharing with a new bitwise steganographic property recently numerous studies have been conducted in the area of secret image sharing and steganography the main objective of these schemes is to produce high quality tampering resistant stego images a number of these methods are based on least significant bit embedding and hence the presence of hidden data can be detected by well designed steganalysis algorithms this paper proposes a new sharing scheme for critical images so that stego images are obtained with better visual quality and at the same time the authentication ability can be adjusted to any desired level adaptive in order to achieve these objectives the construction of cellular automata is modified so that visual quality is improved although authentication bits are hidden in cover images furthermore authentication bits are computed in such a way that any tampering with one block affects more than one block for steganographic purposes least significant bit replacement is substituted with a new blockwise xor operation so that the scheme can withstand steganalysis attacks the other interesting property of the proposed method is that the size of blocks is determined dynamically therefore our approach can be adapted with secret cover images of different sizes

eigenvalue convergence in the finite element method in static force deflection applications of the finite element method convergence rates for the p version in which the polynomial degree of element interpolation functions is increased while the mesh remains fixed are superior to those for the h version in which the element degree remains fixed while the mesh is refined so that element size approaches zero in structural dynamics applications one does not seek to approximate a single solution as in static applications but seeks estimates for a number of the lower system eigenvalues this paper identifies factors responsible for poorer accuracy in higher computed eigenvalues in addition it explains why the p version of the finite element method can be expected to exhibit significantly better eigenvalue convergence than the h version numerical examples demonstrate the superiority of the p version over the h version they also show the effects of various mechanisms limiting eigenvalue convergence

intertwining relations and darboux transformations for schrodinger equations in n 1 dimensions we evaluate the intertwining relation for schrodinger equations in n 1 dimensions the conditions for the existence of a darboux transformation are analyzed and compared to their 1 1 dimensional counterparts a complete solution of the conditions is given for 2 1 dimensions and a darboux transformation is constructed

lsb steganographic method based on reversible histogram transformation function for resisting statistical steganalysis statistical steganalysis schemes detect the existence of secret information embedded by steganography the x 2 detection and regular singular rs attack methods are two well known statistical steganalysis schemes used against lsb least significant bit steganography the embedded message length can be estimated accurately by these two steganalysis schemes for secret communication the resistance of steganography against steganalysis is very important for information security to avoid the enemy s attempts the statistical features between stego images and cover images should be as similar as possible for better resistance to steganalysis in this manuscript a reversible histogram transformation function based lsb steganographic method is proposed to resist statistical steganalysis the experimental results show that the proposed method resists not only rs attack but also x 2 detection methods

reversible data hiding based on block median preservation this paper proposes a reversible data hiding scheme for gray level images it exploits the high correlation among image block pixels to produce a difference histogram secret data is embedded based on a multi level histogram shifting mechanism with reference to the integer median of each block the image blocks are divided into four categories due to four corresponding embedding strategies aiming at preserving the medians during data embedding in decoder the median pixels are retrieved first followed by the hidden data extraction and the host image can be accurately recovered via an inverse histogram shifting mechanism after removing the secret data from the marked image experimental results validate the effectiveness of our scheme and demonstrate that it outperforms several previous methods in terms of capacity and marked image s quality

a general procedure for improving substructures representation in dynamic synthesis in the general substructure synthesis method for the dynamic analysis of complex flexible structures developed earlier by the authors the motion of each substructure is represented by a given number of substructure admissible functions and the otherwise disjoint substructures are connected together to form a whole structure by imposing approximate geometric compatibility conditions by means of weighted residuals in this paper a general procedure for improving the admissible functions representing each substructure in the synthesis is developed the procedure is an iterative one and it leads to an improved eigensolution for the intermediate structure i e a fictitious structure defined by the approximate compatibility conditions where the improved eigensolution is obtained while always using the same number of degrees of freedom to represent a given substructure in any iteration the computations associated with each substructure are independent of those for all other substructures and they can be performed in parallel by increasing the number of iterations the eigensolution for the intermediate structure is approached the procedure is applicable to assembled structures that are either positive definite or positive semidefinite moreover the procedure represents an extension of the concept of subspace iteration to structures composed of substructures

new modal synthesis technique using mixed modes a new modal synthesis technique using mixed modes is introduced the method not only has a simple form high precision and efficiency but it also provides two reliable criteria for determining the truncation frequency of system synthesis modes these have been demonstrated in detail by the numerical examples the key point of the method is as follows the exact residual modes containing the effects of higher order free interface modes are expressed analytically in terms of some lower order fixed interface modes and then the substructural displacements are expressed accurately in terms of some lower order mixed modes i e the linear combinations of the lower order fixed interface modes and lower order free interface modes instead of the assumed substructural displacements employed in general modal synthesis so that only linear synthesis equations are involved in this new method although the contributions of all higher order modes are included

two families of superintegrable and isospectral potentials in two dimensions as an extension of the intertwining operator idea an algebraic method which provides a link between supersymmetric quantum mechanics and quantum super integrability is introduced by realization of the method in two dimensions two infinite families of superintegrable and isospectral stationary potentials are generated the method makes it possible to perform darboux transformations in such a way that in addition to the isospectral property they acquire the superintegrability preserving property symmetry generators are second and fourth order in derivatives and all potentials are isospectral with one of the smorodinsky winternitz potentials explicit expressions of the potentials their dynamical symmetry generators and the algebra they obey as well as their degenerate spectra and corresponding normalizable states are presented

rigorous implementation of the galerkin method for uniform and stepped columns the aim of this paper is to deal with the often occurring mistake in the implementation of the galerkin method and its correction it is shown that the flexural rigidity should be represented as a

two dimensional magnetic schrodinger equations darboux transformations and solutions of associated auxiliary equations we extend the formalism of darboux transformations to magnetic schrodinger equations in two dimensions the partner potentials associated with the darboux transformation are obtained in explicit form through an integral formula we apply our construction to a particular spectral problem of dirichlet type obtaining the darboux partner its spectrum and the corresponding solutions in explicit form

on a new iterative approach of component mode synthesis a wholly new concept of intermediate structure is developed in this paper based on this a new component mode iteration cmi or subdomain subspace iteration method is proposed in the new cmi method the ordinarily required step of ensuring interface compatibility is eliminated an outstanding achievement of this method is that it retains the merit of the standard subspace iteration ssi technique concerning the number of vectors required in computation in the present method iteraton is carried out at subdomain levels on machines capable of parallel processing this work can be performed simultaneously numerical examples clearly demonstrate the excellence of this new method

the historical bases of the rayleigh and ritz methods abstract rayleigh s classical book theory of sound was first published in 1877 in it are many examples of calculating fundamental natural frequencies of free vibration of continuum systems strings bars beams membranes plates by assuming the mode shape and setting the maximum values of potential and kinetic energy in a cycle of motion equal to each other this procedure is well known as rayleigh s method in 1908 ritz laid out his famous method for determining frequencies and mode shapes choosing multiple admissible displacement functions and minimizing a functional involving both potential and kinetic energies he then demonstrated it in detail in 1909 for the completely free square plate in 1911 rayleigh wrote a paper congratulating ritz on his work but stating that he himself had used ritz s method in many places in his book and in another publication subsequently hundreds of research articles and many books have appeared which use the method some calling it the ritz method and others the rayleigh ritz method the present article examines the method in detail as ritz presented it and as rayleigh claimed to have used it it concludes that although rayleigh did solve a few problems which involved minimization of a frequency these solutions were not by the straightforward direct method presented by ritz and used subsequently by others therefore rayleigh s name should not be attached to the method

a general dynamic synthesis for structures with discrete substructures abstract this paper presents a substructure synthesis method for the dynamic simulation of complex structures where the structures consist of an assemblage of discrete substructures an analogy between distributed and discrete structures is extensively invoked to stimulate the motion of discrete substructures the concept of admissible vectors is introduced where admissible vectors represent the discrete counterpart of admissible functions for distributed substructures the individual substructures are forced to act as a whole structure by imposing certain geometric compatibility on internal boundaries shared by any two substructures a numerical example illustrating the method is presented

image complexity and feature mining for steganalysis of least significant bit matching steganography the information hiding ratio is a well known metric for evaluating steganalysis performance in this paper we introduce a new metric of image complexity to enhance the evaluation of steganalysis performance in addition we also present a scheme of steganalysis of least significant bit lsb matching steganography based on feature mining and pattern recognition techniques compared to other well known methods of steganalysis of lsb matching steganography our method performs the best results also indicate that the significance of features and the detection performance depend not only on the information hiding ratio but also on the image complexity

harmonic balance galerkin method for non smooth dynamic systems models of non linear systems frequently introduce forces with bounded continuity resulting in non smooth even discontinuous flow examples include systems with clearances backlash friction and impulses asymptotic methods require smooth differentiable flow and are therefore ill suited for analyzing non smooth systems in these cases the traditional harmonic balance method may be used to obtain approximate periodic solutions but the method suffers from extremely slow convergence in general generalizations of the traditional harmonic balance method are introduced in this paper that result in superior convergence rates and superior modes of convergence these improvements derive from the introduction of one or more expansion functions that possesses the same degree of continuity as the exact solution in particular forming an infinite series of such functions results in an expansion in the same function space of the exact solution this expansion converges pointwise to the exact solution and to all derivatives thereof these improvements are illustrated by example upon re evaluating a classical single degree of freedom model for friction induced vibration

estimating natural frequencies and mode shapes from forced response calculations a method is proposed for condensing a structural eigenvalue problem by using more than one forced response vector in a condensation the method approximates an eigenvector by a linear combination of forced response vectors resulting in a significantly smaller eigenvalue problem that retains the eigenpairs that were most excited by the force vectors the condensation is extremely economical in cases where the forced response vectors have been computed for other purposes in cases where some eigenpairs are approximately known the method produces accurate eigenvalue estimates by choosing the force vectors to be parallel to the approximate eigenvectors this idea forms the basis of an iterative procedure that finds all of the eigenvalues in a specified frequency range theoretical error bounds on the estimated eigenvalues are also presented numerical examples illustrate unique features of the condensation in its noniterative and iterative forms

on proximity of rayleigh quotients for different vectors and ritz values generated by different trial subspaces abstract the rayleigh quotient is unarguably the most important function used in the analysis and computation of eigenvalues of symmetric matrices the rayleigh ritz method finds the stationary values of the rayleigh quotient called ritz values on a given trial subspace as optimal in some sense approximations to eigenvalues in the present paper we derive upper bounds for proximity of the ritz values in terms of the proximity of the trial subspaces without making an assumption that the trial subspace is close to an invariant subspace the main result is that the absolute value of the perturbations in the ritz values is bounded by a constant times the gap between the original trial subspace and its perturbation the constant is the spread in the matrix spectrum i e the difference between the largest and the smallest eigenvalues of the matrix it s shown that the constant cannot be improved we then generalize this result to arbitrary unitarily invariant norms but we have to increase the constant by a factor of 2 our results demonstrate in particular the stability of the ritz values with respect to a perturbation in the trial subspace

accurate computing of higher vibration modes of thin flexible structures motivated by the need for high fidelity modeling and accurate control of future hypersonic vehicles subjected to complex aerothermomechanical loads and many other such applications a novel scheme is proposed to accurately compute higher modes of vibration for one dimensional structures by coupling the classic ritz method as a predictor and the linear two point boundary value problem solver supore as a corrector the ritz method is used to compute a preliminary estimate of the natural frequencies for the desired modes these estimates are then used as initial guesses by supore which employs superposition and reorthonormalization to accurately solve the governing boundary value problem compared to a high fidelity ritz approximation or a highly refined finite element modeling procedure this is a simple computationally less expensive and yet highly accurate method to compute mode shapes for applications that require higher modes this scheme is used to compute mode shapes within an absolute and relative

eigensolution of augmented graph products using shifted inverse iteration method two important matrices associated with graphs are adjacency and laplacian matrices in this paper efficient methods are presented for eigensolution of graph products augmented by other graphs for augmentations that do not destroy the symmetry of the graph products a method is proposed for decomposition of matrices resulting in considerable simplification of their eigensolution for graphs composed of two non overlapping graph products joined through a small number of link members a method based on shifted inverse iteration is proposed which utilizes all eigenvalues and eigenvectors of each individual graph products owing to the availability of fast methods for eigensolution of graph products this method simplifies the eigensolution of a variety of graph models and proves to be very efficient in determining the few smallest eigenpairs of these models with high levels of accuracy

existence and analytical predictions of periodic motions in a periodically forced nonlinear friction oscillator the grazing bifurcation stick phenomena and periodic motions in a periodically forced nonlinear friction oscillator are investigated the nonlinear friction force is approximated by a piecewise linear kinetic friction model with the static force the total forces for the input and output flows to the separation boundary are introduced and the force criteria for the onset and vanishing of stick motions are developed through such input and output flow forces the periodic motions of such an oscillator are predicted analytically through the corresponding mapping structure illustrations of the periodic motions in such a piecewise friction model are given for a better understanding of the stick motion with the static friction the force responses are presented which agreed very well with the force criteria if the fully nonlinear friction force is modeled by several portions of piecewise linear functions the periodically forced nonlinear friction oscillator can be predicted more accurately however for the fully nonlinear friction force model only the numerical investigation can be carried out

analytical study of vibrating systems with strong non linearities by employing saw tooth time transformations abstract a special saw tooth temporal transformation technique is formulated it is simple enough to allow analytical computation of strongly non linear free and forced dynamic responses but at the same time can be applied to the analysis of general classes of non linear problems

a comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems the high order purely frequency based harmonic balance method hbm presented by cochelin and vergez 2009 1 and extended by karkar et al 2013 2 now allows to follow the periodic solutions of regularized non smooth systems stiff systems this paper compares its convergence property to a reference method in applied mathematics orthogonal collocation with piecewise polynomials a first test is conducted on a nonlinear smooth 2 degree of freedom spring mass system showing better convergence of the hbm the second test is conducted on a one degree of freedom vibro impact system with a very stiff regularization of the impact law the hbm continuation of the nonlinear mode was found to be very robust even with a very large number of harmonics surprisingly the hbm was found to have a better convergence than the collocation method for this vibro impact system

adaptive image data hiding in edges using patched reference table and pair wise embedding technique reference table rt based embedding method embeds secret digits into pixel pairs under the guidance of a reference table most of the existing rt based methods either require elaborate conversions among different bases or have limited embedding capacity in this paper we use a patched reference table prt as a guide and propose a prt method to provide a better image quality and extendable embedding capacity we also exploit the concept of pixel value differencing pvd and propose another method prt pvd in the traditional pvd based methods the shape of the difference histograms of the stego images is significantly altered and thus vulnerable to some steganalyzers prt pvd adopts the prt method and uses a specially designed embedding sequence to preserve the difference histogram shape experimental results reveal that the proposed prt and prt pvd methods not only have better embedding efficiency over the existing methods but also are robust to detection by modern steganalysis tools

natural modes of bernoulli euler beams with symmetric cracks abstract an approximate galerkin solution to the one dimensional cracked beam theory developed by christides and barr for the free bending motion of beams with pairs of symmetric open cracks is suggested the series of comparison functions considered in the galerkin procedure consists of the mode shapes of corresponding uncracked beam the number of terms in the expansion is determined by the covnergence of the natural frequencies and confirmed by studying the stress concentration profile near the crack this approach allows the determination of the higher natural frequencies and mode shapes of the cracked beam it is found that the christides and barr original solution was not fully converged and that cracks render the convergence of the galerkin s procedure very slow by affecting the continuity characteristics of the solution of the boundary value problem to validate the theoretical results a two dimensional finite element approach is proposed which also allows one to determine the parameter that controls the stress concentration profile near the crack tip in the theoretical formulation without requiring the use of experimental results very good agreement between the theoretical and finite element results is observed

on the determination of approximate periodic solutions of some non linear ode abstract we propose a numerical symbolic method for the approximation of periodic solutions of a type of non linear ode the efficiency of our method is contrasted with the harmonic balance method and with another one which combines the differential transformation method with pade approximants on a non trivial example the relativistic oscillator it is shown that our method is computationally more reliable

a reversible data hiding scheme using complementary embedding strategy obtaining good visual quality and high hiding capacity with reversible data hiding systems is a technically challenging problem in this paper we propose a simple reversible data hiding scheme that uses a complementary hiding strategy the proposed method embeds one secret bit horizontally and vertically into one cover pixel of a grayscale cover image by decreasing odd valued pixels and increasing even valued pixels by one experimental results show that the hiding capacity measured by bit per pixel bpp of the proposed scheme is at least 1 21bpp with a psnr peak signal to noise ratio value greater than 52db for all standard test images especially in the case of four layer embedding the psnr value of the proposed method is still greater than 51db at a hiding capacity of about 5bpp for all standard test images in addition the proposed method is quite simple because it primarily uses additions and subtractions these results indicate that the proposed scheme is superior to many existing reversible data hiding schemes introduced in the literature

gibbs phenomenon in structural mechanics the concepts of complementary boundary condition and interior condition are discussed guidelines are developed to eliminate the gibbs effect when selecting trial functions for the series expansion

a new exact substructure method using mixed modes in this paper the use of free or fixed interface modes in exact substructure displacement expansions is briefly summarized then the substructural displacements are expressed exactly in terms of mixed modes i e the displacements consist of linear combinations of fixed and free interface modes this yields a new exact mixed mode substructure method it is demonstrated that the exact substructure methods with fixed or free interfaces are two limiting cases of this new mixed mode exact method thus the exact substructure method variants with free interface fixed interface or mixed modes form a systematic theory of substructure methods which is unified by the new mixed mode variant this new exact variant not only has this important theoretical significance but also has great practical significance because it can lead to new approximate methods and to a deeper understanding of existing ones e g quasi comparison function methods dynamic condensation methods or substructure modal synthesis methods

optimal a priori error bounds for the rayleigh ritz method we derive error bounds for the rayleigh ritz method for the approximation to extremal eigenpairs of a symmetric matrix the bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector we also present a sharp bound

domain decomposition methods for eigenvalue problems abstract this paper proposes several domain decomposition methods to compute the smallest eigenvalue of linear self adjoint partial differential operators let us be given a partial differential operator on a domain which consists of two nonoverlapping subdomains suppose a fast eigenvalue solver is available for each of these subdomains but not for the union of them the first proposed method is a scheme which determines an appropriate boundary condition at the interface separating the two regions this boundary condition can be derived from the zero of a nonlinear operator which plays the same role for the eigenvalue problem as the steklov poincare operator for the linear equation an iterative method can be used to solve this nonlinear equation yielding the exact boundary condition at the interface this enables the determination of the eigenpair on the whole domain the same concept can be applied to a schwarz alternating method for the eigenvalue problem in case the subdomains overlap a nonoverlapping scheme in the spirit of schur complement will also be discussed these ideas are also applicable to a domain imbedding algorithm

iterative solution of some nonlinear differential equations we propose an iterative method to solve some non linear ordinary differential equations comparing on the mathieu van der pol and hill equation of fourth order we see that this method is much more efficient than the well known methods by lyapunov or picard

component mode iteration for frequency calculations this paper presents component mode iteration a new method for carrying out a form of subspace iteration on the substructure level for structures composed of substructures in component mode iteration substructure displacement is in terms of component modes with the interface displacements as coefficients component modes are chosen such that exact compatibility is assured throughout the structure the reduced structure eigenvalue problem is assembled and solved for lower mode approximations the resulting estimates of lower mode interface motion are used to refine the component modes by approximating the dynamic response of substructures to interface motion with a vector iteration process for this step the substructures are independent and can be processed in parallel reassembly and solution of the reduced structure problem yields improved lower mode estimates further iterations of refinement and reassembly are performed until convergence takes place the initial component modes are generated automatically and at negligible expense and numerical examples show that convergence with these is excellent yielding very accurate results after only one iteration indeed convergence is shown to be significantly faster than in the standard subspace iteration method

the convergence of harmonic ritz values harmonic ritz vectors and refined harmonic ritz vectors this paper concerns a harmonic projection method for computing an approximation to an eigenpair x of a large matrix a given a target point r and a subspace w that contains an approximation to x the harmonic projection method returns an approximation x to x three convergence results are established as the deviation e of x from w approaches zero first the harmonic ritz value r converges to a if a certain rayleigh quotient matrix is uniformly nonsingular second the harmonic ritz vector x converges to x if the rayleigh quotient matrix is uniformly nonsingular and remains well separated from the other harmonic ritz values third better error bounds for the convergence of are derived when x converges however we show that the harmonic projection method can fail to find the desired eigenvalue in other words the method can miss if it is very close to r to this end we propose to compute the rayleigh quotient p of a with respect to x and take it as a new approximate eigenvalue p is shown to converge to once x tends to x no matter how r is close to finally we show that if the rayleigh quotient matrix is uniformly nonsingular then the refined harmonic ritz vector or more generally the refined eigenvector approximation introduced by the author converges we construct examples to illustrate our theory

a procedure for improving discrete substructure representation in dynamic synthesis n important problem in the dynamic analysis for flexible structures is that of determining the natural frequencies and associated natural modes of vibration particularly the lower ones complex structures are often represented by mathematical models such as finite element models possessing a very large number of degrees of freedom where the number can reach into the tens of thousands because of the large number of degrees of freedom a direct iterative method for obtaining a partial eigensolution know as subspace iteration was developed the subspace iteration method has a long history an extensive bibliography is given in ref 1 and the current status of the method is discussed in refs 2 4 in the context of structural dynamics even the subspace iteration method however can be overwhelmed by the large number of degrees of freedom in the mathematical model so that a method for prior reduction of the number of degrees of freedom is desirable complex structures are often modeled by breaking the structure into a number of simpler components or substructures the substructure models are then coupled together to form the whole structure model the technique is known as substructure synthesis and its origin can be found in refs 5 and 6 the idea of refs 5 and 6 is to represent the motion of each substructure by a set of substructure normal modes obtained by solving an eigenvalue problem for each substructure then each substructure is represented in the synthesis process by a reduced number of lower substructure modes the synthesis leads to an eigenvalue problem for the assembled structure of a substantially smaller order than that of the original formulation the price paid in reducing the order of the eigenvalue problem is that its solution is only an approximation of the actual eigensolution of the original structure

elimination of gibbs phenomena from error analysis of finite element results a change of variables is presented that improves the accuracy of fourier half range sine series used in numerical harmonic analysis the change in variables results in an interpolation formula that passes through the endpoints of tabulated data

angles between infinite dimensional subspaces with applications to the rayleigh ritz and alternating projectors methods we define angles for infinite dimensional subspaces of hilbert spaces inspired by the work of e j hannan 1961 1962 the angles of dixmier and friedrichs and the gaps are characterized we establish connections between the angles corresponding to orthogonal complements the sensitivity of angles with respect to subspaces is estimated we show that the squared cosines of the angles from one subspace to another can be interpreted as ritz values in the rayleigh ritz method the hausdorff distance between the ritz values corresponding to different trial subspaces is shown to be bounded by a constant times the gap between the subspaces we prove a similar eigenvalue perturbation bound that involves the gap squared an ultimate acceleration of the classical alternating projectors method is proposed its convergence rate is estimated in terms of the angles we illustrate the acceleration for a domain decomposition method with a small overlap for the 1d diffusion equation

gibbs phenomenon free fourier series for vibration and stability of complex beams the gibbs phenomenon in fourier series has long been recognized as a drawback in its applications in particular when it is used to represent a function having discontinuities one category namely intrinsic discontinuities could be derived from the nature of the physical problems another namely inherent discontinuities is created undesirably through the employment of fourier series to alleviate these drawbacks two techniques are developed the first aims at eliminating the inherent discontinuities the size of the original domain 0 l is first doubled with a virtual function 0 defined over the neighboring domain l 0 the augmented domain l l is then further extended periodically the virtual function 0 y is chosen so that continuities are achieved at y 0 l 2l consequently no gibbs phenomena will occur at the boundaries the second aims at reproducing the intrinsic discontinuities in the representation function by incorporating piecewise cubic polynomials into the fourier base function the enlarged basis function namely the gibbs phenomenon free fourier series function is able to represent accurately any specific boundary conditions and interior intrinsic discontinuous conditions examples of vibration and buckling analysis of complex beams show that the present method is versatile accurate and efficient

a new exactly solvable two dimensional quantum model not amenable to separation of variables the supersymmetric intertwining relations with second order supercharges allow us to investigate a new two dimensional model which is not amenable to standard separation of variables the corresponding potential being the two dimensional generalization of a well known one dimensional poschl teller model is proven to be exactly solvable for an arbitrary integer value of the parameter p all its bound state energy eigenvalues are found analytically and the algorithm for analytical calculation of all wavefunctions is given the shape invariance of the model and its integrability are of essential importance to obtain these results

on the substructure synthesis method substructure synthesis is a model reduction method whereby a complex structure is regarded as an assemblage of substructures the motion of each of the substructures is represented by a series of admissible functions vectors and the substructures are made to act as a single structure by imposing certain geometric compatibility conditions at the boundary between any two adjacent substructures because the series of admissible functions vectors represents the motion of the substructures only approximately and because the geometric compatibility conditions are only approximations of the true conditions the computed eigensolution is only an approximation of the actual one convergence of computed eigenvalues to actual eigenvalues requires two limiting processes one in which the number of admissible functions vectors is increased and the other in which the number of geometric compatibility conditions is increased

an efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems abstract the design of high q resonators such as xylophone bar resonators xbrs capable of being fabricated using micro electro mechanical systems mems processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance this paper is concerned with vibration analysis and q optimisation of an xbr with the method extending directly to other planar frames and straightforwardly to more complex structures the rayleigh ritz method is discussed in some detail first treating the discrete case followed by developing and applying a kinematical procedure to an l frame structure attention is given to geometric interpretation of the rayleigh ritz procedure and to developing an intuitive understanding the method before turning to the xbr case having developed an approximation for system dynamics the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support q factor natural frequencies mode shapes and support q values are presented and compared to finite element models of the same problem with excellent agreement observed at substantially lower computational cost for the first time in the literature the geometric impedance tuning principle underlying the xbr design is validated and quantified including sensitivity to manufacturing error

kron s method for symmetric eigenvalue problems kron s method has been used successfully by engineers for over 30 years to find eigenvalues of large symmetric matrices these matrices arise from domain decomposition of nonoverlapping domains of self adjoint partial differential operators this paper discusses some theoretical aspects of kron s method specifically the poles and zeroes of eigenvalues of the kron matrix and their relationships with the eigenvalues of the original matrix are given

numerical modal analysis of structures based on a revised substructure synthesis approach the classical substructuring approach to the problem of modal analysis of structures suffers from a number of drawbacks which can sometimes lead the analyst to prefer other often more cumbersome techniques a modified rayleigh ritz based approach is presented which circumvents most of the drawbacks and improves the precision of the method while also enhancing its applicability to complex structures the scheme is also particularly well suited to symbolic implementation in view of its systematic problem independent formulation the theoretical results are validated by case studies chosen to highlight various features of the approach viz a beam structure a hinged simple square plate a hinged plate structure of fairly complicated shape and a rectangular plate with two cutouts

pauli equation and the method of supersymmetric factorization we consider different variants of factorization of a 2 2 matrix schrodinger pauli operator in two spatial dimensions they allow us to relate its spectrum to the sum of spectra of two scalar schrodinger operators in a manner similar to one dimensional darboux transformations we consider both the case when such factorization is reduced to the ordinary two dimensional supersymmetric quantum mechanics quasifactorization and a more general case which involves covariant derivatives the admissible classes of electromagnetic fields are described and some illustrative examples are given

another look at admissible functions abstract problems associated with using global admissible functions in boundary value problems are discussed it is shown that if care is not taken it is possible to construct sets of trial functions that yield inaccurate results which take too long to converge the concept of complementary boundary conditions is introduced and their existence is established complementary boundary conditions indicate that the solution to the boundary value problem cannot take certain values at the boundaries it is shown that trial functions that yield incorrect or very slowly converging results are those that violate the complementary boundary conditions a revision for the definition of admissible and comparison functions is proposed that takes the complementary boundary conditions into consideration

on three modal synthesis variants abstract a unified formulation of fixed free and loaded interface variants of modal synthesis is presented a formal proof of the exactness of all three variants in the absence of modal truncation is established the sensitivity of the truncation error to the different interface conditions is studied

approximate eigensolution of laplacian matrices for locally modified graph products laplacian matrices and their spectrum are of great importance in algebraic graph theory there exist efficient formulations for eigensolutions of the laplacian matrices associated with a special class of graphs called product graphs in this paper the problem of determining a few approximate smallest eigenvalues and eigenvectors of large scale product graphs modified through the addition or deletion of some nodes and or members is investigated the eigenproblem associated with a modified graph model is reduced using the set of master eigenvectors and linear approximated slave eigenvectors from the original model implicitly restarted lanczos method is employed to obtain the required eigenpairs of the reduced problem examples of large scale models are included to demonstrate the efficiency of the proposed method compared to the direct application of the irl method

error estimates and adaptive refinement for plate bending problems the zienkiewicz zhu error estimator is shown to be effective in problems of plate flexure when used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed very fast adaptive convergence for results of specified accuracy is achieved

convergence of the classical rayleigh ritz method and the finite element method it is demonstrated in this paper that convergence of the classical rayleigh ritz method can be vastly improved by introducing a new class of admissible functions called quasi comparison functions

intertwined isospectral potentials in an arbitrary dimension the method of intertwining with n dimensional nd linear intertwining operator l is used to construct nd isospectral stationary potentials it has been proven that the differential part of l is a series in euclidean algebra generators integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each n 2 3 4 5 the most general forms of 2d and 3d isospectral potentials are considered in detail and construction of their hierarchies is exhibited the followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1d systems it has been shown that in choice of coordinates and l there are a number of alternatives increasing with n that enlarge the set of available potentials some salient features of higher dimensional extension as well as some applications of the results are presented

steganalysis of lsb matching based on statistical modeling of pixel difference distributions this paper presents a least significant bit lsb matching steganography detection method based on statistical modeling of pixel difference distributions previous research indicates that natural images are highly correlated in a local neighborhood and that the value zero appears most frequently in intensity differences between adjacent pixels the statistical model of the distribution of pixel difference can be established using the laplace distribution lsb matching steganography randomly increases or decreases the pixel value by 1 when the message is embedded thus the frequency of occurrence of the value zero in pixel differences changes most dramatically during message embedding based on the laplacian model of pixel difference distributions this paper proposes a method to estimate the number of the zero difference value using the number of non zero difference values from stego images and uses the relative estimation error between the estimated and actual values of the number of the zero difference value as the classification feature experimental results indicate that the proposed algorithm is effective in detecting lsb matching steganography and can achieve better detection performance than the local extreme method under most circumstances

up to lowest 100 frequencies of rectangular plates using jacobi polynomials and tsndt abstract this paper finds up to lowest 100 free vibration frequencies of isotropic and linearly elastic plates with thickness to side length ratio varying from 0 001 to 0 5 by using the ritz method a third order shear and normal deformable plate theory tsndt and weighted jacobi polynomials as admissible functions that are mutually orthogonal and exactly satisfy essential boundary conditions the numerical method is stable even for 18th degree polynomials as basis functions it is shown that this approach requires fewer degrees of freedom than those in the traditional finite element method fem to find converged lowest 100 frequencies and the corresponding mode shapes no shear correction factor is employed in the tsndt the presently computed results agree well with those from either analytical or numerical solutions of the corresponding 3 dimensional linearly elastic problems obtained with the commercial fe software abaqus furthermore results for plates made of an incompressible material can be computed by setting poisson s ratio 0 49

steganography of capacity required using modulo operator for embedding secret image in this paper a novel mechanism using modulus operations to incorporate secret data with image form into a host image is proposed the used modulus is a threshold value that indicates how many bits of the secret image are being incorporated into the host image in our scheme there are two kinds of secret images processed the capacities of these two types are half the size and a quarter the size of the chosen host image respectively as can be seen in the result of our experiment not only can the secret images be totally embedded but the extra information such as the auxiliary table assisting the secret extraction is released as well even then there is still space remaining after the hiding procedure is completed the result is a higher capacity exploration for embedding the secret into a host image upon inspection of the quality of the stego image using the measurement of psnr it is noted that not only does the image display make the grade of the human vision system i e it is imperceptible by human eyes as far as the embedded secret is concerned but also the valued results of psnr remain sufficiently stable for a variety of host image selections therefore our proposal scheme is notably superior to those in the previous literature iee proc vision image signal process 147 1 2000 29 the advantages of this proposed scheme are the higher capacity exploration on secret embedding and better stability on stego image displays