the c 3 theorem and a d 2 algorithm for large scale stochastic mixed integer programming set convexification this paper considers the two stage stochastic integer programming problem with an emphasis on instances in which integer variables appear in the second stage drawing heavily on the theory of disjunctive programming we characterize convexifications of the second stage problem and develop a decomposition based algorithm for the solution of such problems in particular we verify that problems with fixed recourse are characterized by scenario dependent second stage convexifications that have a great deal in common we refer to this characterization as the c3 common cut coefficients theorem based on the c3 theorem we develop a decomposition algorithm which we refer to as disjunctive decomposition d2 in this new class of algorithms we work with master and subproblems that result from convexifications of two coupled disjunctive programs we show that when the second stage consists of 0 1 milp problems we can obtain accurate second stage objective function estimates after finitely many steps this result implies the convergence of the d2 algorithm

a finite branch and bound algorithm for two stage stochastic integer programs this paper addresses a general class of two stage stochastic programs with integer recourse and discrete distributions we exploit the structure of the value function of the second stage integer problem to develop a novel global optimization algorithm the proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination computational experiments on standard test problems indicate superior performance of the proposed algorithm in comparison to those in the existing literature

texture segmentation using voronoi polygons textures are defined in terms of primitives called tokens a texture segmentation algorithm based on the voronoi tessellation is discussed the algorithm first builds the voronoi tessellation of the tokens that make up the textured image it then computes a feature vector for each voronoi polygon these feature vectors are used in a probabilistic relaxation labeling on the tokens to identify the interior and the border regions of the textures some experimental results are shown

probabilistic analysis of a generalized bin packing problem and applications we give a unified probabilistic analysis for a general class of bin packing problems by directly analyzing corresponding mathematical programs in this general class of packing problems objects are described by a given number of attribute values some attributes may be discrete others may be continuous bins are sets of objects and the collection of feasible bins is merely required to satisfy some general consistency properties we characterize the asymptotic optimal value as the value of an easily specified linear program whose size is independent of the number of objects to be packed or as the limit of a sequence of such linear program values we also provide bounds for the rate of convergence of the average cost to its asymptotic value the analysis suggests an a s asymptotically optimal heuristic that runs in linear time the heuristics can be designed to be asymptotically optimal while still running in polynomial time we also show that in several important cases the algorithm has both po

vibration analysis of non circular curved panels by the differential quadrature method free vibration characteristics of cantilever non circular curved panels are analyzed by using the differential quadrature method dqm in this paper the equations of motion of a curved panel are based on the love s hypothesis and are expressed in an orthogonal curvilinear co ordinate system by applying the differential quadrature formulation and the proposed modified relationships for specified boundary conditions the free vibration equations of motion of the curved panel are transformed to a set of algebraic equations natural frequencies of a cantilever flat plate and a circular curved panel are obtained for verifying the applicability of the present approach good convergent trend and accuracy are observed effects of shallowness thickness and aspect ratios on the natural frequencies of a cantilever curved panel are also investigated furthermore natural frequencies of parabolic curved panels are obtained in all cases studied the efficiency and convenience of the dqm are illustrated

stability and accuracy of differential quadrature method in solving dynamic problems in this paper the differential quadrature method is used to solve dynamic problems governed by second order ordinary differential equations in time the legendre radau chebyshev chebyshev gauss lobatto and uniformly spaced sampling grid points are considered besides two approaches using the conventional and modified differential quadrature rules to impose the initial conditions are also investigated the stability and accuracy properties are studied by evaluating the spectral radii and truncation errors of the resultant numerical amplification matrices it is found that higher order accurate solutions can be obtained at the end of a time step if the gauss and radau sampling grid points are used however the conventional approach to impose the initial conditions in general only gives conditionally stable time step integration algorithms unconditionally stable algorithms can be obtained if the modified differential quadrature rule is used unfortunately the commonly used chebyshev gauss lobatto sampling grid points would not generate unconditionally stable algorithms

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution in this paper free vibration of beams annular plates and rectangular plates with free boundaries are analyzed by using the discrete singular convolution dsc a novel method to apply the free boundary conditions is proposed detailed derivations are given to validate the proposed method eight examples including the free vibrations of beams annular plates and rectangular plates with free boundaries are analyzed two kernels the regularized shannon s kernel and the non regularized lagrange s delta sequence kernel are tested dsc results are compared with either analytical solutions or and differential quadrature dq data it is demonstrated that the proposed method to incorporate the free boundary conditions is simple to use and can yield accurate frequency data for beams with a free end and plates with free edges thus the proposed method for applying the boundary conditions extends the application range of the dsc

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

nonlinear free transverse vibrations of in plane moving plates without and with internal resonances in this paper nonlinear free transverse vibrations of in plane moving plates subjected to plane stresses are investigated the hamilton principle is applied to derive the governing equation and the associated boundary conditions the method of multiple scales is employed to analyze the nonlinear partial differential equation the solvability conditions are established in the cases without internal resonance and with 3 1 or 1 1 internal resonances some numerical examples are presented to demonstrate the effects of in plane moving speeds on the frequencies the nonlinear frequencies of the in plane moving plate without internal resonances are numerically calculated the relationship between the nonlinear frequencies and the initial amplitudes is showed at different in plane moving speeds and the nonlinear coefficients respectively it is feasible to investigate resonances without the modes not involved in the resonances the effects of the related parameters are demonstrated for the case of 3 1 and 1 1 internal resonances respectively the differential quadrature scheme is developed to solve numerically the governing equation and confirm results via the method of multiple scales

on solving discrete two stage stochastic programs having mixed integer first and second stage variables in this paper we propose a decomposition based branch and bound dbab algorithm for solving two stage stochastic programs having mixed integer first and second stage variables a modified benders decomposition method is developed where the benders subproblems define lower bounding second stage value functions of the first stage variables that are derived by constructing a certain partial convex hull representation of the two stage solution space this partial convex hull is sequentially generated using a convexification scheme such as the reformulation linearization technique rlt or lift and project process which yields valid inequalities that are reusable in the subsequent subproblems by updating the values of the first stage variables a branch and bound algorithm is designed based on a hyperrectangular partitioning process using the established property that any resulting lower bounding benders master problem defined over a hyperrectangle yields the same objective value as the original stochastic program over that region if the first stage variable solution is an extreme point of the defining hyperrectangle or the second stage solution satisfies the binary restrictions we prove that this algorithm converges to a global optimal solution some numerical examples and computational results are presented to demonstrate the efficacy of this approach

solution of helmholtz equation by differential quadrature method the polynomial based differential quadrature pdq and the fourier expansion based differential quadrature fdq methods are applied in this work to solve the two dimensional helmholtz equation it is demonstrated through some sample examples that accurate numerical solution can be obtained by using only 2 to 3 mesh points per wavelength it was found that the fdq approach is more suitable for solving the helmholtz equation

feasibility of integer knapsacks given a matrix a in mathbb z m times n satisfying certain regularity assumptions we consider the set mathcal f a of all vectors boldsymbol b in mathbb z m such that the associated knapsack polytope p a boldsymbol b boldsymbol x in mathbb r n geq0 a boldsymbol x boldsymbol b contains an integer point when m 1 the set mathcal f a is known to contain all consecutive integers greater than the frobenius number associated with a in this paper we introduce the diagonal frobenius number mathrm g a which reflects in an analogous way feasibility properties of the problem and the structure of mathcal f a in the general case we give an optimal upper bound for mathrm g a and also estimate the asymptotic growth of the diagonal frobenius number on average

l shaped decomposition of two stage stochastic programs with integer recourse we consider two stage stochastic programming problems with integer recourse the l shaped method of stochastic linear programming is generalized to these problems by using generalized benders decomposition nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques finite convergence of the method is established when gomory s fractional cutting plane algorithm or a branch and bound algorithm is applied

logic based benders decomposition benders decomposition uses a strategy of learning from one s mistakes the aim of this paper is to extend this strategy to a much larger class of problems the key is to generalize the linear programming dual used in the classical method to an inference dual solution of the inference dual takes the form of a logical deduction that yields benders cuts the dual is therefore very different from other generalized duals that have been proposed the approach is illustrated by working out the details for propositional satisfiability and 0 1 programming problems computational tests are carried out for the latter but the most promising contribution of logic based benders may be to provide a framework for combining optimization and constraint programming methods

improved bi dimensional emd and hilbert spectrum for the analysis of textures an improved bi dimensional empirical mode decomposition ibemd is proposed structure of image extremas represents the important feature of images and is useful for the information extraction and analysis the image extrema are classified into the five different sets which are called as the structural extrema the structural extrema are used instead of the classical extrema and the bemd bi dimensional empirical mode decomposition algorithms based on the structural extrema are more accurate through interpolating the up and down envelopes specially the ibemd has the least nmse normalised mean square error and the biggest snr signal to noise ratio for the mode decomposition and greatly improves the robustness of the bemd moreover quaternion hilbert transform based space spatial frequency tool is improved and applied to the texture analysis the experiments of texture analysis show that the new approach is efficient for the application in texture analysis

differential quadrature for static and free vibration analyses of anisotropic plates abstract the differential quadrature method is used to analyse the deflection buckling and free vibration behavior of anisotropic rectangular plates under various boundary conditions the roots of chebyshev polynomials are used to obtain grid point locations and a new approach is used to apply boundary conditions results compare very well with existing numerical data and less computational effort is required for the problems considered

application of differential quadrature to transport processes the methodology and numerical solution of problems concerning transport processes via the method of differential quadrature are presented application of the method is demonstrated by solving a simple one dimensional time dependent transient diffusion process involving an irreversible reaction without any flux across the end boundary in addition the same technique is used for the first time to the authors knowledge to solve a steady state problem for this purpose a convection diffusion problem involving an irreversible reaction is considered the demonstration is carried out in two ways 1 using the bellman et al technique which employs approximation formulas for higher order partial derivatives derived by iterating the linear quadrature approximation for the first order partial derivative and 2 using individual quadratures to approximate the partial derivatives of first as well as higher orders as suggested by mingle both approaches give the same results however the latter saves an appreciable amount of iterative computing effort despite the fact that it requires separate weighting coefficients for each individual quadrature since the technique of differential quadrature can produce solutions with sufficient accuracy even when using as few as three discrete points both the programming task and computational effort are alleviated considerably for these reasons the differential quadrature approach appears to be very practical in solving a variety of problems related to transport phenomena

an efficient mixed methodology for free vibration and buckling analysis of orthotropic rectangular plates abstract in this paper a simple and efficient mixed ritz differential quadrature dq method is presented for free vibration and buckling analysis of orthotropic rectangular plates the mixed scheme combines the simplicity of the ritz method and high accuracy and efficiency of the dq method the accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature it is shown that highly accurate results can be obtained using a small number of ritz terms and dq sample points the proposed method is suitable for the problem considered due to its simplicity and potential for further development

high accuracy mixed finite element ritz formulation for free vibration analysis of plates with general boundary conditions abstract a high order accurate mixed finite element ritz method is introduced and developed to study the vibration problem of plates with general boundary conditions the finite element method fem with higher order interpolation functions is first used to discretize the spatial partial derivatives with respect to a co ordinate direction of the plate the ritz method is then employed to analogize the resulting system of ordinary differential equations a novel technique is also presented to exactly satisfy the mixed natural boundary conditions the proposed method is applied here to solve some benchmark vibration problems of plates including isotropic and anisotropic rectangular plates variable thickness rectangular plates multi span rectangular plates and skew plates comparisons with existing numerical and analytical solutions show that the proposed mixed method can yield highly accurate results for vibration problem of plates involving free edges free corners and irregular boundaries using a small number of finite elements and ritz terms

a geometric buchberger algorithm for integer programming let ip a c denote the family of integer programs of the form min cx ax b x nn obtained by varying the right hand side vector b but keeping a and c fixed a test set for ipa c is a set of vectors in zn such that for each nonoptimal solution to a program in this family there is at least one element g in this set such that g has an improved cost value as compared to we describe a unique minimal test set for this family called the reduced grobner basis of ip a c an algorithm for its construction is presented which we call a geometric buchberger algorithm for integer programming and we show how an integer program may be solved using this test set the reduced grobner basis is then compared with some other known test sets from the literature we also indicate an easy procedure to construct test sets with respect to all cost functions for a matrix a zn 2 n of full row rank

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

combination and principal parametric resonances of axially accelerating viscoelastic beams recognition of longitudinally varying tensions abstracts nonlinear parametric vibration is investigated for axially accelerating viscoelastic beams subject to parametric excitations resulting from longitudinally varying tensions and axial speed fluctuations the effects of the longitudinally varying tension due to the axial acceleration are highlighted while the tension was assumed to be longitudinally uniform in previous studies the dependence of the tension on the finite axial support rigidity is also modeled the governing equations of coupled planar vibration and the associated boundary conditions are derived from the generalized hamilton principle and the viscoelastic constitutive relation the equation is simplified into a governing equation of transverse nonlinear vibration in small but finite stretching problems the governing equation of transverse vibration is a nonlinear integro partial differential equation with time dependent and space dependent coefficients the method of multiple scales is employed to analyze the combination and the principal parametric resonances with the focus on steady state responses in the difference resonance there is only trivial zero response which is always stable in the summation and the principal resonances the trivial responses may become unstable and bifurcate into nontrivial responses for certain excitation frequencies some numerical examples indicate that the longitudinal tension variation makes the instability frequency intervals of trivial responses small and the nontrivial response amplitudes large small in the summation principal resonance it is also found that the nontrivial responses are not sensitive to the axial support rigidity numerical solutions are calculated via the differential quadrature to support results via the method of multiple scales

on the solution of the thomas fermi equation by differential quadrature on utilise la methode de quadrature differentielle pour resoudre l equation de thomas fermi

out of plane static analysis of circular arches by dqm the differential quadrature dq methodology introduced by the authors see comput methods appl mech engng 191 2002a 3509 int j solids struct 39 19 2002b 4927 int j numer methods engng 54 3 2003a 847 j sound vibrat 263 2 2003b 415 is employed for out of plane static analysis of circular arches under a wide spectrum of boundary conditions in addition to the classical boundary conditions elastic restraints against translation and rotation are also considered different loading conditions are examined several examples of arches with uniform continuous or stepped varying cross sections are presented to demonstrate the accuracy of the methodology the domain decomposition technique in conjunction with the present dq methodology is examined for certain cases the results are compared with those of exact solutions for several uniform or stepped sections arches and also for arches on elastic foundations accurate converged numerical solutions are obtained with only few grid points

an efficient differential quadrature methodology for free vibration analysis of arbitrary straight sided quadrilateral thin plates in this paper a new differential quadrature dq methodology is employed to study free vibration of irregular quadrilateral straight sided thin plates a four nodded super element is used to map the irregular physical domain into a square domain in the computational domain second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains the only degree of freedom within the domain is the displacement whereas along the boundaries the displacement as well as the second order derivative of the displacement with respect to associated normal co ordinate variable in computational domain are the two degrees of freedom implementing the method the formulation for the dq method for the free vibration analysis of plates of straight sided shapes was presented together with the implementation procedure for the different boundary conditions to demonstrate the accuracy convergency and stability of the new methodology detail studies are made on isotropic plates at acute angles with different geometries boundary and loading conditions including dq free edge boundary condition implementations accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved

differential quadrature element method for static analysis of reissner mindlin polar plates abstract in this paper a new numerical technique the differential quadrature element method dqem has been developed for static analysis of the two dimensional polar reissner mindlin plate in the polar coordinate system by integrating the domain decomposition method ddm with the differential quadrature method dqm the detailed formulations for the sectorial dqem plate bending element and the compatibility conditions between each element are presented the convergence properties and the accuracy of the dqem for bending of thick polar plates are investigated through a number of numerical computations consequently the dqem has been successfully applied to analyze several annular sector plates with discontinuous loading and boundary conditions and cutouts to illustrate the simplicity and flexibility of this method for solving reissner mindlin plates in polar coordinate system which are not solvable directly using the differential quadrature method the numerical results are verified by the existing exact solutions or the fem solutions obtained using the software package ansys version 5 3

application of a new differential quadrature methodology for free vibration analysis of plates a new methodology is introduced in the differential quadrature dq analysis of plate problems the proposed approach is distinct from other dq methods by employing the multiple boundary conditions in a different manner for structural and plate problems the methodology employs the displacement within the domain as the only degree of freedom whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently in order to demonstrate the capability of the new methodology all cases of free vibration analysis of rectangular isotropic plates in which the conventional dq methods have had some sort of difficulty to arrive at a converged or accurate solution are carried out excellent convergence behaviour and accuracy in comparison with exact results and or results obtained by other approximate methods were obtained the analogous dq formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised it must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods copyright 2002 john wiley sons ltd

vibration analysis of edge cracked beam on elastic foundation with axial loading using the differential quadrature method abstract the eigenvalue problems of clamped free and hinged hinged bernoulli euler beams on elastic foundation with a single edge crack axial loading and excitation force were numerically formulated using the differential quadrature method dqm appropriate boundary conditions accompanied the dqm to transform the partial differential equation of a bernoulli euler beam with a single edge crack into a discrete eigenvalue problem the dqm results for the natural frequencies of cracked beams agree well with other literature values the sampling point number effect the location of the crack effect and the depth of the crack effect on the accuracy variation of calculated natural frequencies are presented by using two elements in this work the effects of axial loading foundation stiffness opening crack and closing crack are also studied

asymptotic stability analysis with numerical confirmation of an axially accelerating beam constituted by the standard linear solid model stability of an axially accelerating viscoelastic beam constituted by the standard linear solid model is investigated the material time derivative is used in the viscoelastic constitutive relation the instability condition is determined for combination and principal parametric resonances via the asymptotic analysis the differential quadrature scheme is developed to solve numerically the partial differential equation governing transverse motion of axially accelerating viscoelastic beams the stability boundaries are numerically located in the excitation amplitude and the excitation frequency plane numerical simulation demonstrates the effects of the stiffness the viscosity and constant mean speed of beam the numerical calculations validate the analytical results in the principal parametric resonance

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

the generalized differential quadrature rule for initial value differential equations abstract the generalized differential quadrature rule gdqr proposed recently by the authors is applied here to solve initial value differential equations of the 2nd to 4th order differential quadrature expressions are derived based on the gdqr for these equations the hermite interpolation functions are used as trial functions to obtain the explicit weighting coefficients for an easy and efficient implementation of the gdqr the numerical solutions for example problems demonstrate that the gdqr has high efficiency and accuracy a detailed discussion on the present method is presented by comparing with other existing methods the present method can be extended to other types of differential equation systems

accurate free vibration analysis of the completely free orthotropic rectangular plate by the method of superposition abstract the method of superposition is exploited to obtain highly accurate analytical type solutions for the free vibration of completely free orthotropic rectangular plates eigenvalues for 12 modes are provided for a particular set of problems representative of reinforced concrete and similar materials for a wide range of plate aspect ratios while it is recognized that data covering the entire range of possible problems cannot be tabulated it is hoped that the data provided will prove useful to some designers and provide a reference for other researchers to compare their results this appears to be the first study devoted to this problem to appear in the literature

hypercomplex signals a novel extension of the analytic signal to the multidimensional case the construction of gabor s 1946 complex signal which is also known as the analytic signal provides direct access to a real one dimensional 1 d signal s local amplitude and phase the complex signal is built from a real signal by adding its hilbert transform which is a phase shifted version of the signal as an imaginary part to the signal since its introduction the complex signal has become an important tool in signal processing with applications for example in narrowband communication different approaches to an n d analytic or complex signal have been proposed in the past we review these approaches and propose the hypercomplex signal as a novel extension of the complex signal to n d this extension leads to a new definition of local phase which reveals information on the intrinsic dimensionality of the signal the different approaches are unified by expressing all of them as combinations of the signal and its partial and total hilbert transforms examples that clarify how the approaches differ in their definitions of local phase and amplitude are shown an example is provided for the two dimensional 2 d hypercomplex signal which shows how the novel phase concept can be used in texture segmentation

the value function of an integer program we consider integer programs in which the objective function and constraint matrix are fixed while the right hand side varies the value function gives for each feasible right hand side the criterion value of the optimal solution we provide a precise characterization of the closed form expression for any value function

numerical study of grid distribution effect on accuracy of dq analysis of beams and plates by error estimation of derivative approximation the accuracy of global methods such as the differential quadrature dq approach is usually sensitive to the grid point distribution this paper is to numerically study the effect of grid point distribution on the accuracy of dq solution for beams and plates it was found that the stretching of grid towards the boundary can improve the accuracy of dq solution especially for coarse meshes the optimal grid point distribution corresponding to optimal stretching parameter depends on the order of derivatives in the boundary condition and the number of grid points used the optimal grid distribution may not be from the roots of orthogonal polynomials this differs somewhat from the conventional analysis this paper also proposes a simple and effective formulation for stretching the grid towards the boundary the error distribution of derivative approximation is also studied and used to analyze the effect of grid point distribution on accuracy of numerical solutions copyright 2001 john wiley sons ltd

imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method one of the important issues in the implementation of the differential quadrature method is the imposition of the given boundary conditions there may be multiple boundary conditions involving higher order derivatives at the boundary points the boundary conditions can be imposed by modifying the weighting coefficient matrices directly however the existing method is not robust and is known to have many limitations in this paper a systematic procedure is proposed to construct the modified weighting coefficient matrices to overcome these limitations the given boundary conditions are imposed exactly furthermore it is found that the numerical results depend only on those sampling grid points where the differential quadrature analogous equations of the governing differential equations are established the other sampling grid points with no associated boundary conditions are not essential copyright 2002 john wiley sons ltd

an estimation algorithm for 2 d polynomial phase signals we consider nonhomogeneous 2 d signals that can be represented by a constant modulus polynomial phase model a novel 2 d phase differencing operator is introduced and used to develop a computationally efficient estimation algorithm for the parameters of this model the operation of the algorithm is illustrated using an example

decomposing finitely generated integral monoids by elimination abstract a finitely generated integral monoid can always be decomposed into a finite although generally exponential number of integral monoids having special structure in that their related integer programming feasibility problems can be solved in polynomial time the decomposition can be constructed using an elimination scheme due to presburger and williams that generalizes fourier motzkin elimination

numerical experiments on the determination of natural frequencies of transverse vibrations of rectangular plates of non uniform thickness abstract a comparison of natural frequencies of transverse vibration of thin rectangular plates of non uniform thickness with different combinations of boundary conditions is presented in this paper as obtained by using the following methodologies 1 the rayleigh ritz method with characteristic orthogonal polynomial shape functions 2 the rayleigh ritz method with a shape function which includes two exponents that are to be determined by minimizing the fundamental frequency coefficient 3 the optimized kantorovich method which has been proposed rather recently 4 the finite element method the results are presented in tabular form and discussed

parameter estimation of 2 d random amplitude polynomial phase signals phase information has fundamental importance in many two dimensional 2 d signal processing problems in this paper we consider 2 d signals with random amplitude and a continuous deterministic phase the signal is represented by a random amplitude polynomial phase model a computationally efficient estimation algorithm for the signal parameters is presented the algorithm is based on the properties of the mean phase differencing operator which is introduced and analyzed assuming that the signal is observed in additive white gaussian noise and that the amplitude field is gaussian as well we derive the cramer rao lower bound crb on the error variance in jointly estimating the model parameters the performance of the algorithm in the presence of additive white gaussian noise is illustrated by numerical examples and compared with the crb

application of differential quadrature to static analysis of structural components the numerical technique of differential quadrature for the solution of linear and non linear partial differential equations first introduced by bellman and his associates is applied to the equations governing the deflection and buckling behaviour of one and two dimensional structural components separate transformations are used for higher order derivatives as suggested by mingle thus extending the method to treat fourth order equations and to include multiple boundary conditions in the respective co ordinate directions results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods the application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort

the generalized differential quadrature rule for fourth order differential equations the generalized differential quadrature rule gdqr proposed here is aimed at solving high order differential equations the improved approach is completely exempted from the use of the existing point technique by applying multiple conditions in a rigorous manner the gdqr is used here to static and dynamic analyses of bernoulli euler beams and classical rectangular plates numerical error analysis caused by the method itself is carried out in the beam analysis independent variables for the plate are first defined the explicit weighting coefficients are derived for a fourth order differential equation with two conditions at two different points it is quite evident that the gdqr expressions and weighting coefficients for two dimensional problems are not a direct application of those for one dimensional problems the gdqr are implemented through a number of examples good results are obtained in this work copyright 2001 john wiley sons ltd

texture segmentation using fractal dimension this paper deals with the problem of recognizing and segmenting textures in images for this purpose the authors employ a technique based on the fractal dimension fd and the multi fractal concept six fd features are based on the original image the above average high gray level image the below average low gray level image the horizontally smoothed image the vertically smoothed image and the multi fractal dimension of order two a modified box counting approach is proposed to estimate the fd in combination with feature smoothing in order to reduce spurious regions to segment a scene into the desired number of classes an unsupervised k means like clustering approach is used mosaics of various natural textures from the brodatz album as well as microphotographs of thin sections of natural rocks are considered and the segmentation results to show the efficiency of the technique supervised techniques such as minimum distance and k nearest neighbor classification are also considered the results are compared with other techniques

high accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain summary based on the differential quadrature dq rule the gauss lobatto quadrature rule and the variational principle a dq finite element method dqfem is proposed for the free vibration analysis of thin plates the dqfem is a highly accurate and rapidly converging approach and is distinct from the differential quadrature element method dqem and the quadrature element method qem by employing the function values themselves in the trial function for the title problem the dqfem without using shape functions essentially combines the high accuracy of the differential quadrature method dqm with the generality of the standard finite element formulation and has superior accuracy to the standard fem and fdm and superior efficiency to the p version fem and qem in calculating the stiffness and mass matrices by incorporating the reformulated dq rules for general curvilinear quadrilaterals domains into the dqfem a curvilinear quadrilateral dq finite plate element is also proposed the inter element compatibility conditions as well as multiple boundary conditions can be implemented simply and conveniently as in fem through modifying the nodal parameters when required at boundary grid points using the dq rules thus the dqfem is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter element compatibilities a series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the dqfem copyright q 2009 john wiley sons ltd

on analysis of bi dimensional component decomposition via bemd this paper investigates how the bi dimensional empirical mode decomposition bemd behaves in digital images via two components first some definitions of components are given then the theoretical analysis is presented to show that in digital images there might be sparse extrema sets and the sifting process of bemd converges to the true component provided that the sparse extrema sets do exist also the feature of 2d component in digital images is explored via composite two component signals the three dimensional cubes disclosing the performance of bemd are presented which turn out to be in good agreement with intuition and physical interpretation this paper has also shown that the sampling period the cross angle the amplitude ratio and the frequency ratio between the components will affect the separation of them and some instructive conclusions are achieved as well the theoretical analysis is provided for analyzing the observed behaviors and supported by numerical experiments the main aim of this study is primarily to contribute to a better understanding of the possibilities and limitations offered by bemd in digital images

segmentation of textured images using a multiresolution gaussian autoregressive model we present a new algorithm for segmentation of textured images using a multiresolution bayesian approach the new algorithm uses a multiresolution gaussian autoregressive mgar model for the pyramid representation of the observed image and assumes a multiscale markov random field model for the class label pyramid the models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid the criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice the estimate which satisfies this criterion is referred to as the multiresolution maximization of the posterior marginals mmpm estimate and is a natural extension of the single resolution maximization of the posterior marginals mpm estimate previous multiresolution segmentation techniques have been based on the maximum a posterior map estimation criterion which has been shown to be less appropriate for segmentation than the mpm criterion it is assumed that the number of distinct textures in the observed image is known the parameters of the mgar model the means prediction coefficients and prediction error variances of the different textures are unknown a modified version of the expectation maximization em algorithm is used to estimate these parameters the parameters of the gibbs distribution for the label pyramid are assumed to be known experimental results demonstrating the performance of the algorithm are presented

integer programming duality price functions and sensitivity analysis recently a duality theory for integer programming has been developed here we examine some of the economic implications of this theory in particular the necessity of using price functions in place of prices and the possibility of carrying out sensitivity analysis of optimal solutions in addition we consider the form of price functions that are generated by known algorithms for integer programming

a theoretical analysis of piezoelectric composite laminate with larger amplitude deflection effect part ii hermite differential quadrature method and application incorporating the effects of larger amplitude deflection and electro elastical properties of piezoelectric lamina the hamilton s variation principle was used to deduce the fundamental formulations of smart anisotropic composite plate in part i in terms of reddy s simple higher order theory in order to solve the five highly coupled nonlinear partial differential equations with complicated overlapping boundary conditions a novel numerical method hermite differential quadrature hdq method was developed to implement the differential equations with complicated overlapping boundary conditions based on the presently developed hdq method any orders derivatives of the unknown functions or any boundary conditions can be point collocation based discretized by a set of point values along x and y direction then a system of complete algebraic nonlinear equations can be constructed to calculate out the final point values of the mid plane displacements by using the governing equations and relative boundary conditions with hdq method finally some detailed numerical examples for the anisotropic piezoelectric composite laminate with the distributed poling directions of piezoelectric layer and fiber orientations of composite layers were studied to validate the developed theoretical analysis model and hdq numerical method

direct expansion method of boundary condition for solving 3d elliptic equations with small parameters in the irregular domain in this article a new methodology direct expansion method of boundary condition dembc is developed to solve 3d elliptic equations in the irregular domain first the previous rational differential quadrature method rational spectral collocation method in berrut et al 2005 8 developed by berrut et al 2005 8 has been generalized to solve 3d elliptic equations second it is showed that direct expansion method of boundary condition is capable of handling boundary problems with higher efficiency finally with the help of conformal mapping tee and trefethen 2006 9 and domain decomposition method dembc and 3d rdqm are able solve three kinds of 3d elliptic equations with small parameters in the irregular domain numerous test results justify the accuracy and efficiency of our approach