exact algorithms for l 1 tv regularization of real valued or circle valued signals we consider l 1 tv regularization of univariate signals with values on the real line or on the unit circle while the real data space leads to a convex optimization problem the problem is nonconvex for circle valued data in this paper we derive exact algorithms for both data spaces a key ingredient is the reduction of the infinite search spaces to a finite set of configurations which can be scanned by the viterbi algorithm to reduce the computational complexity of the involved tabulations we extend the technique of distance transforms to nonuniform grids and to the circular data space in total the proposed algorithms have complexity mathcal o kn where n is the length of the signal and k is the number of different values in the data set in particular the complexity is mathcal o n for quantized data it is the first exact algorithm for total variation regularization with circle valued data and it is competitive with the state of the art methods for scalar data assuming that the

vibrations of axially moving viscoelastic plate with parabolically varying thickness based on the two dimensional viscoelastic differential constitutive relation the differential equation of motion of the axially moving viscoelastic rectangular plate constituted by the kelvin voigt model with parabolically varying thickness in the y direction is derived the dimensionless complex frequencies of axially moving viscoelastic plate with different boundary conditions versus the dimensionless moving speed for various aspect ratio thickness parameter and the dimensionless delay time are analyzed by the differential quadrature method the effects of various parameters such as aspect ratio thickness parameter the dimensionless moving speed and the dimensionless delay time on the vibration characteristics of the axially moving viscoelastic rectangular plate with parabolically varying thickness are discussed

modeling via differential quadrature method three dimensional solutions for rectangular plates this paper presents the formulation and numerical analysis of the three dimensional plate model using the differential quadrature dq method the equilibrium equations stress displacement relations and boundary conditions for the three dimensional plate model are first presented these equations are then normalised and discretised using the dq procedure example problems for rectangular plates with generic boundary conditions are selected to illustrate the computational efficiency and applicability of the dq procedure the convergence characteristics of the method are first conducted based on numerical studies the solutions are then compared where possible with the analytical or exact solutions it is found that the differential quadrature method yields accurate results for the plate problems under the current investigation

a differential quadrature procedure for three dimensional buckling analysis of rectangular plates abstract this paper presents an application of the differential quadrature dq method for three dimensional buckling analysis of rectangular plates the governing equations of the plate model are first presented in terms of displacement stress displacement relationship and boundary conditions with three dimensional flexibility these equations are then normalised and discretised using the dq procedure example problems pertaining to the buckling of rectangular plates with generic boundary conditions are selected to illustrate the efficiency and simplicity of implementing the dq procedure the convergence characteristics of the method are first conducted based on numerical studies the dq solutions are then compared where possible with exact or approximate solutions it is found that the differential quadrature method yields accurate results for the plate problems under the current investigation in addition to the above some parametric studies are carried out by varying the plates aspect ratio boundary conditions and thickness to width ratio under axial and biaxial loading

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

sobolev active contours all previous geometric active contour models that have been formulated as gradient flows of various energies use the same l 2 type inner product to define the notion of gradient recent work has shown that this inner product induces a pathological riemannian metric on the space of smooth curves however there are also undesirable features associated with the gradient flows that this inner product induces in this paper we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with sobolev type inner products we call the resulting flows sobolev active contours sobolev metrics induce favorable regularity properties in their gradient flows in addition sobolev active contours favor global translations but are not restricted to such motions they are also less susceptible to certain types of local minima in contrast to traditional active contours these properties are particularly useful in tracking applications we demonstrate the general methodology by reformulating some standard edge based and region based active contour models as sobolev active contours and show the substantial improvements gained in segmentation

three dimensional free vibrations of thick skewed cantilevered plates abstract the natural frequencies of skewed cantilevered thick plates are determined by using the ritz method the present work is the first known three dimensional study of the problem assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete accurate natural frequencies are calculated for skewed thick plates having arbitrary degrees of skewness detailed numerical studies reveal interesting trends concerning the variation of frequencies with increasing skew angle results obtained by using the present method are compared with those obtained by using three dimensional finite elements

a variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness a new variable kinematic ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented carrera s unified formulation and the versatile pb 2 ritz method are properly combined to build a powerful yet simple modeling and solution framework the proposed technique allows to generate arbitrarily accurate ritz solutions from a large variety of refined two dimensional plate theories by expanding so called ritz fundamental nuclei of the plate mass and stiffness matrices theoretical development of the present methodology is described in detail convergence and accuracy of the method are examined through several examples on thin moderately thick and very thick plates of rectangular skew trapezoidal and general quadrilateral shapes with an arbitrary combination of clamped free and simply supported edges present results are compared with existing three dimensional solutions from open literature maximum and average differences of various higher order plate theories and three dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters

robust solutions of linear programming problems contaminated with uncertain data optimal solutions of linear programming problems may become severely infeasible if the nominal data is slightly perturbed we demonstrate this phenomenon by studying 90 lps from the well known netlib collection we then apply the robust optimization methodology ben tal and nemirovski 1 3 el ghaoui et al 5 6 to produce robust solutions of the above lps which are in a sense immuned against uncertainty surprisingly for the netlib problems these robust solutions nearly lose nothing in optimality

geodesic regression and the theory of least squares on riemannian manifolds this paper develops the theory of geodesic regression and least squares estimation on riemannian manifolds geodesic regression is a method for finding the relationship between a real valued independent variable and a manifold valued dependent random variable where this relationship is modeled as a geodesic curve on the manifold least squares estimation is formulated intrinsically as a minimization of the sum of squared geodesic distances of the data to the estimated model geodesic regression is a direct generalization of linear regression to the manifold setting and it provides a simple parameterization of the estimated relationship as an initial point and velocity analogous to the intercept and slope a nonparametric permutation test for determining the significance of the trend is also given for the case of symmetric spaces two main theoretical results are established first conditions for existence and uniqueness of the least squares problem are provided second a maximum likelihood criteria is developed for a suitable definition of gaussian errors on the manifold while the method can be generally applied to data on any manifold specific examples are given for a set of synthetically generated rotation data and an application to analyzing shape changes in the corpus callosum due to age

an eight node curvilinear differential quadrature formulation for reissner mindlin plates a first endeavour to exploit the differential quadrature dq method as a simple accurate and efficient numerical technique for the bending of quadrilateral reissner mindlin plates with curvilinear boundaries is made the curvilinear quadrilateral is mapped onto a square domain by using the geometric coordinate transformation this geometric mapping technique is employed to transform the governing differential equations and boundary conditions of the problem from the physical domain onto the computational domain the dq procedures are then applied to discretise the transformed set of differential equations and boundary conditions into a set of linear algebraic equations the numerical solutions to the problem are obtained by solving this set of linear algebraic equations examples illustrating the accuracy and convergence of the dq method for reissner mindlin plates with curvilinear boundaries are presented the great development potential of the dq method as an alternative to other approximate techniques for solving problems related to engineering sciences and structural mechanics is exploited in the present study

a continuum mechanical approach to geodesics in shape space in this paper concepts from continuum mechanics are used to define geodesic paths in the space of shapes where shapes are implicitly described as boundary contours of objects the proposed shape metric is derived from a continuum mechanical notion of viscous dissipation a geodesic path is defined as the family of shapes such that the total amount of viscous dissipation caused by an optimal material transport along the path is minimized the approach can easily be generalized to shapes given as segment contours of multi labeled images and to geodesic paths between partially occluded objects the proposed computational framework for finding such a minimizer is based on the time discretization of a geodesic path as a sequence of pairwise matching problems which is strictly invariant with respect to rigid body motions and ensures a 1 1 correspondence along the induced flow in shape space when decreasing the time step size the proposed model leads to the minimization of the actual geodesic length where the hessian of the pairwise matching energy reflects the chosen riemannian metric on the underlying shape space if the constraint of pairwise shape correspondence is replaced by the volume of the shape mismatch as a penalty functional one obtains for decreasing time step size an optical flow term controlling the transport of the shape by the underlying motion field the method is implemented via a level set representation of shapes and a finite element approximation is employed as spatial discretization both for the pairwise matching deformations and for the level set representations the numerical relaxation of the energy is performed via an efficient multi scale procedure in space and time various examples for 2d and 3d shapes underline the effectiveness and robustness of the proposed approach

shape analysis of elastic curves in euclidean spaces this paper introduces a square root velocity srv representation for analyzing shapes of curves in euclidean spaces under an elastic metric in this srv representation the elastic metric simplifies to the il2 metric the reparameterization group acts by isometries and the space of unit length curves becomes the unit sphere the shape space of closed curves is the quotient space of a submanifold of the unit sphere modulo rotation and reparameterization groups and we find geodesics in that space using a path straightening approach these geodesics and geodesic distances provide a framework for optimally matching deforming and comparing shapes these ideas are demonstrated using 1 shape analysis of cylindrical helices for studying protein structure 2 shape analysis of facial curves for recognizing faces 3 a wrapped probability distribution for capturing shapes of planar closed curves and 4 parallel transport of deformations for predicting shapes from novel poses

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

analytical three dimensional elasticity solutions to some plate problems and some observations on mindlin s plate theory abstract solutions are obtained using the exact three dimensional theory of elasticity to i the eigenvalue problem or buckling under biaxial compression or the free lateral vibration of a simply supported rectangular plate with orthotropic stress strain properties and ii the static response of the same plate to a lateral load that varies sinusoidally in two directions the eigenvalue in problem i and the lateral deflections of both the surface and middle plane of the plate as well as the bending strains in problem ii are obtained in the form of series expansions in even powers of the plate thickness exact algebraic expressions are presented for the first two coefficients in the case of orthotropic plates additional coefficients can be obtained if required and are given for the much simpler case of isotropic plates in all cases the first term agrees with classical plate theory the solutions are compared with those obtained from mindlin s plate theory in neither problem is it found to be possible in general to choose values for mindlin s effective shear moduli to make the mindlin solution agree with the first two terms of the exact solution there are however two exceptions to this namely a restricted class of orthotropic materials embracing all isotropic ones in which the elastic constants satisfy a certain condition and the case of cylindrical bending when the mindlin plate reduces to a timoshenko beam of wide rectangular cross section in both these exceptional cases appropriate values for the effective shear moduli are obtained

three dimensional vibration analysis of a cantilevered parallelepiped exact and approximate solutions the paper investigates the hypothetical assumption of neglecting transverse normal stress in vibration analysis for cantilevered thick plates and rectangular parallelepiped the analysis solves the three dimensional elasticity energy functional including as well as excluding transverse normal stress and obtains free vibration solutions for a cantilevered parallelepiped although it is widely accepted the omission of transverse normal stress is well justified in kirchhoff love thin plate theory and higher order thick plate models the transverse normal stress effects and thickness extent to which the thick plate models apply as the thickness increases are practically unknown the inconsistency of assuming constant transverse normal displacement through thickness for thick plate models is also addressed the paper concludes that for a rectangular parallelepiped with thickness exceeding a certain limit there is considerable discrepancy if transverse normal stress is neglected

a study on the linear elastic stability of mindlin plates the debate on the performance of lagrangian and serendipity elements in mindlin s plate theory has been going on for quite some time limited published results for static and vibration analysis based on exact integration demonstrated a drastic deterioration in accuracy as the thickness of the plate decreases and reduced selective integration schemes have been suggested to improve their performance appreciable improvement for lagrangian elements has been recorded but it is only marginal for the serendipity elements on the strength of such observations one would then be tempted to rule out the exact integration schemes and serendipity elements in this paper the above problem is reviewed for stability analysis of plates two elements are chosen from each family one representing the higher order and the other the lower order element contrary to published results all elements can attain very accurate solutions independent of the integration schemes for a sufficiently restrained plate although in general the serendipity elements will require a more refined mesh than the lagrangian ones however for loosely restrained plates the solution failed when integration is performed by reduced selective schemes the failure marks the limitation of the reduced selective schemes which have somehow introduced spurious modes into the system but on the other hand it is ironical that these spurious modes in fact contribute to the improvement of performance of the restrained cases therefore one can equally improve the serendipity elements by a selective scheme which can introduce additional zero modes a scheme based on 5 5 integration points for flexural stiffness and 3 3 integration points for shear stiffness improved the 17se serendipity elements remarkably however because of the lack of bounds in most cases the use of reduced selected schemes is still not recommended finally this paper also proposed an approximate formulation of the geometric stiffness matrices to replace the full formulation such an approximate formulation reduces the number of variables considerably in the eigenvalue search and can still give reasonably accurate results for thin plates with a t 15

comparative accuracy of dq and hdq methods for three dimensional vibration analysis of rectangular plates an accuracy study between the differential quadrature dq and harmonic differential quadrature hdq methods for three dimensional elasticity solutions of free vibration of rectangular plates is carried out the solution capability of the dq and hdq methods is first studied then the numerical performance of both the methods is compared it is found that the dq method displays more superior convergence characteristics over the hdq method for the lower modes of vibration however the hdq method is advantageous over the dq method for computing higher modes of vibration it is also discovered that the dq and hdq methods produce better convergent solutions than the finite element method fem when a similar number of discrete points nodes are used copyright 1999 john wiley sons ltd

coarse to fine segmentation and tracking using sobolev active contours recently proposed sobolev active contours introduced a new paradigm for minimizing energies defined on curves by changing the traditional cost of perturbing a curve and thereby redefining gradients associated to these energies sobolev active contours evolve more globally and are less attracted to certain intermediate local minima than traditional active contours and it is based on a well structured riemannian metric which is important for shape analysis and shape priors in this paper we analyze sobolev active contours using scale space analysis in order to understand their evolution across different scales this analysis shows an extremely important and useful behavior of sobolev contours namely that they move successively from coarse to increasingly finer scale motions in a continuous manner this property illustrates that one justification for using the sobolev technique is for applications where coarse scale deformations are preferred over fine scale deformations along with other properties to be discussed the coarse to fine observation reveals that sobolev active contours are in particular ideally suited for tracking algorithms that use active contours we will also justify our assertion that the sobolev metric should be used over the traditional metric for active contours in tracking problems by experimentally showing how a variety of active contour based tracking methods can be significantly improved merely by evolving the active contour according to the sobolev method

three dimensional vibration analysis of rectangular thick plates on pasternak foundation the free vibration characteristics of rectangular thick plates resting on elastic foundations have been studied based on the three dimensional linear and small strain elasticity theory the foundation is described by the pasternak two parameter model the ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation the chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction the approach is suitable for rectangular plates with arbitrary boundary conditions convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions it is shown that the present method has a rapid convergent rate stable numerical operation and very high accuracy parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail with respect to different thickness span ratios and foundation parameters some results found for the first time have been given and some important conclusions have been drawn

inverse optimization for the recovery of constraint parameters abstract most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set we propose two approaches to impute unspecified left hand side constraint coefficients in addition to a cost vector for a given linear optimization problem the first approach identifies parameters minimizing the duality gap while the second minimally perturbs prior estimates of the unspecified parameters to satisfy strong duality if it is possible to satisfy the optimality conditions exactly we apply these two approaches to the general linear optimization problem we also use them to impute unspecified parameters of the uncertainty set for robust linear optimization problems under interval and cardinality constrained uncertainty each inverse optimization model we propose is nonconvex but we show that a globally optimal solution can be obtained either in closed form or by solving a linear number of linear or convex optimization problems

three dimensional elasticity solutions to some orthotropic plate problems abstract this paper presents a three dimensional analysis of rectangular orthotropic plates by employing the differential quadrature dq method the derivation of the governing equations from the governing equations and the stress strain relationship of the three dimensional elasticity model is detailed the constrained conditions of the orthotropic plate edges are given the governing equations and boundary conditions are first normalized and discretized according to the dq procedure example problems pertaining to the bending buckling and free vibration of orthotropic plates with generic boundary conditions are selected to illustrate the simplicity and applicability of the dq method the convergence characteristics of the dq method are first obtained based on numerical studies after which the dq solutions are compared where possible with exact solutions it is found that the dq method yields accurate results for the plate problems under investigation

three dimensional vibration analysis of thick rectangular plates using chebyshev polynomial and ritz method this paper describes a method for free vibration analysis of rectangular plates with any thicknesses which range from thin moderately thick to very thick plates it utilises admissible functions comprising the chebyshev polynomials multiplied by a boundary function the analysis is based on a linear small strain three dimensional elasticity theory the proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions a very simple and general programme has been compiled for the purpose for a plate with geometric symmetry the vibration modes can be classified into symmetric and antisymmetric ones in that direction in such a case the computational cost can be greatly reduced while maintaining the same level of accuracy convergence studies and comparison have been carried out taking square plates with four simply supported edges as examples it is shown that the present method enables rapid convergence stable numerical operation and very high computational accuracy parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail with respect to different thickness side ratios aspect ratios and poissons ratios these results may serve as benchmark solutions for validating approximate two dimensional theories and new computational techniques in future 2002 elsevier science ltd all rights reserved

numerical aspects for free vibration of thick plates part i formulation and verification abstract this paper investigates the numerical aspects for free vibration analysis of a class of thick relative thickness ratio t b 0 2 shear deformable rectangular plates with all possible combinations of edge conditions these thick plate vibration frequencies most probably cannot be accurately determined using the classical thin plate theory or the mindlin plate theory the effect of transverse shear strain has been considered by using a higher order plate theory without the need for a shear correction factor unlike some domain discretization methods this analysis assumes a single global element for the entire plate the strain and kinetic energy integrals of the global plate element are formulated and the energy functional is minimized to yield the natural frequencies a set of boundary compliant admissible shape functions is developed to obtain solutions which are unattainable using the classical trigonometric admissible functions the numerical efficiency of symmetry classification is investigated and on certain computational platforms more than 80 of the execution time can be saved while maintaining the same level of accuracy

differential quadrature method based on the highest derivative and its applications the numerical differentiation is often used when dealing with the differential equations using the numerical differentiation the differential equations can be transformed into algebraic equations then we can get the numerical solution from the algebraic equations but the numerical differentiation process is very sensitive to even a small level of errors in contrast it is expected that on average the numerical integration process is much less sensitive to errors in this paper we provide a new method using the dq method based on the interpolation of the highest derivative dqihd for the differential equations the original function is then obtained by integration in this paper the dqihd method was applied to the buckling analysis of thin isotropic plates and winkler plates the numerical results agree well with the analytic solutions and the results show that our method is of high accuracy of good convergence with little computational efforts and it is easy to deal with the boundary conditions

free vibration of thick layered rectangular plates with point supports by finite layer method in this paper the free vibration of thick isotropic and laminated composite rectangular plates with point supports is analyzed by the finite layer method a new set of two dimensional basic functions which satisfies the kinematic boundary conditions at the edges of the plate and the zero displacement conditions at point supports is developed to describe the variation of three dimensional displacements in the plane of a thin finite layer one dimensional linear or quadratic shape functions are adopted to describe the variation of the displacements through the thickness layer the governing eigenvalue equation of the plate is derived via the conventional displacement method numerical results for the three dimensional vibration of rectangular plates with point supports are presented herein for the first time the eigenfrequencies of simply supported rectangular plates with a central point support are studied in detail by considering the variations of aspect ratio side to thickness ratio properties of materials number of laminates and stacking sequences comparison with known thin plate and mindlin plate solutions is carried out to verify the applicability and accuracy of the proposed method

free vibration analysis of three dimensional solids by bem in practical applications it is often necessary to determine the natural frequencies and mode shapes of a solid in addition to the static response under a variety of loading conditions this paper discusses the calculation of natural frequencies and mode shapes of three dimensional solids using the boundary element method the method developed is based on the use of particular integrals of the elastic equilibrium equations and employs only real arithmetic it represents an extension to three dimensions of work previously carried out for two dimensional problems in references 1 and 15 the method has been incorporated for multiregion analysis in the best3d boundary element solution technology three dimensional computer program 11 results of the boundary element calculations are compared with analytical finite element and experimental results

tracking deforming objects using particle filtering for geometric active contours tracking deforming objects involves estimating the global motion of the object and its local deformations as a function of time tracking algorithms using kalman filters or particle filters have been proposed for finite dimensional representations of shape but these are dependent on the chosen parametrization and cannot handle changes in curve topology geometric active contours provide a framework which is parametrization independent and allow for changes in topology in the present work we formulate a particle filtering algorithm in the geometric active contour framework that can be used for tracking moving and deforming objects to the best of our knowledge this is the first attempt to implement an approximate particle filtering algorithm for tracking on a theoretically infinite dimensional state space

analytical 3 d p element for quadrilateral plates part 1 thick isotropic plate structures an analytical three dimensional 3 d p version element for the vibration analysis of arbitrary quadrilateral thick plates is presented with the additional hierarchical shape functions and analytically integrated element matrices the computed accuracy is considerably improved the computed natural frequencies of cantilever and simply supported square plates show that the convergence rate of the present element is very fast with respect to the number of hierarchical terms and it can predict very accurate modes the element is applicable to the free vibration analysis of quadrilateral polygonal plates as well as 3 d space structures the continuous wavelet transform cwt is applied for the identification of damping ratios based on the rayleigh damping model the damped vibration response is obtained a simple experiment is performed to verify the predicted vibration responses the results show that the proposed element is also efficient for the vibration response analysis of plates

3 d vibration analysis of generalized super elliptical plates using chebyshev ritz method the three dimensional free vibration of generalized super elliptical plates is analysed based on the exact small strain and linear elasticity theory the ritz method is applied to derive the frequency equation the triplicate chebyshev polynomial series form the backbones of the admissible functions as modified by a characteristic boundary function to ensure the satisfaction of geometric boundary conditions of the plate utilizing the symmetry of the plate under consideration eight distinct vibration modes can be classified and individually solved while maintaining the same level of accuracy the accuracy of the present method has been examined by the convergence and comparison studies the effect of geometric parameters on vibration behaviour of the generalized super elliptical plates with free and fixed perimeters have been studied for different powers thickness ratios and aspect ratios

on the three dimensional vibrations of the cantilevered rectangular parallelepiped a solution is presented for the three dimensional problem of determining the free vibration frequencies and mode shapes for a rectangular parallelepiped which is completely fixed on one face and free on the other five faces this problem apparently is previously unsolved in the published literature the ritz method is used with displacements assumed in the form of algebraic polynomials convergence is studied numerical results are given for the first five frequencies of each of the four symmetry classes of vibration for five thick parallelepiped configurations including the cube contour plots are exhibited for the modal displacements of the cube the effects of varying poisson s ratio are also observed

a new rectangular beam theory abstract a new theory for beams of rectangular cross section which includes warping of the cross sections is presented in the present work by satisfying the shear free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required it is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in timoshenko beam theory provided that for the timoshenko equation the shear coefficient is taken to be 5 6 this value lies within the range of values 0 822 0 870 appearing in the literature for the beam of rectangular cross section results for two typical static examples are given for both the new theory and timoshenko beam theory these results are compared with the solutions of the comparable problems in the linear theory of elasticity for the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while timoshenko beam theory underestimates the shear correction term by 20 for the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution

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

three dimensional vibration of rectangular plates variance of simple support conditions and influence of in plane inertia plate models developed on the basis of the three dimensional elasticity theory are crucial to the correct solutions in dynamics problems in a three dimensional setting there exist numerous possible definitions of boundary conditions this paper attempts to identify the variance of three dimensional simple support conditions existing in practice the hard simple support condition assumes vanishing normal stresses at the edges and zero transverse and tangential displacement at the peripheries the soft simple support on the other hand imposes zero transverse displacement with vanishing normal and shear stresses at the boundaries to quantify the relative effects of each boundary condition on the vibratory responses of thick plates a global three dimensional ritz formulation is employed for analysis this technique uses sets of finite polynomial series in cartesian co ordinates to approximate the global normal mode variations of the plate these separable one dimensional polynomials are orthogonally generated within the plate domain such that all the essential edge conditions are identically satisfied the accuracy of the proposed three dimensional ritz method is assured from the convergence and comparison studies numerical experiments have been conducted to study firstly the effects of geometric parameters on the overall normal mode characteristics of simply supported plates and secondly the effects of in plane inertia on the vibration frequencies of plates with different thicknesses the three dimensional deformed mode shapes for selected cases have also been computed these have served to describe more vividly the normal mode characteristics of different types of simply supported rectangular plates

vibration and stability of an initially stressed thick plate according to a high order deformation theory in this paper the average stress method is used to derive the governing equation for a thick rectangular plate according to a high order deformation theory the applied load is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate the buckling loads and natural frequencies of simply supported plates are also investigated present results based on high order theory are compared with the results of brunelle s theory and reddy s theory in addition the effects of various parameters on the natural frequencies are studied more accurate results can be obtained by using the present theory than those of the other theories

semi analytical analysis for multi directional functionally graded plates 3 d elasticity solutions semi analytical 3 d elasticity solutions are presented for orthotropic multi directional functionally graded plates using the differential quadrature method dqm based on the state space formalism material properties are assumed to vary not only through the thickness but also in the in plane directions following an exponential law the graded in plane domain is solved numerically via the dqm while exact solutions are sought for the thickness domain using the state space method convergence studies are performed and the present hybrid semi analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate finally effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed copyright 2009 john wiley sons ltd

static analysis of thick rectangular laminated plates three dimensional elasticity solutions via differential quadrature element method this article presents the first endeavor to develop the differential quadrature element method for static solution of three dimensional elasticity equations of thick rectangular laminated composite plates the domain decomposition technique is employed to decompose a laminated plate into elements according to material layers the differential quadrature dq method is then applied to each element where the material properties are continuous to form the element weighting coefficient matrix and element force vector the discretized element weighting coefficient matrices and element force vectors are assembled together to form the global weighting coefficient matrix and global force vector for the whole plate using connection conditions the solution for the entire plate is obtained by solving the final algebraic equation system detailed formulations and numerical procedures are presented and the convergence characteristics of the method are investigated the numerical results are then compared where possible with the analytical solutions to verify the present solutions consequently some new numerical results are computed and analyzed using the present numerical method for laminated rectangular plates with different boundary conditions which are not solvable directly by the global dq method

three dimensional vibration of rectangular plates effects of thickness and edge constraints abstract a continuum three dimensional ritz formulation is presented for the free vibration analysis of homogeneous isotropic thick rectangular plates the method is applied specifically to investigate the effects of boundary constraints and thickness ratios on the vibration responses of these plates a general switching of transverse vibratory motions to surface parallel modes at the higher thickness ratio is manifested vividly through three dimensional deformed mode shape plots the present formulation is based on the linear three dimensional small strain elasticity energy principle in the solution process sets of self generating polynomial shape functions are used to derive the governing eigenvalue equation in essence these functions comprise a class of orthogonal polynomial functions and a basic function which is chosen to satisfy the essential geometric boundary conditions at the outset they are found very suitable for the computationally intensive task of 3 d modelling due to the ease of generation and numerical implementation several numerical examples have been computed to demonstrate the accuracy and efficiency of the method the influences of plate thickness and boundary constraints on the overall vibratory characteristics of thick plates are also discussed in detail

deformotion deforming motion shape average and the joint registration and approximation of structures in images what does it mean for a deforming object to be moving how can we separate the overall motion a finite dimensional group action from the more general deformation a diffeomorphism in this paper we propose a definition of motion for a deforming object and introduce a notion of shape average as the entity that separates the motion from the deformation our definition allows us to derive novel and efficient algorithms to register non identical shapes using region based methods and to simultaneously approximate and align structures in greyscale images we also extend the notion of shape average to that of a moving average in order to track moving and deforming objects through time the algorithms we propose extend prior work on landmark based matching to smooth curves and involve the numerical integration of partial differential equations which we address within the framework of level set methods

joint segmentation and shape regularization with a generalized forward backward algorithm this paper presents a method for the simultaneous segmentation and regularization of a series of shapes from a corresponding sequence of images such series arise as time series of 2d images when considering video data or as stacks of 2d images obtained by slicewise tomographic reconstruction we first derive a model where the regularization of the shape signal is achieved by a total variation prior on the shape manifold the method employs a modified kendall shape space to facilitate explicit computations together with the concept of sobolev gradients for the proposed model we derive an efficient and computationally accessible splitting scheme using a generalized forward backward approach our algorithm treats the total variation atoms of the splitting via proximal mappings whereas the data terms are dealt with by gradient descent the potential of the proposed method is demonstrated on various application examples dealing with 3d data we explain how to extend the proposed combined approach to shape fields which for instance arise in the context of 3d t imaging modalities and show an application in this setup as well

3 d theory versus 2 d approximate theory of free orthotropic isotropic plate and shell vibrations part 1 derivation of governing equations in part 1 of the paper the basic assumptions of the shells with added masses considered are introduced they serve for a derivation of the governing equations which are analyzed in part 2 of the paper

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

three dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method this paper presents accurate three dimensional elasticity solutions for free vibrations of six types of plates having free lateral surfaces two opposite sides simply supported and two other sides having combinations of simply supported clamped and free boundary conditions the solution methodology adopted in the present work first reduces the spatial variables in the governing elasticity equations to two by using displacement functions in the forms which satisfy the boundary conditions of the assumed simply supported sides the eigenvalue equations are then formulated from the reduced governing equations and the boundary conditions via the differential quadrature method the numerical results include the first nine natural frequencies of the six plate configurations for combinations of three aspect ratios and two thickness ratios these results are supported by appropriate convergence studies and comparisons with the results of other authors

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

a continuum three dimensional vibration analysis of thick rectangular plates abstract this paper presents a continuum three dimensional ritz formulation for the vibration analysis of homogeneous thick rectangular plates with arbitrary combinations of boundary constraints this model is formulated on the basis of the linear three dimensional small deformation elasticity theory to predict the vibratory responses of these thick rectangular plates the displacement fields in the transverse and in plane directions are expressed by sets of orthogonally generated polynomial functions these shape functions are intrinsically a product of a class of orthogonal polynomial functions and a basic function which are chosen to satisfy the essential geometric boundary conditions at the outset sets of frequency data for plates with various aspect ratios and thickness ratios have been presented these data are used to examine the merits and limitations of the classical plate theory and mindlin plate theory by direct comparisons finally using the three dimensional continuum approach sets of first known deformed mode shapes have been generated thus helping to understand the vibratory motion furthermore these results may also serve as the benchmark to further research into the refined plate theories

data driven estimation in equilibrium using inverse optimization equilibrium modeling is common in a variety of fields such as game theory and transportation science the inputs for these models however are often difficult to estimate while their outputs i e the equilibria they are meant to describe are often directly observable by combining ideas from inverse optimization with the theory of variational inequalities we develop an efficient data driven technique for estimating the parameters of these models from observed equilibria we use this technique to estimate the utility functions of players in a game from their observed actions and to estimate the congestion function on a road network from traffic count data a distinguishing feature of our approach is that it supports both parametric and nonparametric estimation by leveraging ideas from statistical learning kernel methods and regularization operators in computational experiments involving nash and wardrop equilibria in a nonparametric setting we find that a we effectively estimate the unknown demand or congestion function respectively and b our proposed regularization technique substantially improves the out of sample performance of our estimators

combined tensor fitting and tv regularization in diffusion tensor imaging based on a riemannian manifold approach in this paper we consider combined tv denoising and diffusion tensor fitting in dti using the affine invariant riemannian metric on the space of diffusion tensors instead of first fitting the diffusion tensors and then denoising them we define a suitable tv type energy functional which incorporates the measured dwis using an inverse problem setup and which measures the nearness of neighboring tensors in the manifold to approach this functional we propose generalized forward backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional we validate the performance of the derived algorithms on synthetic and real dti data in particular we work on real 3d data to our knowledge the present paper describes the first approach to tv regularization in a combined manifold and inverse problem setup

data driven inverse optimization with imperfect information in data driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal thus the observer seeks the agent s objective function that best explains a historical sequence of signals and corresponding optimal actions we formalize this inverse optimization problem as a distributionally robust program minimizing the worst case risk that the estimated decision i e the decision implied by a particular candidate objective differs from the agent s actual response to a random signal we show that our framework offers attractive out of sample performance guarantees for different prediction errors and that the emerging inverse optimization problems can be reformulated as or approximated by tractable convex programs when the prediction error is measured in the space of objective values a main strength of the proposed approach is that it naturally generalizes to situations where the observer has imperfect information e g when the agent s true objective function is not contained in the space of candidate objectives when the agent suffers from bounded rationality or implementation errors or when the observed signal response pairs are corrupted by measurement noise

generalized gradients priors on minimization flows this paper tackles an important aspect of the variational problem underlying active contours optimization by gradient flows classically the definition of a gradient depends directly on the choice of an inner product structure this consideration is largely absent from the active contours literature most authors explicitely or implicitely assume that the space of admissible deformations is ruled by the canonical l 2 inner product the classical gradient flows reported in the literature are relative to this particular choice here we investigate the relevance of using i other inner products yielding other gradient descents and ii other minimizing flows not deriving from any inner product in particular we show how to induce different degrees of spatial consistency into the minimizing flow in order to decrease the probability of getting trapped into irrelevant local minima we report numerical experiments indicating that the sensitivity of the active contours method to initial conditions which seriously limits its applicability and efficiency is alleviated by our application specific spatially coherent minimizing flows we show that the choice of the inner product can be seen as a prior on the deformation fields and we present an extension of the definition of the gradient toward more general priors

generalized inverse multiobjective optimization with application to cancer therapy we generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible in multiobjective linear optimization given a solution that is not a weakly efficient solution to the forward problem our method generates objective function weights that make the given solution a near weakly efficient solution our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem we provide a novel interpretation of our inverse formulation as the dual of the well known benson s method and by doing so develop a new connection between inverse optimization and pareto surface approximation techniques we apply our method to prostate cancer data obtained from princess margaret cancer centre in toronto canada we demonstrate that clinically acceptable treatments can be generated using a small number of objective

buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method abstract in this article a combination of the finite element fe and differential quadrature dq methods is used to solve the eigenvalue buckling and free vibration equations of rectangular thick plates resting on elastic foundations the elastic foundation is described by the pasternak two parameter model the three dimensional linear and small strain theory of elasticity and energy principle are employed to derive the governing equations the in plane domain is discretized using two dimensional finite elements the spatial derivatives of equations in the thickness direction are discretized in strong form using dqm buckling and free vibration of rectangular thick plates of various thicknesses to width and aspect ratios with pasternak elastic foundation are investigated using the proposed fe dq method the results obtained by the mixed method have been verified by the few analytical solutions in the literature it is concluded that the mixed fe dq method has good convergancy behavior and acceptable accuracy can be obtained by the method with a reasonable degrees of freedom

frequency analysis of symmetrically laminated plates with free edges abstract this paper is concerned with the estimation of natural frequencies of undamaged symmetrically laminated plates rectangular circular annular and elliptical having completely free edges the rayleigh ritz energy approach is employed here to obtain the approximate natural frequencies and the associated mode shapes the plates are considered to be thin and to undergo small deflections satisfying kirchhoff s hypothesis a complete power series is used as admissible functions for in plane and out of plane displacements in the numerical examples the accuracy of the present results is compared with the other analytical results available in the literature the effects of the shape and size of the plate number of plies and the fiber orientation on the natural frequencies flexural mode of symmetrically laminated plates are documented the mode shape corresponding to each frequency has been identified in this paper

buckling of rectangular mindlin plates with internal line supports this paper considers the elastic buckling of rectangular mindlin plates under normal inplane forces the plates may have any number of internal line straight or curved supports that span between any two edges based on the energy functional derived from the incremental total potential energy approach the newly developed pb 2 rayleigh ritz method is applied for solution the special feature of this method is the pb 2 ritz function which consists of the product of 1 a two dimensional polynomial function and 2 a basic function formed from taking the product of the equations of the boundaries and internal line supports with each equation raised to appropriate powers as shown herein the method is convenient for analysts since no discretization is required and very accurate results can be obtained buckling load intensity factors for rectangular plates with various boundary conditions and various thickness and aspect ratios are tabulated for designers these may also serve as benchmark values for the testing of other numerical methods

three dimensional vibration analysis of cantilevered skew plates three dimensional 3 d free vibration of cantilevered thick skew plates is analyzed based on the exact linear and small strain elasticity theory the skew domain of the plate is mapped onto a cubic domain a set of triplicate chebyshev polynomials multiplied by a boundary function is developed as the trial functions of each displacement components using the ritz method the eigenvalue equation is derived from the strain energy and kinetic energy of the plate the vibration modes are divided into the antisymmetric and symmetric ones in the thickness direction therefore can be studied individually the convergence study shows that the first eight frequency parameters for each mode categories can be obtained with an accuracy of at least four significant figures the effect of geometric parameters such as skew angle aspect ratio and span thickness ratio on frequency parameters is studied the results are compared with those obtained by using the algebraic polynomials as trial functions and the 3 d finite element solutions respectively it is shown that the chebyshev polynomials can provide better numerical stability than the algebraic polynomials especially for the plates with large skew angle the present results can serve as the benchmark data for the accuracy evaluation of other computational techniques

differential quadrature for multi dimensional problems the technique of differential quadrature for the solution of partial differential equations introduced by bellman et al is extended and generalized to encompass partial differential equations involving multiple space variables approximation formulae for a variety of first and second order partial derivatives and typical weighting coefficients are presented application of these formulae is demonstrated on the solution of the convection diffusion equation for the two and three dimensional space dependent cases and for both the transient and steady state dispersion of inert neutrally buoyant pollutants from continuous sources into an unbounded atmosphere

vibrations of cantilevered skewed plates with corner stress singularities in conjunction with classical thin plate theory the ritz trial space of assumed transverse displacement functions consists of algebraic polynomials which are mathematically complete and corner functions which account for the singular behaviour of bending stresses at the reentrant corner

application of generalized differential quadrature method to structural problems summary this paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate efficient and simple numerical technique for structural analysis firstly drawbacks existing in the method of differential quadrature dq are evaluated and discussed then an improved and simpler generalized differential quadrature method gdq is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients subsequently the generalized differential quadrature is systematically employed to solve problems in structural analysis numerical examples have shown the superb accuracy efficiency convenience and the great potential of this method numerical approximation methods for solving partial differential equations have been widely used in various engineering fields classical techniques such as finite element and finite difference methods are well developed and well known these methods can provide very accurate results by using a large number of grid points however in a large number of cases reasonably approximate solutions are desired at only a few specific points in the physical domain in order to get results even at or around a point of interest with acceptable accuracy conventional finite element and finite difference methods still require the use of a large number of grid points consequently the requirement for computer capacity is often unnecessarily large in such cases in seeking an alternate numerical method using fewer grid points to find results with acceptable accuracy the method of differential quadrature dq was introduced by bellman et a the method of dq is a global approximate method this method is based on the ideas that the derivative of a function with respect to a co ordinate direction can be expressed as a weighted linear sum of all the function values at all mesh points along that direction and that a continuous function can be approximated by a higher order polynomial in the overall domain the dq method differs from the finite element method fem in two aspects firstly the fem uses lower order polynomials to approximate a function on a local element level while the dq method approximates a function on the global area using higher order polynomials secondly the dq method directly approximates the derivatives of a function at a point while the fem approximates a function over a local element and the derivatives can then be derived from the approximate function in this aspect the dq method is more similar to the finite difference method fdm however the fdm is also a local approximation method based on lower order polynomial approximation in fact it can be shown that the fdm is just a special case of the dq method where it is applied locally on the range xi xi l owing to the higher order

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

new possibilities with sobolev active contours recently the sobolev metric was introduced to define gradient flows of various geometric active contour energies it was shown that the sobolev metric outperforms the traditional metric for the same energy in many cases such as for tracking where the coarse scale changes of the contour are important some interesting properties of sobolev gradient flows include that they stabilize certain unstable traditional flows and the order of the evolution pdes are reduced when compared with traditional gradient flows of the same energies in this paper we explore new possibilities for active contours made possible by sobolev metrics the sobolev method allows one to implement new energy based active contour models that were not otherwise considered because the traditional minimizing method render them ill posed or numerically infeasible in particular we exploit the stabilizing and the order reducing properties of sobolev gradients to implement the gradient descent of these new energies we give examples of this class of energies which include some simple geometric priors and new edge based energies we also show that these energies can be quite useful for segmentation and tracking we also show that the gradient flows using the traditional metric are either ill posed or numerically difficult to implement and then show that the flows can be implemented in a stable and numerically feasible manner using the sobolev gradient

three dimensional free vibration analysis of isotropic rectangular plates using the b spline ritz method abstract this paper presents three dimensional free vibration analysis of isotropic rectangular plates with any thicknesses and arbitrary boundary conditions using the b spline ritz method based on the theory of elasticity the proposed method is formulated by the ritz procedure with a triplicate series of b spline functions as amplitude displacement components the geometric boundary conditions are numerically satisfied by the method of artificial spring to demonstrate the convergence and accuracy of the present method several examples with various boundary conditions are solved and the results are compared with other published solutions by exact and other numerical methods based on the theory of elasticity and various plate theories rapid stable convergences as well as high accuracy are obtained by the present method the effects of geometric parameters on the vibrational behavior of cantilevered rectangular plates are also investigated the results reported here may serve as benchmark data for finite element solutions and future developments in numerical methods

free vibrations of a simply supported rectangular plate an exact elasticity solution abstract an exact three dimensional solution for the free vibrations of simply supported rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper the solution obtained in a semi inverse fashion as was the solution of the elastostatic problem for such plates satisfies all of the boundary conditions of the problem in a pointwise manner it is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi inverse solution other modes of oscillation may exist in the three dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes the two types of modes found are analogous to the flexural modes of classical plate theory and the thickness twist modes here called breathing modes of mindlin plate theory some numerical results are given which indicate that the predictions of mindlin plates are uncannily good approximations to the flexural frequencies given by the present three dimensional analysis even for very thick plates however the predictions of mindlin plate theory for the thickness twist or breathing frequencies are not nearly so good these discrepancies are discussed briefly in an appendix

incremental proximal methods for large scale convex optimization we consider the minimization of a sum sum i 1 mf i x consisting of a large number of convex component functions f i for this problem incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective we propose new incremental methods consisting of proximal iterations applied to single components as well as combinations of gradient subgradient and proximal iterations we provide a convergence and rate of convergence analysis of a variety of such methods including some that involve randomization in the selection of components we also discuss applications in a few contexts including signal processing and inference machine learning

normal modes in a continuum model of vocal fold tissues the ritz method is used to calculate eigenmodes and eigenfrequencies in a continuum model of the vocal folds the investigation represents a rectification and extension of previous studies emphasizing the indispensability of utilizing natural boundary conditions when computing the characteristic modes of a system concurring with previous assertions two of the lower order eigenmodes are theorized to play a major role in facilitating self oscillation of the folds during phonation one mode related to vertical phasing is shown to have a more direct control over glottal convergence divergence than indicated in previous calculations unlike lumped element models the continuum model predicts that the eigenfrequencies of the two modes are closely spaced over an extensive range of tissue sizes and stiffnesses this finding may help explain why the two modes entrain so naturally over a wide range of phonatory adjustments in human phonation

bem analysis of free vibration problems using polynomial particular integrals abstract the development of a boundary element method for free vibration analysis using particular solutions is discussed the formulation presented is based on treating the forcing function in the governing differential equation as an initially unknown distributed body force within the domain the volume integral due to this body force is then eliminated by approximating the inertia force by global interpolation and polynomial function representations and finding particular solutions for the governing inhomogeneous equations the resulting non symmetric system matrix is solved by using a modified arnoldi s algorithm that takes advantage of the special structure of the substructured boundary element method the techniques described here are embedded in a computer program gpbest and the numerical examples arc solved by using this computer code

on the three dimensional vibration analysis of simultaneously skewed and twisted cantilevered parallelepipeds the natural frequencies of simultaneously skewed and twisted cantilevered parallelepipeds are determined using the ritz method the present work is the first known three dimensional study of the problem assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete reasonably accurate natural frequencies are calculated for low aspect ratio thick parallelepipeds having arbitrary degrees of twist and skewness detailed numerical studies show that a three dimensional analysis is essential in monitoring complicated coupled mode sensitivities in the variation of non dimensional natural frequencies with increasing skew and twist angles and thickness ratio results obtained using the present method are compared with those obtained in a detailed three dimensional finite element analysis where the suitability and limitations of s version solid element discretizations are clearly brought out

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

dynamic stability of a non conservative viscoelastic rectangular plate abstract based on the thin plate theory and the two dimensional 2d viscoelastic differential constitutive relation the differential equation of motion of the viscoelastic rectangular plate subjected to uniformly distributed tangential follower force in laplace domain is deduced the equation is suitable for various viscoelastic models of differential type the differential equation of motion of the viscoelastic plate constituted by the kelvin voigt model under the action of uniformly distributed tangential follower force in time domain is also derived the generalized eigenequations of non conservative viscoelastic rectangular plate with four edges simply supported two opposite edges simply supported and other two edges clamped are established by the differential quadrature method and the curves of real parts and imaginary parts of the first three order dimensionless complex frequencies vs uniformly distributed tangential follower force are obtained the factors influencing the dynamic stability of the visoelastic rectangular plate are discussed

computing medians and means in hadamard spaces the geometric median as well as the frechet mean of points in a hadamard space are important in both theory and applications surprisingly no algorithms for their computation are hitherto known to address this issue we use a splitting version of the proximal point algorithm for minimizing a sum of convex functions and prove that this algorithm produces a sequence converging to a minimizer of the objective function which extends a recent result of bertsekas math program 129 2011 pp 163 195 into hadamard spaces the method is quite robust and not only does it yield algorithms for the median and the mean but also it applies to various other optimization problems we moreover show that another algorithm for computing the frechet mean can be derived from the law of large numbers due to sturm ann probab 30 2002 pp 1195 1222 in applications computing medians and means is probably most needed in tree space which is an instance of a hadamard space invented by billera holmes and vo

on coupled longitudinal and lateral vibrations of elastic rods abstract in this paper the coupled longitudinal and lateral vibrations of a rectangular parallelepiped composed of a uniform isotropic elastic body are examined the one dimensional model for the body was developed by green naghdi and several of their co workers it is based on a cosserat or directed rod theory the frequency spectrum is found to divide naturally into three regions which are separated by degenerate cases when the cross section of the body is square a natural splitting of the modes occurs one half of this split involves motions coupling the axial extension and symmetric lateral deformation of the body the other half involves asymmetric lateral deformations the cases of a free free rod and a cantilevered rod are discussed and the results compared to existing works in the literature which use the three dimensional theory of elasticity to model the vibrations