jacobi ritz method for free vibration analysis of uniform and stepped circular cylindrical shells with arbitrary boundary conditions a unified formulation abstract a semi analytical approach is employed to analyze free vibration characteristics of uniform and stepped circular cylindrical shells subject to arbitrary boundary conditions the analytical model is established on the basis of multi segment partitioning strategy and flugge thin shell theory the admissible displacement functions are handled by unified jacobi polynomials and fourier series in order to obtain continuous conditions and satisfy arbitrary boundary conditions the penalty method about the spring technique is adopted the solutions about free vibration behavior of circular cylindrical shells were obtained by approach of rayleigh ritz to confirm the reliability and accuracy of this method convergence study and numerical verifications for circular cylindrical shells subject to different boundary conditions jacobi parameters spring parameters and maximum degree of permissible displacement function are carried out through comparative analyses it is obvious that the present method has a good stable and rapid convergence property and the results of this paper agree closely with the published literature in addition some interesting results about the geometric dimensions are investigated

free vibrations of multilayered doubly curved shells based on a mixed variational approach and global piecewise smooth functions abstract this paper presents the extension of a two dimensional model that recently appeared in literature deals with freely vibrating laminated plates the extension takes into account the corresponding theory describing the dynamic of freely vibrating multilayered doubly curved shells the relevant governing differential equations associated boundary conditions and constitutive equations are derived from one of reissner s mixed variational theorems both the governing differential equations and the related boundary conditions are presented in terms of resultant stresses and displacements in spite of the multi layer nature of the shell the theory is developed as if the shell were virtually made of a single layer this choice does not limit the performances of the model which are comparable to the corresponding three dimensional theory this ability is accomplished by an appropriate global expansion of the relevant kinetic and stress quantities through the thickness of the multilayered shell the mentioned expansion is realized by a novel selection of global piecewise smooth functions numerical tests illustrate the performance of the model with respect to several elements subjected to a class of simply supported boundary conditions plates circular cylindrical shells spherical and saddle shape laminates the model is first tested by comparing its resulting eigen parameters with those few existing of exact or approximate three dimensional models and finally new results are provided for several geometrical and material characteristics for plates and shells

regular formal moduli spaces and arithmetic transfer conjectures we define various formal moduli spaces of p divisible groups which are regular and morphisms between them we formulate arithmetic transfer conjectures which are variants of the arithmetic fundamental lemma conjecture of the third author in the presence of ramification these conjectures include the at conjecture of our previous joint work we prove these conjectures in low dimensional cases

displays and formal p divisible groups over p adic nagata rings formal p divisible groups are classified by nilpotent displays according to t zink we extend this result to arbitrary p adic rings the proof uses the grothendieck illusie deformation theory of truncated p divisible groups

the contourlet transform an efficient directional multiresolution image representation the limitations of commonly used separable extensions of one dimensional transforms such as the fourier and wavelet transforms in capturing the geometry of image edges are well known in this paper we pursue a true two dimensional transform that can capture the intrinsic geometrical structure that is key in visual information the main challenge in exploring geometry in images comes from the discrete nature of the data thus unlike other approaches such as curvelets that first develop a transform in the continuous domain and then discretize for sampled data our approach starts with a discrete domain construction and then studies its convergence to an expansion in the continuous domain specifically we construct a discrete domain multiresolution and multidirection expansion using nonseparable filter banks in much the same way that wavelets were derived from filter banks this construction results in a flexible multiresolution local and directional image expansion using contour segments and thus it is named the contourlet transform the discrete contourlet transform has a fast iterated filter bank algorithm that requires an order n operations for n pixel images furthermore we establish a precise link between the developed filter bank and the associated continuous domain contourlet expansion via a directional multiresolution analysis framework we show that with parabolic scaling and sufficient directional vanishing moments contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves finally we show some numerical experiments demonstrating the potential of contourlets in several image processing applications

anisotropic solid like shells modeled with nurbs based isogeometric approach vibration buckling and divergence analyses abstract we proposed an iga formulation for free vibration buckling and divergence analyses of generally anisotropic solid like composite shells recently developed rayleigh ritz based methods are not accurate enough for curved shells since they are not able to capture twisting mode shapes here we use the advantages of isogeometric analysis iga and develop a three dimensional higher order continuous solid like shell sls model since the continuity of material orientation is crucial in numerical analysis of anisotropic shells non uniform rational b splines nurbs are used to establish a smooth interpolation through the thickness and on the middle surface of the shell for both the geometry and displacement fields the developed isogeometric sls is coupled with bezier extraction operators to represent continuity between multi patch anisotropic domains numerical solutions for composite laminated shells with different boundary conditions are compared with analytical solutions or other solutions from the literature in this context we study the influence of span to thickness ratios different shapes modulus ratios member aspect ratios and various layouts on the mechanical response with the presented model we were able to obtain the twisting mode shapes which are not frequently observed in orthotropic and isotropic ones we also study the influence of the polynomial order of the iga formulation on the results

free vibration analysis of a cylindrical shell circular plate system with general coupling and various boundary conditions abstract the free vibration of a structure consisting of a finite circular cylindrical shell closed at one end by a circular plate is analyzed in this paper emphasis is given to the characterization of structural coupling and boundary conditions these are incorporated into the model by means of continuous distributions of springs along the shell and the plate interface a general formulation based on a variational principle is used this formulation allows a wide spectrum of boundary conditions and coupling conditions between the shell and the plate an issue the importance of which is clearly shown by a literature review very good accuracy of the method is demonstrated by solving test problems for lower order modes of the plate and of the shell for which some results are available in the literature comparisons are also made using finite element analysis on a plate ended shell showing that the proposed approach is a convenient effecient and accurate one for determining the modal behavior of such a complex structural system other numerical results are then presented for a shell rigidly attached to a plate to illustrate the coupling phenomena between the shell and the plate it is shown that there exist three different types of modes for this combined structure they are termed plate controlled modes shell controlled modes and strongly coupled modes respectively it is also shown that each type is closely related to the modal character of each of uncoupled elements

planelets a piecewise linear fractional model for preserving scene geometry in intra coding of indoor depth images geometrical wavelets have already proved their strength in approximation compression and denoising of piecewise constant and piecewise linear images in this paper we extend this family by introducing planelets toward an effective representation of indoor depth images it uses a linear fractional model to capture non linearity of depth values in the planar regions of the output images of kinect like sensors a block based compression framework based on planelet approximation is then presented which uses quadtree decomposition along with spatial predictions as an effective intra coding scheme compared with both classical geometric wavelets and some state of the art image coding algorithms our method provides desirable quality by explicitly representing edges and planar patches

wedgelets nearly minimax estimation of edges we study a simple horizon model for the problem of recovering an image from noisy data in this model the image has an edge with fi holder regularity adopting the viewpoint of computational harmonic analysis we develop an overcomplete collection of atoms called wedgelets dyadically organized indicator functions with a variety of locations scales and orientations the wedgelet representation provides nearly optimal representations of objects in the horizon model as measured by minimax description length we show how to rapidly compute a wedgelet approximation to noisy data by flnding a special edgelet decorated recursive partition which minimizes a complexity penalized sum of squares this estimate using su cient sub pixel resolution achieves nearly the minimax mean squared error in the horizon model in fact the method is adaptive in the sense that it achieves nearly the minimax risk for any value of the unknown degree of regularity of the horizon 1 fi 2 wedgelet analysis and de noising may be used successfully outside the horizon model we study images modelled as indicators of star shaped sets with smooth bound aries and show that complexity penalized wedgelet partitioning achieves nearly the minimax risk in that setting also

rate distortion optimized tree structured compression algorithms for piecewise polynomial images this paper presents novel coding algorithms based on tree structured segmentation which achieve the correct asymptotic rate distortion r d behavior for a simple class of signals known as piecewise polynomials by using an r d based prune and join scheme for the one dimensional case our scheme is based on binary tree segmentation of the signal this scheme approximates the signal segments using polynomial models and utilizes an r d optimal bit allocation strategy among the different signal segments the scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying r d behavior d r spl sim c sub 0 2 sup c1r thus improving over classic wavelet schemes we also prove that the computational complexity of the scheme is of o nlogn we then show the extension of this scheme to the two dimensional case using a quadtree this quadtree coding scheme also achieves an exponentially decaying r d behavior for the polygonal image model composed of a white polygon shaped object against a uniform black background with low computational cost of o nlogn again the key is an r d optimized prune and join strategy finally we conclude with numerical results which show that the proposed quadtree coding scheme outperforms jpeg2000 by about 1 db for real images like cameraman at low rates of around 0 15 bpp

platelets a multiscale approach for recovering edges and surfaces in photon limited medical imaging the nonparametric multiscale platelet algorithms presented in this paper unlike traditional wavelet based methods are both well suited to photon limited medical imaging applications involving poisson data and capable of better approximating edge contours this paper introduces platelets localized functions at various scales locations and orientations that produce piecewise linear image approximations and a new multiscale image decomposition based on these functions platelets are well suited for approximating images consisting of smooth regions separated by smooth boundaries for smoothness measured in certain holder classes it is shown that the error of m term platelet approximations can decay significantly faster than that of m term approximations in terms of sinusoids wavelets or wedgelets this suggests that platelets may outperform existing techniques for image denoising and reconstruction fast platelet based maximum penalized likelihood methods for photon limited image denoising deblurring and tomographic reconstruction problems are developed because platelet decompositions of poisson distributed images are tractable and computationally efficient existing image reconstruction methods based on expectation maximization type algorithms can be easily enhanced with platelet techniques experimental results suggest that platelet based methods can outperform standard reconstruction methods currently in use in confocal microscopy image restoration and emission tomography

representation and compression of multidimensional piecewise functions using surflets we study the representation approximation and compression of functions in m dimensions that consist of constant or smooth regions separated by smooth m 1 dimensional discontinuities examples include images containing edges video sequences of moving objects and seismic data containing geological horizons for both function classes we derive the optimal asymptotic approximation and compression rates based on kolmogorov metric entropy for piecewise constant functions we develop a multiresolution predictive coder that achieves the optimal rate distortion performance for piecewise smooth functions our coder has near optimal rate distortion performance our coder for piecewise constant functions employs surflets a new multiscale geometric tiling consisting of m dimensional piecewise constant atoms containing polynomial discontinuities our coder for piecewise smooth functions uses surfprints which wed surflets to wavelets for piecewise smooth approximation both of these schemes achieve the optimal asymptotic approximation performance key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity we also extend our results to the corresponding discrete function spaces for sampled data we provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities for approximation of discrete data we propose a new scale adaptive dictionary that contains few elements at coarse and fine scales but many elements at medium scales simulation results on synthetic signals provide a comparison between surflet based coders and previously studied approximation schemes based on wedgelets and wavelets

o displays and π divisible formal o modules abstract in this paper we construct an o display theory and prove that under certain conditions on the base ring the category of nilpotent o displays and the category of divisible formal o modules are equivalent starting with this result we then construct a dieudonne o display theory and prove a similar equivalence between the category of dieudonne o displays and the category of divisible o modules we also show that this equivalence is compatible with duality these results generalize the corresponding results of zink and lau on displays and p divisible groups

three dimensional vibration analysis of joined thick conical cylindrical shells of revolution with variable thickness abstract a three dimensional 3 d method of analysis is presented for determining the free vibration frequencies of joined thick conical cylindrical shells of revolution with variable thickness unlike conventional shell theories which are mathematically two dimensional 2 d the present method is based upon the 3 d dynamic equations of elasticity displacement components ur u and uz in the radial circumferential and axial directions respectively are taken to be periodic in and in time and algebraic polynomials in the r and z directions potential strain and kinetic energies of the joined shells are formulated and the ritz method is used to solve the eigenvalue problem thus yielding upper bound values of the frequencies by minimizing the frequencies as the degree of the polynomials is increased frequencies converge to the exact values convergence to four digit exactitude is demonstrated for the first five frequencies natural frequencies are presented for different boundary conditions comparisons are made between the frequencies from the present 3 d ritz method and 2 d thin shell theories by previous researchers

theoretical analysis of view interpolation with inaccurate depth information a problem of view interpolation from a pair of rectified stereo images with inaccurate depth information is addressed errors in geometric information greatly affect the quality of the resulting images since inaccurate geometry causes miscorrespondences between the input images a new theory for quantitatively analyzing the effect of depth errors and providing a principled optimization scheme based on the mean squared error metric is proposed the theory clarifies that if the probabilistic distribution of the depth errors is given an optimized view interpolation scheme that outperforms conventional linear interpolation can be derived it also reveals that under specific conditions linear interpolation is acceptable as an approximation of the optimized interpolation scheme furthermore band limitation combined with linear interpolation is also analyzed leading to an optimal cutoff frequency which achieves better results than the antialias scheme proposed in previous studies experimental results using real scenes are also presented to confirm this theory

eigensolutions of joined hermetic shell structures using the state space method abstract a substructure synthesis method based on state space mathematics is proposed for the eigensolution of axisymmetric joined hermetic thin shell structures in the state space method ssm a system of eight coupled first order differential equations is solved for each shell substructure using the pade approximation for matrix exponentiation the substructures are then joined by matching all of the displacement and force boundary variables the pade method allows a space invariant substructure e g uniform cylinder to be treated as a continuum further a space variant substructure e g cone is assumed to be a piecewise continuum which allows one to still use the pade method ssm is validated by applying it to structural elements such as a cylinder a cone a sphere and a toroidal segment and comparing the predicted natural frequencies with well known theoretical solutions the strength of ssm from the substructure synthesis viewpoint is demonstrated by analyzing several shell structures including a hermetic capsule and a refrigeration compressor shell in all examples finite element method fem predictions are used to support ssm results for the compressor shell ssm results compare well with the limited experimental data

a semi analytical method for the free vibration of doubly curved shells of revolution abstract in this paper a semi analytical method is used to investigate the free vibration of doubly curved shells of revolution with arbitrary boundary conditions the doubly curved shells of revolution are divided into their segments in the meridional direction and the theoretical model for vibration analysis is formulated by applying flugge s thin shell theory regardless of the boundary conditions the displacement functions of shell segments are composed by the jacobi polynomials along the revolution axis direction and the standard fourier series along the circumferential direction the boundary conditions at the ends of the doubly curved shells of revolution and the continuous conditions at two adjacent segments were enforced by the penalty method then the natural frequencies of the doubly curved shells are obtained by using the rayleigh ritz method for arbitrary boundary conditions this method does not require any changes to the mathematical model or the displacement functions and it is very effective in the analysis of free vibration for doubly curved shells of revolution the credibility and exactness of proposed method are compared with the results of finite element method fem and some numerical results are reported for free vibration of the doubly curved shells of revolution under classical and elastic boundary conditions results of this paper can provide reference data for future studies in related field

depth map coding optimization using rendered view distortion for 3d video coding in order to improve 3d video coding efficiency we propose methods to estimate rendered view distortion in synthesized views as a function of the depth map quantization error our approach starts by calculating the geometric error caused by the depth map error based on the camera parameters then we estimate the rendered view distortion based on the local video characteristics the estimated rendered view distortion is used in the rate distortion optimized mode selection for depth map coding a lagrange multiplier is derived using the proposed distortion metric which is estimated based on an autoregressive model experimental results show the efficiency of the proposed methods with average savings of 43 in depth map bitrate as compared with encoding the depth maps using the same coding tools but with the rate distortion optimization based on the conventional distortion metric

an exact solution for free vibration of cross ply laminated composite cylindrical shells with elastic restraint ends abstract in this paper a new exact solution based on the classical shell theory cst for free vibration of cross ply laminated composite cylindrical shells with elastic restraint ends is proposed the present exact solution can be summed up in the following steps firstly the displacement functions are constructed by the governing differential equations with the exact closed form solutions then the artificial spring technology is introduced to simulate the general boundary conditions of the two end edges of shell thirdly the equation for natural frequencies is obtained by means of the method of reverberation ray matrix mrrm lastly the vibration results are presented by the modified golden section search mgss algorithm by comparing the present method with published papers the accuracy of present method is verified on the basis of that some new exact nature frequencies and mode shapes of the cross ply laminated composite cylindrical shells with various classical boundary conditions and elastic restraints are performed and they can be served as the benchmark data for the future

free vibration analysis of doubly curved shallow shells using the superposition galerkin method abstract this paper demonstrates the applicability of the superposition method for free vibration analysis of doubly curved thin shallow shells of rectangular planform with any possible combination of simply supported and clamped edges the same building block yields the natural frequencies for 55 combinations of edge conditions the natural frequency parameters of the shells were obtained using the superposition galerkin method sgm for seven sets of boundary conditions several different curvature ratios and two aspect ratios the sgm uses approximate steady state solutions as building blocks but the method proves to be accurate and efficient it has also been shown that even with approximate building blocks the monotonic nature of convergence of the natural frequencies with respect to the number of driving coefficients holds as long as the number of admissible functions in the steady state solution is kept constant the results for natural frequencies of the seven boundary conditions may be considered as benchmarks