on quantum coding for ensembles of mixed states we consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states although the optimal rate is unknown we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states we also discuss a classical analogue of the problem

solution of the poisson equation by differential quadrature the method of differential quadrature is demonstrated by solving the two dimensional poisson equation the results for three test problems are compared with the exact analytical solutions and the numerical solutions obtained by others for the galerkin the control volume and the five point finite difference methods the method of differential quadrature leads to more accurate results for comparable levels of computational effort

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

application of a version of the rayleigh technique to problems of bars beams columns membranes and plates abstract a review is presented together with some new material of the application of a little known version of the rayleigh technique to a variety of problems in solid and structural mechanics this method was originally applied by rayleigh in 1894 to the one dimensional problem of determining the fundamental frequency of a stretched string undergoing small amplitude vibrations the essence of the method is that instead of using a specific trial function with an undetermined coefficient for the deflection as in the ordinary rayleigh method here one uses a function containing a power law term with an undetermined exponent application of the usual variational procedure for the quantity of interest such as the buckling load fundamental frequency or deflection results in a dimensionless quantity which is a function only of the undetermined exponent finally the best exponent is the one which minimizes the lagrangian and thus the buckling load natural frequency or reciprocal of deflection in the past five years the non integer exponent idea has been applied to elastic torsion buckling of columns and plates vibration of bars beams columns membranes and plates and deflection of beams and plates also it has been incorporated into the finite element method all of these applications are discussed and some additional original work of the present investigator is presented

coordination capacity we develop elements of a theory of cooperation and coordination in networks rather than considering a communication network as a means of distributing information or of reconstructing random processes at remote nodes we ask what dependence can be established among the nodes given the communication constraints specifically in a network with communication rates ri j between the nodes we ask what is the set of all achievable joint distributions p x1 xm of actions at the nodes of the network several networks are solved including arbitrarily large cascade networks distributed cooperation can be the solution to many problems such as distributed games distributed control and establishing mutual information bounds on the influence of one part of a physical system on another

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

differential quadrature layerwise modeling technique for three dimensional analysis of cross ply laminated plates of various edge supports abstract in this paper a differential quadrature model is proposed which is established within a layerwise framework for the bending analysis of composite laminates three dimensional theory of elasticity is implemented and all physical governing equations are satisfied including characteristics of the continuity and discontinuity of interfacial transverse and in plane displacements strains and stresses along interfaces of the composite laminates thus delivering highly accurate numerical solutions variation in boundary conditions plate aspect and thickness ratios and loading conditions are examined demonstrating the applicability accuracy and stability of the present methodology numerical examples for rectangular cross ply laminated plates subjected to a uniform load sinusoidal load or uniformly distributed moment are studied selected results from these examples are compared with those available in existing published literature

application of the boundary integral equation method to reissner s plate model numerical solution of reissner s model for the bending of elastic plates by an advanced boundary integral equation method is outlined construction of fundamental solutions and computational strategy is fully described implementation of the resulting one dimensional model is illustrated by two test problems including comparison to analytical solutions

generalized differential quadrature method for the free vibration of truncated conical panels abstract this paper presents an improved generalized differential quadrature gdq method for the investigation of the effects of boundary conditions on the free vibration characteristics of truncated conical panels the truncated conical panel is an important geometrical shape in the fields of aerospace marine and structural engineering however despite this importance few works in free vibration analysis have dealt with this particular geometry in this work the vibration characteristics of clamped and simply supported truncated conical shells are obtained for various circumferential wave numbers further the effects of the vertex and subtended angles on the frequency parameters are also examined in detail due to limited published results in the open literature results for a range of cases are compared with those generated from the commercial finite element solver mcneal schwendler corporation nastran and excellent agreement is observed

elastoplastic buckling analysis of thick rectangular plates by using the differential quadrature method the paper investigates the elastoplastic buckling behavior of thick rectangular plates by using the differential quadrature dq method mindlin plate theory is adopted to take the transverse shear effect into considerations both incremental theory and deformation theory are employed due to the material non linearity iteration processes are involved for obtaining solutions detailed methodology and procedures are derived the elastoplastic buckling behavior of thick rectangular plates with ten combinations of boundary conditions and under various loadings is studied to verify the dq solution procedures dq results are compared with existing analytical solutions for plates with two boundaries simply supported and the others simply supported clamped or free then the dq method is used to obtain solutions of rectangular thick plates with other combinations of boundary conditions since no analytical solutions for such cases are available the buckling loads obtained by the dq method could serve as a reference the phenomenon reported in the literature namely the deformation theory generally gives consistently lower buckling loads than the incremental theory and large discrepancy in predictions between the two theories exists with increasing of plate thickness e s 0 and c in the ramberg osgood relations is also observed for the cases studied herein apart from the phenomenon reported earlier by durban that deformation theory predicted a progressively lower in plane shear modulus as the level of plasticity increased thus predicted lower buckling loads another reason is given herein to explain the large discrepancy in predictions for thicker plates with the deformation theory and incremental theory

post buckling analysis of shear deformable shallow shells by the boundary element method this paper presents four boundary element formulations for post buckling analysis of shear deformable shallow shells the main differences between the formulations rely on the way non linear terms are treated and on the number of degrees of freedom in the domain boundary integral equations are obtained by coupling boundary element formulation of shear deformable plate and two dimensional plane stress elasticity four different sets of non linear integral equations are presented some domain integrals are treated directly with domain discretization whereas others are dealt indirectly with the dual reciprocity method each set of non linear boundary integral equations are solved using an incremental approach where loads and prescribed boundary conditions are applied in small but finite increments the resulting systems of equations are solved using a purely incremental technique and the newton raphson technique with the arc length method finally the effect of imperfections obtained from a linear buckling analysis on the post buckling behaviour of axially compressed shallow shells is investigated results of several benchmark examples are compared with the published work and good agreement is obtained copyright 2010 john wiley sons ltd

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

the koiter newton approach using von karman kinematics for buckling analyses of imperfection sensitive structures the koiter newton approach is a reduced basis method for nonlinear structural analyses the method combines koiter s approach as a predictor step and the newton arc length technique as a corrector step to trace the entire load displacement equilibrium path of a structure in a step by step manner this computationally highly efficient and accurate solution method has recently demonstrated a superior performance in nonlinear analyses compared to standard techniques in this paper we propose an extension to buckling imperfection sensitivity analyses exploiting the method s stability and reliability we present two different modeling techniques for imperfection loads that both profit from the koiter newton approach reducing the initial computation steps to a small fraction thereof we introduce von karman kinematics which neglect some nonlinear terms of the green strain displacement relations to further increase the computational efficiency of the analysis by an essential reduction of the computation effort required to obtain higher order derivatives of the strain energy using various numerical examples and benchmark tests we demonstrate the overall high quality and performance of the proposed method

non linear bending analysis of plates and shells by using a mixed spline boundary element and finite element method in this paper a mixed spline boundary element and finite element method is suggested to analyse non linear bending of plates and shells only the fundamental solutions for plates are required in order to establish the boundary integral equations a quadratic rectangular spline element is adopted to deal with the membrane effects of plates and shells numerical examples show that the approach developed in this paper is very effective and especially promising for the non linear analysis of plates and shells

fault diameter of interconnection networks abstract we introduce the concept of fault diameter of interconnection networks the motivation is to estimate the degradation of performance under maximally fault conditions we derive fault diameter of specific classes of commonly used interconnection networks and various types of product graphs

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

the direct boundary element method in plate bending the direct boundary element method based on the rayleigh green identity is employed for the static analysis of kirchhoff plates the starting point is a slightly modified version of stern s equations the focus is on the implementation of the method for linear elements and a hermitian interpolation for the deflection w the concept of element matrices is developed and the cauchy principal values of the singular integrals are given in detail the treatment of domain integrals the handling of internal supports the properties of the solution and the effect of singularities are discused numerical examples illustrate the various techniques in the appendix the influence functions for the second and third derivatives of the deflection w are given

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

second order asymptotics of visible mixed quantum source coding via universal codes the simplest example of a quantum information source with memory is a mixed source which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities considering a mixed source consisting of a general one parameter family of memoryless sources we derive the second order asymptotic rate for fixed length visible source coding furthermore we specialize our main result to a mixed source consisting of two memoryless sources our results provide the first example of the second order asymptotics for a quantum information processing task employing a resource with memory for the case of a classical mixed source using a finite alphabet our results reduce to those obtained by nomura and han to prove the achievability part of our main result we introduce universal quantum source codes achieving the second order asymptotic rates these are obtained by an extension of hayashi s construction of their classical counterparts

a boundary element analysis of symmetric laminated composite shallow shells this paper presents a boundary element formulation for the analysis of symmetric laminated composite shallow shells where only the boundary is discretized classical plate bending and plane elasticity formulations are coupled and effects of curvature are treated as body forces fundamental solutions for elastostatic formulations are used and body forces are written as a sum of approximation functions multiplied by unknown coefficients two approximation functions are used domain integrals which arise in the formulation are transformed into boundary integrals by the radial integration method results for the approximation functions are compared and the accuracy of the proposed formulation is assessed by results from literature it was shown that results obtained with the approximation function called augmented thin plate spline present very good agreement with literature even for shells that are not so shallow

nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method the geometric nonlinear buckling problem of a thin doubly curved shallow shell with all edges hinged is complicated and difficult to obtain an exact analytical solution thus differential equations are solved incrementally by using the differential quadrature method in this paper detailed formulations are worked out convergence study is performed several examples with various material properties curvatures and dimensions are investigated comparisons are made with existing semi analytical data or finite element data it is shown that the critical loads are lower than the data obtained by either so called adjacent equilibrium method or partitioned solution method the possible reasons to cause the difference are discussed

vibration analysis of functionally graded thin walled rotating blades under high temperature supersonic flow using the differential quadrature method in this study differential quadrature dq vibration analysis of a rotating thin walled blade made of functionally graded materials fgms operating under high temperature supersonic gas flow is investigated the governing equations are based on the first order shear deformation theory of beams which include the effects of the rotary inertias and the blade presetting angle quasi steady aerodynamic pressure loadings and steady wall temperature assumptions are made the explicit dq discretized form of the equations of motion and the related boundary conditions are presented the convergence of the method is examined and to verify its accuracy the results are compared with those of the galerkin method where excellent agreements are observed the effects of the mach number rotating speed geometric parameters and blade material properties on the natural frequencies are examined

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

ordering trees with algebraic connectivity and diameter abstract this paper is motivated by abreu s paper which proposed finding a total ordering of trees by their algebraic connectivity is still an open problem we first discuss how to find a total ordering of trees with diameter 4 then these results are used to determine first several orderings of trees by algebraic connectivity in nonincreasing order in last we present a class of trees with large diameter whose algebraic connectivity is larger than that of a tree with diameter 3

on optimal selection of interior points for applying discretized boundary conditions in dq vibration analysis of beams and plates the direct implementation of derivative boundary conditions at edge points was demonstrated to be simple flexible and computationally efficient in the vibration analysis of beams and plates by using the differential quadrature dq method in the approach the discretized governing equations at certain interior points need to be replaced by the discretized boundary conditions naturally one may have questions as to whether the replacement points can be selected arbitrarily and how to choose the optimal replacement points this paper tries to answer these questions and its focus is to investigate systematically the effect of the replacement location on the accuracy of the numerical solution from the error distribution analysis of derivative approximation it is found that the optimal position for the replacement is the interior point just adjacent to the boundary this conclusion is confirmed by the numerical experiments of free vibration analysis for beams and plates with various boundary conditions

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

free vibration analysis of curvilinear quadrilateral plates by the differential quadrature method a methodology for applying the differential quadrature dq method to the free vibration analysis of arbitrary quadrilateral plates is developed in our approach the irregular physical domain is transformed into a rectangular domain in the computational space the governing equation and the boundary conditions are also transformed into relevant forms in the computational space then all the computations are based on the computational domain as compared to the approach proposed by c w bert and m malik int j mech sci 38 589 1996 the present approach requires much less computational effort and virtual storage in addition the present work uses a simple and convenient way to implement clamped and simply supported boundary conditions an exact mapping technique is used to perform the coordinate transformation in this study some numerical examples are provided to show the computational efficiency of the present scheme

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

rectangular thick plates on winkler foundation differential quadrature element solution abstract this paper deals with the static analysis of homogenous isotropic rectangular plates on winkler foundation on the basis of first order shear deformation theory an improved differential quadrature dq method called the differential quadrature element method dqem has been developed for this analysis the plates considered are subjected to a patch load or a concentrated line load which are not solvable by the global dq method the convergence and comparison studies are carried out to establish the reliability of the dqem results then the numerical results for different boundary conditions i e ssss cccc s s s s and sfsf are presented showing the parametric effects of dimensions of loading area line relative thickness ratio and elastic foundation modulus on the deflection bending and twisting moments and shear forces at selected locations most of these data are new and due to the high accuracy of the dq solution they can be useful for benchmarking future work

a semi analytical dqem for free vibration analysis of thick plates with two opposite edges simply supported this paper is introducing a semi analytical differential quadrature element method dqem based on first order shear deformation theory for free vibration analysis of thick plates by decomposing the plate into a series of sub domains or elements any discontinuity in geometry material properties and elastic foundations in one direction can be handled conveniently classical as well as non classical boundary conditions can be imposed one benefits of this semi analytical dqem is reducing the storage requirements and the computational efforts needed to assemble the global equations the method would also increase the computational efficiency in comparison with the finite element method fem or differential quadrature method dqm analysis of such problems the accuracy versatility stability and convergence of the algorithm are certified

an accurate and efficient implementation of initial geometrical imperfections in the predictor corrector reduced order modeling method abstract a predictor corrector reduced order modeling method based on koiter theory is proposed for nonlinear buckling analysis of thin walled structures with initial geometric imperfections the imperfections are implemented into the von karman kinematics and are considered using an a priori and a posteriori manners respectively in buckling analysis since the nonlinear predictor obtained from the reduced order model with imperfections provides a fairly large step size in path tracing the a priori account of imperfections still shows advantages in computational efficiency the advantages are more significant when considering a posteriori the effects of imperfections in the reduced order model of the structure without imperfections which means building once and for all by simply adding some independent imperfection terms in the reduced system the a posteriori accounts of imperfections with the first second order accuracies are developed respectively to deal with the linear nonlinear prebuckling behaviors and small large imperfection amplitudes the good performance of the proposed method in terms of reliability accuracy and computational effort is demonstrated with several examples using the linear buckling modes or measured geometric shapes as whole field geometric imperfections

free vibration analysis of functionally graded conical cylindrical shell and annular plate structures with a four parameter power law distribution based on the first order shear deformation theory fsdt this paper focuses on the dynamic behavior of moderately thick functionally graded conical cylindrical shells and annular plates the last two structures are obtained as special cases of the conical shell formulation the treatment is developed within the theory of linear elasticity when materials are assumed to be isotropic and inhomogeneous through the thickness direction the two constituent functionally graded shell consists of ceramic and metal these constituents are graded through the thickness from one surface of the shell to the other a generalization of the power law distribution presented in literature is proposed two different four parameter power law distributions are considered for the ceramic volume fraction some material profiles through the functionally graded shell thickness are illustrated by varying the four parameters of power law distributions for the first power law distribution the bottom surface of the structure is ceramic rich whereas the top surface can be metal rich ceramic rich or made of a mixture of the two constituents and on the contrary for the second one symmetric and asymmetric volume fraction profiles are presented in this paper the homogeneous isotropic material can be inferred as a special case of functionally graded materials fgm the governing equations of motion are expressed as functions of five kinematic parameters by using the constitutive and kinematic relationships the solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell the discretization of the system equations by means of the generalized differential quadrature gdq method leads to a standard linear eigenvalue problem where two independent variables are involved without using the fourier modal expansion methodology numerical results concerning six types of shell structures illustrate the influence of the power law exponent of the power law distribution and of the choice of the four parameters on the mechanical behaviour of shell structures considered

on the reversible extraction of classical information from a quantum source consider a source of pure quantum states with von neumann entropy s by the quantum source coding theorem arbitrarily long strings of signals may be encoded asymptotically into s qubits per signal the schumacher limit in such a way that entire strings may be recovered with arbitrarily high fidelity suppose that classical storage is free while quantum storage is expensive and suppose that the states of do not fall into two or more orthogonal subspaces we show that if can be compressed with arbitrarily high fidelity into a qubits per signal plus any amount of auxiliary classical storage then a must still be at least as large as the schumacher limit s of thus no part of the quantum information content of can be faithfully replaced by classical information if the states do fall into orthogonal subspaces then a may be less than s but only by an amount not exceeding the amount of classical information specifying the subspace for a signal from the source

on algebraic connectivity and spectral integral variations of graphs abstract let g be a simple connected graph and l g be the laplacian matrix of g let a g be the second smallest eigenvalue of l g an eigenvector of l g corresponding to the eigenvalue a g is called a fiedler vector of g let y be a fiedler vector of g a characteristic vertex is a vertex u of g such that y u 0 and such that there is a vertex w adjacent to u satisfying y w 0 a characteristic edge is an edge u v such that y u y v

twice ramanujan sparsifiers we prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices as linear sized spectral sparsifiers of complete graphs are expanders our sparsifiers of arbitrary graphs can be viewed as generalizations of expander graphs in particular we prove that for every d 1 and every undirected weighted graph g v e w on n vertices there exists a weighted graph h v f tilde w with at most lceil d n 1 rceil edges such that for every x in mathbb r v x t l g x leq x t l h x leq bigl frac d 1 2 sqrt d d 1 2 sqrt d bigr cdot x t l g x where l g and l h are the laplacian matrices of g and h respectively thus h approximates g spectrally at least as well as a ramanujan expander with dn 2 edges approximates the complete graph we give an elementary deterministic polynomial time algorithm for constructing h

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

free vibration analysis of mindlin sector plates numerical solutions by differential quadrature method abstract in this paper the free vibration analysis of moderately thick sector plates based on mindlin s first order shear deformation theory is examined the solutions to this problem are determined using the differential quadrature dq method for numerical evaluation the dq formulations for free vibration of the mindlin sector plates in two dimensional polar co ordinate system are derived to demonstrate the accuracy of the dq method convergence and comparison studies are carried out in parametric study the first eight frequency parameters are computed for sector plates with different boundary conditions relative thickness ratios and sector angles 30 360 the effects of sector angle and relative thickness ratio on the frequency parameters are discussed

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

communicating probability distributions a rate distortion problem is solved that is motivated by a quantum data compression problem the goal is to send information about a source string x so that a receiver can construct a second string y for which the joint empirical probability distribution of x and y is close to some desired distribution the problem differs from the usual rate distortion problems in that one must consider both remote sources and distortion functions that are not averages of per letter distortion functions

two sided bounds on minimum error quantum measurement on the reversibility of quantum dynamics and on maximum overlap using directional iterates in a unified framework we estimate the following quantities of interest in quantum information theory 1 the minimum error distinguishability of arbitrary ensembles of mixed quantum states 2 the approximate reversibility of quantum dynamics in terms of entanglement fidelity this is referred to as channel adapted quantum error recovery when applied to the composition of an encoding operation and a noise channel 3 the maximum overlap between a bipartite pure quantum state and a bipartite mixed state that may be achieved by applying a local quantum operation to one part of the mixed state and 4 the conditional min entropy of bipartite quantum states a refined version of the author s techniques j tyson j math phys 50 032016 2009 for bounding the first quantity is employed to give two sided estimates of the remaining three quantities we obtain a closed form approximate reversal channel using a state dependent kraus decomposition our reversal may be interpreted as a quadratically

on quantum fidelities and channel capacities for the discrete memoryless quantum channel we show the equivalence of two different notions of quantum channel capacity that which uses the entanglement fidelity as its criterion for success in transmission and that which uses the minimum fidelity of pure states in a subspace of the input hilbert space as its criterion as a corollary any source with entropy rate less than the capacity may be transmitted with high entanglement fidelity we also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel this enables us to simplify a known upper bound for the channel capacity it also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity

a boundary element formulation for geometrically nonlinear analysis of shear deformable shells abstract a new boundary element method to solve geometrically nonlinear deflection problems of shear deformable shallow shells having quadratic mid surface is presented the displacement integral equations have been derived to obtain five integral equations in term of displacements two rotations one out of plane displacement and two in plane displacements the boundary is discretised into quadratic isoparametric elements and the domain is transferred to the boundary using the dual reciprocity technique a simple yet efficient load incremental technique is developed to solve the nonlinear problem several examples are presented and the results are in good agreement with the finite element method

second order asymptotics for source coding dense coding and pure state entanglement conversions we introduce two variants of the information spectrum relative entropy defined by tomamichel and hayashi which have the particular advantage of satisfying the data processing inequality i e monotonicity under quantum operations this property allows us to obtain one shot bounds for various information processing tasks in terms of these quantities moreover these relative entropies have a second order asymptotic expansion which in turn yields tight second order asymptotics for optimal rates of these tasks in the independent and identically distributed setting the tasks studied in this paper are fixed length quantum source coding noisy dense coding entanglement concentration pure state entanglement dilution and transmission of information through a classical quantum channel in the latter case we retrieve the second order asymptotics obtained by tomamichel and tan our results also yield the known second order asymptotics of fixed length classical source coding derived by hayashi the second order asymptotics of entanglement concentration and dilution provide a refinement of the inefficiency of these protocols a quantity which in the case of entanglement dilution was studied by harrow and lo we prove how the discrepancy between the optimal rates of these two processes in the second order implies the irreversibility of entanglement concentration established by kumagai and hayashi in addition the spectral divergence rates of the information spectrum approach isa can be retrieved from our relative entropies in the asymptotic limit this enables us to directly obtain the more general results of the isa from our one shot bounds

stationary quantum source coding in this article the quantum version of the source coding theorem is obtained for a completely ergodic source this result extends schumacher s quantum noiseless coding theorem for memoryless sources the control of the memory effects requires some earlier results of hiai and petz on high probability subspaces our result is equivalently considered as a compression theorem for noiseless stationary channels

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

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

differential cubature method for static solutions of arbitrarily shaped thick plates this paper presents the first endeavor to exploit the differential cubature method as an accurate and efficient global technique for fundamental solutions of arbitrarily shaped thick plates the method is examined here for its suitability for solving the boundary value problem of thick plates governing by the first order shear deformation theory using the method the governing differential equations and boundary conditions are transformed into sets of linear algebraic equations boundary conditions are implemented through discrete grid points by constraining displacements bending moments and rotations detailed discussion on the formulation and implementation of the method are presented the applicability efficiency and simplicity of the method are demonstrated through solving example plate problems of different shapes the accuracy of the method is verified by direct comparison with the known values

optimizing algebraic connectivity by edge rewiring robustness in complex networks is an ongoing research effort that seeks to improve the connectivity of networks against attacks and failures among other measures algebraic connectivity has been used to characterize processes such as damped oscillation of liquids in connected pipes similar characterizations include the number of edges necessary to disconnect a network the larger the algebraic connectivity the larger the number of edges required to disconnect a network and hence the more robust a network in this paper we answer the question which edge can we rewire to have the largest increase in algebraic connectivity furthermore we extend the rewiring of a single edge to rewiring multiple edges to realize the maximal increase in algebraic connectivity the answer to this question above can provide insights to decision makers within various domains such as communication and transportation networks who seek an efficient solution to optimize the connectivity and thus increase the robustness of their networks most importantly our analytical and numerical results not only provide insights to the number of edges to rewire but also the location in the network where these edges would effectuate the maximal increase in algebraic connectivity and therefore enable a maximal increase in robustness

general anisotropic doubly curved shell theory a differential quadrature solution for free vibrations of shells and panels of revolution with a free form meridian abstract the generalized differential quadrature gdq method is applied to study the dynamic behavior of anisotropic doubly curved shells and panels of revolution with a free form meridian the first order shear deformation theory fsdt is used to analyze the above mentioned moderately thick structural elements in order to include the effect of the initial curvature in the evaluation of the stress resultants three different approaches specifically qatu approach toorani lakis approach and reissner mindlin approach are considered and compared an improvement of the classical reissner mindlin theory crmt using a different kinematical model is considered by so doing a generalization of the theory of anisotropic doubly curved shells and panels of revolution is proposed four different anisotropic shell theories namely general first order shear deformation theory by qatu gfsdtq general first order shear deformation theory by toorani lakis gfsdttl general first order shear deformation theory by reissner mindlin gfsdtrm and classical reissner mindlin theory crmt are compared in order to show the differences and the accuracy of these theories the solution is given in terms of generalized displacement components of points lying on the middle surface of the shell simple rational bezier curves are used to define the meridian curve of the revolution structures results are obtained taking the meridian and circumferential coordinates into account without using the fourier modal expansion methodology furthermore gdq results are compared with those obtained by using commercial programs such as abaqus ansys nastran straus and pro mechanica very good agreement is observed

communicability graph and community structures in complex networks we use the concept of the network communicability e estrada n hatano communicability in complex networks phys rev e 77 2008 036111 to define communities in a complex network the communities are defined as the cliques of a communicability graph which has the same set of nodes as the complex network and links determined by the communicability function then the problem of finding the network communities is transformed to an all clique problem of the communicability graph we discuss the efficiency of this algorithm of community detection in addition we extend here the concept of the communicability to account for the strength of the interactions between the nodes by using the concept of inverse temperature of the network finally we develop an algorithm to manage the different degrees of overlapping between the communities in a complex network we then analyze the usa airport network for which we successfully detect two big communities of the eastern airports and of the western central airports as well as two bridging central communities in striking contrast a well known algorithm groups all but two of the continental airports into one community

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

compressing quantum mixed state sources by sending classical information we consider visible compression for discrete memoryless sources of mixed quantum states when only classical information can be sent from alice to bob we assume that bob knows the source statistics and that alice and bob have access to the same source of random numbers we put in an information theoretic framework some previous results on visible compression for sources of states with commuting density operators and remove the commutativity requirement we derive a general achievable compression rate which is for the noncommutative case still higher than the known lower bound we also present several related problems of classical information theory and show how they can be used to answer some questions of the mixed state compression problem

quantum data processing we prove a data processing inequality for quantum communication channels which states that processing a received quantum state may never increase the mutual information between input and output states

static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method a new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi boundary conditions in two dimensional problems since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi degree of freedom at the boundary points the method is easier to extend to two or three dimensional problems a new version of the differential quadrature plate element has been established for demonstration the essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined the methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method