saint venant end effects in multilayered piezoelectric laminates the saint venant end effects and stress decay in multilayered laminates of piezoelectric materials are studied a state space approach is developed in the context of generalized plane strain by means of matrix algebra and transfer matrix the characteristics of the stress decay in 2 d piezoelectric strips and laminates are examined their elastic counterparts are included as special cases evaluation of the characteristic decay length for typical materials shows that the saint venant end effects are significant it also indicates that the analysis based on the plane strain assumption is misleading

deconstructing plane anisotropic elasticity part i the latent structure of lekhnitskii s formalism abstract general solutions of the stress and displacements in two dimensional anisotropic elasticity may be represented by eigenvectors and analytic functions of the complex variables x iy but the representation takes different forms for five distinct types of materials as determined by the elastic compliance matrix in this paper explicit expressions of the general solutions are derived for each type of anisotropic materials in terms of the eigenvalues i and the elements of it is shown that for degenerate and extra degenerate materials the generalized eigenvectors and associated eigensolutions may be obtained by the derivative rule the barnett lothe tensors are defined in terms of unnormalized eigenvectors by the same set of relations regardless of material degeneracy explicit expressions of these tensors are given in concise forms depending only on the multiplicity of the eigenvalues the six dimensional matrix formalism and normalization of the eigenvectors are found to be neither essential nor expedient for the analysis except as a device for abridged expressions of matrix identities

wronskian and grammian determinant structure solutions for a variable coefficient forced kadomtsev petviashvili equation in fluid dynamics abstract taking the inhomogeneities of media and nonuniform boundaries into account the variable coefficient equations can describe more realistic physical phenomena than their constant coefficient counterparts in this paper a variable coefficient forced kadomtsev petviashvili equation with inhomogeneous nonlinearity dispersion perturbed term and external force is investigated using a modified dependent variable transformation this equation is first bilinearized then the n soliton solutions in two different kinds of determinant structure that is the wronskian and grammian determinant soliton solutions for the variable coefficient forced kadomtsev petviashvili equation are presented and verified under certain coefficient constraints the sample soliton solutions are given by choosing suitable determinant elements and several kinds of soliton evolution situations are discussed and illustrated

spectral regularization algorithms for learning large incomplete matrices we use convex relaxation techniques to provide a sequence of regularized low rank solutions for large scale matrix completion problems using the nuclear norm as a regularizer we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm our algorithm soft impute iteratively replaces the missing elements with those obtained from a soft thresholded svd with warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter the computationally intensive part of our algorithm is in computing a low rank svd of a dense matrix exploiting the problem structure we show that the task can be performed with a complexity of order linear in the matrix dimensions our semidefinite programming algorithm is readily scalable to large matrices for example soft impute takes a few hours to compute low rank approximations of a 106 x 106 incomplete matrix with 107 observed entries and fits a rank 95 approximation to the full netflix training set in 3 3 hours our methods achieve good training and test errors and exhibit superior timings when compared to other competitive state of the art techniques

kdv and kink antikink solitons in car following models abstract the jams in the congested traffic are related with various density waves which might be governed by the nonlinear wave equations such as the korteweg de vries kdv equation the burgers equation and the modified korteweg de vries mkdv equation three different versions of optimal velocity models are examined the stability conditions of the models are obtained by using the linear stability theory the kdv equation near the neutral stability line and the mkdv equation around the critical point are derived by applying the reductive perturbation method respectively the traffic jams could be thus described by the kdv and kink antikink soliton solutions for the two kinds of equations the general solutions are given for which can lead to specific solutions in previous work moreover they are applied to solve a new model the full velocity difference model and the corresponding kdv and kink antikink soliton solutions could be quickly obtained which demonstrates the general solutions presented herein are useful

non classical symmetry reduction example of the boussinesq equation a symmetry of an equation will leave the set of all solutions invariant a conditional symmetry will leave only a subset of solutions defined by some differential condition invariant the authors show how a specific class of conditional symmetries can be used to reduce a partial differential equation to an ordinary one in particular for the boussinesq equation these conditional symmetries together with the ordinary ones provide all possible reductions to ordinary differential equations a group theoretical explanation of the recently obtained new reductions is provided

detecting deviating data cells a multivariate dataset consists of n cases in d dimensions and is often stored in an n by d data matrix it is well known that real data may contain outliers depending on the situation outliers

semi analytical solutions for free vibration of anisotropic laminated plates in cylindrical bending elasticity solutions for free vibration of angle ply laminates subjected to cylindrical bending are obtained using a newly developed semi analytical approach the thickness domain is solved analytically using the transfer matrix method based on the state space concept while the in plane domain is solved approximately via the technique of differential quadrature the present method is applicable to arbitrarily thick laminates and for treating arbitrary edge conditions the method is verified by comparisons with the exact solutions of pagano s problem effects of variation of ply angle on the vibration properties of laminates are investigated mode shape switching is observed when ply angle varies numerical results for fully clamped thick laminates are presented for future references

a state space formalism for anisotropic elasticity part ii cylindrical anisotropy abstract a state space formalism for thermoelastic analysis of a cylindrically anisotropic elastic body is developed by proper grouping of the stress and taking r ij instead of ij as the stress variables the three dimensional equations of elasticity in the cylindrical coordinates are concisely formulated into a state equation and an output equation using matrix notations the general solution for the generalized plane problems is derived in a simple manner effects of extension torsion bending temperature change and body force are accounted for systematically the eigen relation arising from the solution process and the degenerate cases of repeated eigenvalues are examined to demonstrate the power of the formalism exact solutions to extension torsion bending and thermo mechanical loading of a general cylindrically anisotropic circular tube or bar are obtained the surface tractions and temperature field may vary in but not in z displacement as well as traction boundary conditions are considered it appears that many problems of anisotropic elasticity are best viewed and treated in the state space framework

alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates abstract by introducing two displacement functions and two stress functions the governing equations of the linear theory of magneto electro thermo elasticity with transverse isotropy are simplified on selecting certain physical quantities as the basic unknowns two new state equations are established each of them is order reduced when compared with the one reported recently in literature leading to a higher numerical efficiency the material inhomogeneity along the axis of symmetry z direction can be taken into account and an approximate laminate model is employed to facilitate deriving analytical solutions the validity of new formulations is examined by considering a laminated magneto electro elastic rectangular plate and good agreement is obtained with existent results a plate with a functionally graded property is then analyzed the effect of magnetoelectric coupling in a batio3 cofe2o4 composite predicted from the micromechanics simulation is studied quantitatively

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

state space approach for stress decay in laminates abstract stress decay in laminates due to edge boundary effects are studied through a state space formulation a self equilibrium eigenstress field accounting for the multilayer construction of the laminate is derived using the state variables and the transfer matrix method the eigenvalue determination requires only the solution of 6 6 determinants irrespective of the number of laminae through combinations of the eigenstress field and the interior stress field a complete solution valid in the boundary layer as well as in the interior region of the laminate can be obtained for verification the formulation is first applied to determining the eigenstress in a homogeneous anisotropic layer and then the free edge stress decay in laminates under uniform extension is examined

connection between static electromagnetoelasticity and anisotropic elasticity and its applications connection between electromagnetoelasticity and anisotropic elasticity is explored in the state space setting in the absence of electric charges and currents the basic equations of static electromagnetoelasticity are formulated into a state equation and an output equation which bear a remarkable resemblance to the corresponding equations of elasticity accordingly the solutions for various steady state problems of electromagnetoelasticity can be determined in parallel to their elastic counterparts for illustration the generalized plane problems are treated within the context exact solutions for the electromagnetoelastic fields in a half space subjected to line loads and in an infinite plate with an elliptic notch under extension are determined in a simple way

lie transformations similarity reduction and solutions for the nonlinear madelung fluid equations with external potential the application of lie group methods to a system of coupled nonlinear partial differential equations representing what is usually called a madelung fluid is shown the generating operators of the transformation group that depends on five arbitrary group constants will be constructed and all subclasses of systems of ordinary differential equations derived by similarity reduction will be presented in tabular form two subclasses of physical interest are investigated in detail and the similarity solutions are compared with solutions found earlier by the application of inverse scattering transform techniques to the cubic nonlinear schrodinger equation similarity solutions for the madelung equations with linear external potential x f0x are presented

two layer fluid formation and propagation of periodic solitons induced by 3 1 dimensional kp equation abstract in this paper multi wave solutions of kadomtsev petviashvili kp equation with time variable coefficient are obtained it is found that the formation of two layer with bright and dark soliton which are symmetric these solitons are transversely periodic as periodic of two soliton and two antisoliton in time with cusps localized in space these two types of waves propagate in an opposite direction relative the higher layer the autonomous behavior may be argued to the fact that the kp is composed of the derivative and the anti derivative terms

deconstructing plane anisotropic elasticity part ii stroh s formalism sans frills abstract eigensolutions for all types of anisotropic elastic materials are obtained in terms of the eigenvalues and the anisotropic elastic stiffness the generalized eigenvectors and eigensolutions in the degenerate and extra degenerate cases are obtained by the derivative rule a complete set of unnormlized eigenvectors now given in terms of the elastic moduli define the barnett lothe tensors by the same expressions irrespective of material degeneracy explicit expressions of the barnett lothe tensors are obtained in various forms depending on the multiplicity of eigenvalues these expressions complement the alternative expressions of part i in terms of the elastic compliances a new family of extra degenerate materials is found suggesting the superabundance of such materials a concise proof of the equivalence of the eigensystems of the compliance based and elasticity based formalisms is given eigenrelations applicable to all cases of material degeneracy are presented in both three dimensional and six dimensional matrix formalisms

new solutions to pressuring shearing torsion and extension of a cylindrically anisotropic elastic circular tube or bar the problem of a cylindrically anisotropic elastic circular tube or bar subjected to a uniform pressure shearing torsion or extension has been studied by ting the stroh formalism for twodimensio

an imputation regularized optimization algorithm for high dimensional missing data problems and beyond missing data are frequently encountered in high dimensional problems but they are usually difficult to deal with by using standard algorithms such as the expectation maximization algorithm and its variants to tackle this difficulty some problem specific algorithms have been developed in the literature but there still lacks a general algorithm this work is to fill the gap we propose a general algorithm for high dimensional missing data problems the algorithm works by iterating between an imputation step and a regularized optimization step at the imputation step the missing data are imputed conditionally on the observed data and the current estimates of parameters and at the regularized optimization step a consistent estimate is found via the regularization approach for the minimizer of a kullback leibler divergence defined on the pseudocomplete data for high dimensional problems the consistent estimate can be found under sparsity constraints the consistency of the averaged estimate for the true parameter can be established under quite general conditions the algorithm is illustrated by using high dimensional gaussian graphical models high dimensional variable selection and a random coefficient model

torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity some exact solutions and end effects abstract torsion of elastic circular bars of radially inhomogeneous cylindrically orthotropic materials is studied with emphasis on the end effects to examine the conjecture of saint venant s torsion we consider torsion of circular bars with one end fixed and the other end free on which tractions that results in a pure torque are prescribed arbitrarily over the free end surface exact solutions that satisfy the prescribed boundary conditions point by point over the entire boundary surfaces are derived in a unified manner for cylindrically orthotropic bars with or without radial inhomogeneity and for their counterparts of saint venant s torsion stress diffusion due to the end effect is examined in the light of the exact solutions

a state space formalism for piezothermoelasticity a state space formalism for electrothermoelastic analysis of a linear piezoelectric body is developed a novel feature of the formalism is that by proper grouping of the field variables and using matrix notations the three dimensional equations of piezothermoelasticity are concisely formulated into a state equation and an output equation which bear a striking resemblance to their elastic counterparts the formalism is remarkably simple with which one deals with only three vector quantities with the 13 independent electromechanical variables as their components and six submatrices that represent all the material constants for a piezoelectric material of the most general kind in this work emphasis is placed on the state space formulation and solution to the generalized plane problem exact solutions for a piezoelectric half space under a line of electromechanical loading and an infinite piezoelectric plate with an elliptical notch subjected to inplane loads are determined with relative ease in many cases piezoelectric solutions can be obtained directly from the corresponding elastic solutions by a simple replacement of the corresponding matrices on the basis of the formalism

matrix completion from a few entries let m be an n n matrix of rank r and assume that a uniformly random subset e of its entries is observed we describe an efficient algorithm which we call optspace that reconstructs m from e o rn observed entries with relative root mean square error 1 2 rmse c nr e 1 2 with probability larger than 1 1 n3 further if r o 1 and m is sufficiently unstructured then optspace reconstructs it exactly from e o n log n entries with probability larger than 1 1 n3 this settles in the case of bounded rank a question left open by candes and recht and improves over the guarantees for their reconstruction algorithm the complexity of our algorithm is o e r log n which opens the way to its use for massive data sets in the process of proving these statements we obtain a generalization of a celebrated result by friedman kahn szemeredi and feige ofek on the spectrum of sparse random matrices

piezoelectric solid with an elliptic inclusion or hole the two dimensional problem of an elliptic hole in a solid of anisotropic piezoelectric material is studied the stroh formalism is adopted here real form solutions are obtained along the hole boundary in the case of an arbitrarily prescribed vector field on the hole surface for an elliptic rigid inclusion of electric conductor subjected to a line force a torque and a line charge a real form solution at the interface is obtained finally general solutions for an elliptic piezoelectric inclusion with uniform loading at infinity are investigated

investigation on a nonisospectral fifth order korteweg de vries equation generalized from fluids in this paper a nonisospectral fifth order korteweg de vries equation generalized from fluids is investigated with symbolic computation such equation is transformed into its bilinear form through a proposed dependent variable transformation with one more parameter than those in the existing literature n soliton solutions backlund transformation and lax pair in the explicit forms are constructed based on the above results the characteristic line method is applied to discuss the features of the solitons for the nonisospectral problem i e the controllable solitonic velocities and widths four types of solitonic structures with the different solitonic velocities widths amplitudes and backgrounds are also illustrated

pattern alternating maximization algorithm for missing data in high dimensional problems we propose a novel and efficient algorithm for maximizing the observed log likelihood of a multivariate normal data matrix with missing values we show that our procedure based on iteratively regressing the missing on the observed variables generalizes the standard em algorithm by alternating between different complete data spaces and performing the e step incrementally in this non standard setup we prove numerical convergence to a stationary point of the observed log likelihood for high dimensional data where the number of variables may greatly exceed sample size we perform regularization using a lasso type penalty this introduces sparsity in the regression coefficients used for imputation permits fast computation and warrants competitive performance in terms of estimating the missing entries we show on simulated and real data that the new method often improves upon other modern imputation techniques such as k nearest neighbors imputation nuclear norm minimization or a penalized likelihood approach with an l1 penalty on the concentration matrix

pfaffianization of the generalized variable coefficient kadomtsev petviashvili equation abstract in this paper the pfaffianization procedure is applied to the generalized variable coefficient kadomtsev petviashvili vckp equation which can describe the realistic nonlinear phenomena in the fluid dynamics and plasmas using the pfaffianization procedure the coupled system for the generalized vckp equation is derived together with the wronski type pfaffian solution for this generalized coupled vckp system under certain coefficient constraint furthermore the gramm type pfaffian solution for such a coupled system is presented and verified by virtue of the pfaffian identities

long wave interaction over varying topography abstract the propagation of long waves on the surface of a three dimensional fluid domain bounded below by slowly varying topography is considered there are two important limits if the initial data can be written in terms of a discrete set of one dimensional wavefronts the resulting wave field is described by a set of variable coefficient korteweg de vries kdv equations for each wave along its characteristic curve waves along different characteristics interact with each other yielding phase shifts that depend on the wave amplitudes the angle between the rays and the local depth if the initial data is modulated slowly in the direction parallel to the wavefronts the wave field is described by variable coefficient kadomtsev petviashvili kp equations along rays for topography varying only in one direction we calculate explicit results for the interaction between two sets of periodic or solitary waves and show the equivalence of a single nearly normally incident kdv wave and a normally incident kp wave

extended displacement discontinuity method for an interface crack in a three dimensional transversely isotropic piezothermoelastic bi material part 2 numerical method abstract the extended displacement discontinuity boundary integral differential equation method is developed to analyze interface cracks of arbitrary shape in three dimensional transversely isotropic piezothermoelastic bi materials the fundamental solutions for unit point extended displacement discontinuities on the interface are derived and the induced extended displacements and stresses are all expressed in terms of extended displacement discontinuities an analysis method is proposed based on the analogy between the obtained boundary integral differential equations and those for interface cracks in isotropic thermoelastic bi materials the singular indices and the singular behaviors of the near crack tip fields are studied and two new extended stress intensity factors are obtained meanwhile the extended stress intensity factors sifs including two new fracture modes are derived in terms of the extended displacement discontinuities

hodograph transformations of linearizable partial differential equations in this paper an algorithmic method is developed for transforming quasilinear partial differential equations of the form u t g u u nx f u u x cdots u n 1 x u mx equiv partial m u partial x m where dg du not equiv 0 into semilinear equations i e equations of the above form with g u 1 this crucially involves the use of hodograph transformations i e transformations involving the interchange of dependent and independent variables furthermore the most general quasilinear equation of the above form is found that can be mapped via a hodograph transformation to a semilinear form this algorithm provides a method for establishing whether a given quasilinear equation is linearizable i e is solvable in terms of either a linear partial differential equation or of a linear integral equation in particular this method is used to show how the painleve tests may be applied to quasilinear equations this appears to resolve the problem that solutions of lineariz

laminated composite tubes under extension torsion bending shearing and pressuring a state space approach we present a state space approach to extension torsion bending shearing and pressuring of laminated composite tubes one of the novel features is that we have formulated the basic equations of anisotropic elasticity in the cylindrical coordinate system into a state equation by a judicious arrangement of the displacement and stress variables so that the system matrix is independent of r the formulation suggests a systematic way using matrix algebra and the transfer matrix to determine the stress and deformation in a multilayered cylindrically anisotropic tube under applied loads that do not vary in the axial direction an exact analysis of the tube subjected to uniform surface tractions an axial force a torque and bending moments is presented the solution consists of an axisymmetric state due to extension torsion uniform pressuring and shearing and an asymmetric state due to bending the formalism indicates that extension torsion and pressuring interact uniform shearing causes pure shears in the laminated tube regardless of the number of layers these deformations are uncoupled with bending of the tube

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

symmetries of differential equations from sophus lie to computer algebra the topic of this article is the symmetry analysis of differential equations and the applications of computer algebra to the extensive analytical calculations which are usually involved in it the whole area naturally decomposes into two parts depending on whether ordinary or partial differential equations are considered we show how a symmetry may be applied to lower the order of an ordinary differential equation or to obtain similarity solutions of partial differential equations the computer algebra packages sods and spde respectively which have been developed to perform almost all algebraic manipulations necessary to determine the symmetry group of a given differential equation are presented furthermore it is argued that the application of computer algebra systems has qualitatively changed this area of applied mathematics

the boundary layer phenomena in two dimensional transversely isotropic piezoelectric media by exact symplectic expansion a separable variable method is introduced to find the exact homogeneous solutions of a two dimensional transversely isotropic piezoelectric media to handle general boundary conditions the usual method of separable variables for partial differentiation equations cannot be readily applicable due to the tangling of the unknowns and their derivatives introducing dual variables of stresses we obtain a set of first order hamiltonian equations whose eigensolutions are symplectic spanning over the solution space to cover all possible boundary conditions the solutions consist of two parts the first part is the derogative zero eigenvalue solutions of the saint venant type together with all their jordan chains the second part is the decaying non zero eigenvalue solutions describing the boundary layer effects the classical solutions are actually the zero eigenvalue solutions representing the simple extension bending equipotential field and the uniform electric displacement on the other hand the non zero eigenvalue solutions represent the localized solutions which are sensitive to the boundary conditions and are decaying rapidly with respect to the distance from the boundaries some rate of decay curves of the newly found non zero eigenvalue solutions are shown by numerical examples finally the complete boundary layer effects are quantified for the first time

the power of convex relaxation near optimal matrix completion this paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries this is known as the matrix completion problem and comes up in a great number of applications including the famous netflix prize and other similar questions in collaborative filtering in general accurate recovery of a matrix from a small number of entries is impossible but the knowledge that the unknown matrix has low rank radically changes this premise making the search for solutions meaningful this paper presents optimality results quantifying the minimum number of entries needed to recover a matrix of rank r exactly by any method whatsoever the information theoretic limit more importantly the paper shows that under certain incoherence assumptions on the singular vectors of the matrix recovery is possible by solving a convenient convex program as soon as the number of entries is on the order of the information theoretic limit up to logarithmic factors this convex program simply finds among all matrices consistent with the observed entries that with minimum nuclear norm as an example we show that on the order of nr log n samples are needed to recover a random n x n matrix of rank r by any method and to be sure nuclear norm minimization succeeds as soon as the number of entries is of the form nr polylog n

solutions of a variable coefficient kadomtsev petviashvili equation via computer algebra we apply the truncated painleve expansion and computer algebra to a type of the variable coefficient kadomtsev petviashvilli equations and find a class of the analytical solutions along with the corresponding constraints on the variable coefficients shown in this class are the physically meaningful solutions which possess the usual soliton profile

new soliton like and periodic like solutions for the kdv equation in this paper based on a system of riccati equations a newly generally projective riccati equation expansion method is presented it is direct and more powerful than the tanh function method generally projective riccati equation method and can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics the well known kdv equation is chosen to illustrate the algorithm such that more families of new explicit solutions are obtained which contain soliton like and periodic like solutions this algorithm can also be applied to many other nonlinear differential equations

a revisit of a cylindrically anisotropic tube subjected to pressuring shearing torsion extension and a uniform temperature change abstract the problem of a cylindrically anisotropic tube or bar was seemed to be first examined by lekhnitskii 1981 lekhnitskii s g 1981 theory of elasticity of an anisotropic body trans from the revised 1977 russian edition mir moscow recently a thorough investigation of the subject was performed by ting 1996 ting t c t 1996 pressuring shearing torsion and extension of a circular tube or bar of cylindrically anisotropic material proc roy soc lond a452 2397 2421 in which a formulation akin to that of stroh s formalism is employed to resolve the boundary value problem subjected to a uniform pressure shearing torsion and uniform extension in a continuing paper ting 1999 ting t c t 1999 new solutions to pressuring shearing torsion and extension of a cylindrically anisotropic elastic circular tube or bar proc roy soc lond to appear rederived the solutions based on a modified formalism of lekhnitskii in which the solutions are in terms of elastic compliances reduced elastic compliances as well as doubly reduced compliance the results are much more compact and simpler than those of the earlier one independently in this work we construct the governing system also under the lekhnitskii s framework nevertheless the present work and ting s formulation 1999 are not alike besides the loads considered in ting 1996 1999 we add the effect of a uniform temperature change in the formulation the assumption that the stresses depend only on r makes it possible to incorporate the various loading cases considered in addition to the explicit forms of admissible stresses we derive the admissible displacements which are ensured to be single valued for a multiply connected domain in contrast to the ting s works 1996 1999 which often require superpositions of two or more basic solutions the present solutions offer complete forms of solutions ready for direct calculations we also report that as in rectilinearly anisotropic solids an entire analogy is observed between the fields of a uniform axial extension and a uniform temperature change in cylindrically anisotropic solids

transformations and multi solitonic solutions for a generalized variable coefficient kadomtsev petviashvili equation kadomtsev petviashvili equations with variable coefficients can be used to characterize many nonlinear phenomena in fluid dynamics and plasma physics more realistically than the equations with constant coefficients hereby a generalized variable coefficient kadomtsev petviashvili equation with nonlinearity dispersion and perturbed terms is investigated transformations of which the consistency conditions are exactly the painleve integrability conditions to the korteweg de vries equation cylindrical korteweg de vries equation kadomtsev petviashvili equation and cylindrical kadomtsev petviashvili equation are presented by formal dependent variable transformation assumptions using the hirota bilinear method from the variable coefficient bilinear equation the multi solitonic solution auto backlund transformation and lax pair for the variable coefficient kadomtsev petviashvili equation are obtained moreover the influence of inhomogeneity coefficients on solitonic structures and interaction properties is discussed for physical interest and possible applications

pressuring shearing torsion and extension of a circular tube or bar of cylindrically anisotropic material one of the novel features of the present paper is that we have written the equation of equilibrium and the stress strain law of an inhomogeneous anisotropic linear elastic material in a compact form for cylindrical coordinate system using matrix notation for a two dimensional deformation the result resembles stroh s sextic formalism in a rectangular coordinate system we then consider the material to be cylindrically anisotropic it means that the elastic stiffnesses referred to a cylindrical coordinate system are constants the problem of a circular tube subjected to a uniform normal stress and shearing stresses at the inner and outer surfaces of the tube is studied also studied are the axial extension and torsion of the tube unlike isotropic materials for which the applied normal stress or shear stress induces only the normal or shear stress all three displacement components and most of the six stress components are nonzero for general anisotropic materials this is particularly interesting for the uniform axial extension of the tube for an isotropic material the stress 33 is the only non zero and uniform stress inside the tube for a cylindrically anisotropic material the stresses rr and 3 are also non zero moreover they depend on r and are not uniform a solid cylinder or a cylinder with a pin hole is a special case of a tube it is shown that for the loads mentioned above including the axial extension the stress may be unbounded at the pinhole

on a unified approach to transformations and elementary solutions of painleve equations an algorithmic method is developed for investigating the transformation properties of second order equations of painleve type this method which utilizes the singularity structure of these equations yields explicit transformations which relate solutions of the painleve equations ii vi with different parameters these transformations easily generate rational and other elementary solutions of the equations the relationship between painleve equations and certain new equations quadratic in the second derivative of painleve type is also discussed

the anisotropic heisenberg spin chain and the nonlinear schrodinger equation abstract it is shown that the solutions of the continuous anisotropic heisenberg spin chain ahsc can be obtained from the linear integral equation which was proposed in a previous paper for the solutions of the isotropic heisenberg spin chain ihsc and the nonlinear schrodinger equation nls an explicit expression is obtained for the miura transformation which maps the solutions of the ahsc on solutions of the nls in the second part of the paper we investigate the similarity solutions of these partial differential equations which leads to ordinary differential equations of painleve type as an application we discuss some new solutions of painleve iv

a state space formalism for anisotropic elasticity part i rectilinear anisotropy a state space formalism for anisotropic elasticity including the thermal effect is developed a salient feature of the formalism is that it bridges the compliance based and stiffness based formalisms in a natural way the displacement and stress components and the thermoelastic constants of a general anisotropic elastic material appear explicitly in the formulation yet it is simple and clear this is achieved by using the matrix notation to express the basic equations and grouping the stress in such a way that it enables us to cast neatly the three dimensional equations of anisotropic elasticity into a compact state equation and an output equation the homogeneous solution to the state equation for the generalized plane problem leads naturally to the eigen relation and the sextic equation of stroh extension twisting bending temperature change and body forces are accounted for through the particular solution based on the formalism the general solution for generalized plane strain and generalized torsion of an anisotropic elastic body are determined in an elegant manner

lie transformations nonlinear evolution equations and painleve forms we present the results of a systematic investigation of invariance properties of a large class of nonlinear evolution equations under a one parameter continuous lie group of transformations it is shown that in general the corresponding invariant variables the subclass of which is the usual similarity variables lead to ordinary differential equations of painleve type in the case of inverse scattering transform solvable equations as conjectured by ablowitz ramani and segur this is found to be also true for certain higher spatial dimensional versions such as the kadomtsev petviashivilli two dimensional sine gordon and ernst equations for the nonsolvable equations considered here this invariance study leads to ordinary differential equations with movable critical points

convergence theorems for generalized alternating minimization procedures the em algorithm is widely used to develop iterative parameter estimation procedures for statistical models in cases where these procedures strictly follow the em formulation the convergence properties of the estimation procedures are well understood in some instances there are practical reasons to develop procedures that do not strictly fall within the em framework we study em variants in which the e step is not performed exactly either to obtain improved rates of convergence or due to approximations needed to compute statistics under a model family over which e steps cannot be realized since these variants are not em procedures the standard g em convergence results do not apply to them we present an information geometric framework for describing such algorithms and analyzing their convergence properties we apply this framework to analyze the convergence properties of incremental em and variational em for incremental em we discuss conditions under these algorithms converge in likelihood for variational em we show how the e step approximation prevents convergence to local maxima in likelihood

a refined state space formalism for piezothermoelasticity abstract the state space formalism for piezothermoelasticity tarn j q 2002c a state space formalism for piezothermoelasticity international journal of solids and structures 39 5173 5184 is refined by introducing the generalized displacement vector and generalized stress vectors as the fundamental variables in which appropriate electrical variables are included the basic equations of piezoelectricity with temperature change are formulated neatly into a state equation and an output equation in terms of the generalized displacement vector and generalized stress vectors the formalism bears a remarkable resemblance to its elastic counterpart various problems of piezothermoelasticity can be solved by simple extension of the corresponding solutions of anisotropic elasticity for illustration some fundamental problems are studied within the context and exact solutions are obtained in a systematic and self contained manner

a circular elastic cylinder under its own weight an exact analysis of deformation and stress field in a finite circular elastic cylinder under its own weight is presented with emphasis on the end effect the problem is formulated on the basis of the state space formalism for axisymmetric deformation of a transversely isotropic body upon delineating the hamiltonian characteristics of the formulation a rigorous solution which satisfies the end conditions is determined by using eigenfunction expansion the results show that the end effect is significant but confined to a local region near the base where the displacement and stress distributions are remarkably different from those according to the simplified solution that gives a uniaxial stress state it is more pronounced in the cylinder with the bottom plane being perfectly bonded than in smooth contact with a rigid base