cramer rao induced bounds for candecomp parafac tensor decomposition this paper presents a cramer rao lower bound crlb on the variance of unbiased estimates of factor matrices in canonical polyadic cp or candecomp parafac cp decompositions of a tensor from noisy observations i e the tensor plus a random gaussian i i d tensor a novel expression is derived for a bound on the mean square angular error of factors along a selected dimension of a tensor of an arbitrary dimension the expression needs less operations for computing the bound o nr6 than the best existing state of the art algorithm o n3r6 operations where n and r are the tensor order and the tensor rank insightful expressions are derived for tensors of rank 1 and rank 2 of arbitrary dimension and for tensors of arbitrary dimension and rank where two factor matrices have orthogonal columns the results can be used as a gauge of performance of different approximate cp decomposition algorithms prediction of their accuracy and for checking stability of a given decomposition of a tensor condition whether the crlb is finite or not a novel expression is derived for a hessian matrix needed in popular damped gauss newton method for solving the cp decomposition of tensors with missing elements beside computing the crlb for these tensors the expression may serve for design of damped gauss newton algorithm for the decomposition

blind multiuser detection from moe to subspace methods the minimum output energy moe multiuser receiver has been shown to approach the minimum mean square error mmse receiver at high signal to noise ratio snr however performance degradation is incurred by noise induced channel estimation error in this paper we propose a power of r por technique to significantly improve the performance of the moe receiver it is shown that the new receiver asymptotically converges to the mmse receiver without performance penalty the convergence is established either under high snr with large exponent raised in the power of the covariance matrix or with sufficiently large number of data samples connection between our por method and a widely studied subspace method is investigated from the respective optimization criteria asymptotic equivalence between these two methods is also established extensive simulations based on finite data samples show that the proposed method significantly outperforms the subspace method in systems with medium to heavy loading severe multipath distortion or smaller processing gain moreover adaptive implementation of the proposed method exhibits very robust performance in a dynamic loading environment

on faithfully flat fibrations by a punctured line abstract let r be a noetherian normal domain in this paper we present the structure of a faithfully flat r algebra a whose generic and codimension one fibres are of the form k x 1 f x we also investigate minimal sufficient conditions for such an algebra to be finitely generated over r

some results on codimension one a1 fibrations abstract we prove a few results on the sufficiency of generic and codimension one fibre conditions for determination of the structure of algebras of transcendence degree one we first show that over a noetherian normal domain r a faithfully flat subalgebra of a finitely generated algebra whose generic and codimension one fibres are a 1 is necessarily the symmetric algebra of an invertible ideal of r we next prove a structure theorem for a faithfully flat algebra over a locally factorial krull domain r whose generic and codimension one fibres are a 1 for r local we deduce a minimal sufficient condition for the algebra to be finitely generated and hence a 1

kruskal s uniqueness inequality is sharp abstract kruskal proved that a tensor in v 1 v 2 v m of rank r has a unique decomposition as a sum of r pure tensors if a certain inequality is satisfied we will show the uniqueness fails if the inequality is weakened we give two different constructions for counterexamples

new als methods with extrapolating search directions and optimal step size for complex valued tensor decompositions in signal processing data analysis and scientific computing one often encounters the problem of decomposing a tensor into a sum of contributions to solve such problems both the search direction and the step size are two crucial elements in numerical algorithms such as alternating least squares algorithm als owing to the nonlinearity of the problem the often used linear search direction is not always powerful enough in this paper we propose two higher order search directions the first one geometric search direction is constructed via a combination of two successive linear directions the second one algebraic search direction is constructed via a quadratic approximation of three successive iterates then in an enhanced line search along these directions the optimal complex step size contains two arguments modulus and phase a current strategy is elscs that finds these two arguments alternately so it may suffer from a local optimum we broach a direct method which determines these two arguments simultaneously so as to obtain the global optimum finally numerical comparisons on various search direction and step size schemes are reported in the context of blind separation equalization of convolutive ds cdma mixtures the results show that the new search directions have greatly improve the efficiency of als and the new step size strategy is competitive

coupling of two and three dimensional composite shell elements in linear and non linear applications abstract a numerical model for the non linear analysis of laminates is presented the developed element is based on piecewise polynomial interpolation in thickness direction although the total number of degrees of freedom is comparable to a discretization with 3d brick elements this approach provides several advantages e g a simple mesh generation due to a 2d type data structure and a better bending behavior the developed isoparametric quadrilateral finite element allows prediction of the complete stress state furthermore a transition element is presented which is used to couple the developed element with 5 parameter shell elements several linear and non linear examples are presented to illustrate the performance of the developed numerical model

updated lagrangian formulation of a flat triangular element for thin laminated shells an updated lagrangian formulation of a three node flat triangular shell element is presented for geometrically nonlinear analysis of laminated plates and shells the flat shell element is obtained by combining the discrete kirchhoff theory plate bending element and a membrane element that is similar to the allman element but a derivative of the linear strain triangular element results are presented for large rotation static response analysis of a cantilever beam under end moment cylindrical shell under pinching and stretching loads a hemispherical shell under pinching and stretching loads and a ring plate under a line load for dynamic response analysis of a cylindrical panel and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel to estimate the accuracy of the present formulation in predicting the nonlinear response of large flexible structures static analysis of an apex loaded circular arch is performed the arch is a building block of a large inflatable structure the results are in good agreement with those available in the existing literature and those obtained using the commercial finite element software abaqus demonstrating the accuracy of the present formulation he two most widely adopted approaches in the finite element analysis of shells are use of curved shell elements based on a suitable shell theory and approximation of the curved structure by an assemblage of flat shell elements in which the membranebending coupling is brought about as a result of material anisotropy and transformation of the element stiffness matrices computed in a local coordinate system to the global coordinate system prior to assembly the curved shell elements can be computationally very expensive especially in the case of nonlinear analysis because of the complexity of the formulation and the need to compute the curvature information flat shell elements are more attractive because of their simplicity and the ease with which they can be built from alreadyexisting familiar membrane and plate bending elements though a large number of elements are required to accurately model curved structures the analysis is computational ly less expensive because of extremely simple formulation updated lagrangian formulations have been predominantly used in the flat shell formulations available in the existing literature in an updated lagrangian formulation all of the variables are referred to a known configuration the reference configuration which is updated continuously during the deformation process if the rigid body modes are removed from the total or incremental displacements the resulting deformational translations and rotations are very small and hence a linearized incremental formulation1 can be used in a linearized incremental formulation the stresses are computed using linear strain displacement relations the tangent stiffness matrix contains only the linear stiffness matrix and the initial stress matrix the stiffness matrices resulting from the nonlinear terms in the strain displacement relations are neglected resulting in very economical analysis if the rigid body modes are not removed all nonlinear terms in the strain displacement relations will have to be considered for computing the stresses and the tangent stiffness matrix a three node flat triangular shell element was introduced by argyris et al 2 for nonlinear elastic stability problems this formula

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

nonlinear free vibrations of composite plates abstract the evolution of the natural mode method nmm for finite element analysis of complex composite structures continues in the present study by applying its principles and formulating the kinematically consistent matrix of a model three node multilayered triangular element both translational and rotational inertia are included in the mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element linear eigenfrequencies are validated with experimental and finite element solutions subsequently the large amplitude nonlinear undamped free vibration of composite plates is investigated a computational scheme is conceived whereby the structure is initially displaced by conducting a full geometrically nonlinear static analysis and subsequently set to transient nonlinear free oscillations by removing the static loading in this regard we discuss the two structured eulerian convective computational schemes employed namely the ariban scheme accumulation of rigid body and natural modes for static nonlinear analysis and the cubic hermitian scheme cuherm for large displacement transient deformation numerical examples demonstrate the efficiency of the formulation and the potential of the natural mode method to deal vigorously with intricate nonlinear time dependent phenomena as well as its potential to provide answers for larger and more complex structures the study also indicates the efficiency and tailoring flexibility offered by advanced composite structural systems

tensor space time frequency coding with semi blind receivers for mimo wireless communication systems in this paper we first introduce two new classes of constrained tensor models that we call generalized paratuck n1 n and tucker n1 n models a new tensor space time frequency tstf coding structure is then proposed for mimo ofdm cdma wireless communication systems two semi blind receivers relying on the new generalized paratuck model are derived for solving the problem of joint channel and symbol estimation one is iterative and based on a two step alternating least squares als algorithm the other one is a closed form and low complexity solution which consists of the kronecker product least squares kpls estimation of the symbol matrix and a matrix unfolding of the channel tensor uniqueness of the underlying tensor model is discussed and system design requirements are derived for applicability of the als and kpls receivers we also show that the so called tstf system can be viewed as an extension of three existing tensor based st tst stf coding systems that are described in a unified framework computer simulation results illustrate the good performance of the tstf system which outperforms the considered existing tensor based systems both in terms of symbol estimation quality and allocation flexibility

deterministic and probabilistic conditions for finite completability of low tucker rank tensor we investigate the fundamental conditions on the sampling pattern i e locations of the sampled entries for finite completability of a low rank tensor given some components of its tucker rank in order to find the deterministic necessary and sufficient conditions we propose an algebraic geometric analysis on the tucker manifold which allows us to incorporate multiple rank components in the proposed analysis in contrast with the conventional geometric approaches on the grassmannian manifold this analysis characterizes the algebraic independence of a set of polynomials defined based on the sampling pattern which is closely related to finite completability of the sampled tensor where finite completability simply means that the number of possible completions of the sampled tensor is finite probabilistic conditions are then studied and a lower bound on the sampling probability is given which guarantees that the proposed deterministic conditions on the sampling patterns for finite completability hold with high probability furthermore using the proposed geometric approach for finite completability we propose a sufficient condition on the sampling pattern that ensures there exists exactly one completion of the sampled tensor

candecomp parafac decomposition of high order tensors through tensor reshaping in general algorithms for order 3 candecomp parafac cp also coined canonical polyadic decomposition cpd are easy to implement and can be extended to higher order cpd unfortunately the algorithms become computationally demanding and they are often not applicable to higher order and relatively large scale tensors in this paper by exploiting the uniqueness of cpd and the relation of a tensor in kruskal form and its unfolded tensor we propose a fast approach to deal with this problem instead of directly factorizing the high order data tensor the method decomposes an unfolded tensor with lower order e g order 3 tensor on the basis of the order 3 estimated tensor a structured kruskal tensor of the same dimension as the data tensor is then generated and decomposed to find the final solution using fast algorithms for the structured cpd in addition strategies to unfold tensors are suggested and practically verified in the paper

on finite generation of r subalgebras of r x we show that over a complete discrete valuation ring r whose residue field is algebraically closed any noetherian r subalgebra of r x is finitely generated and present examples of non finitely generated noetherian r subalgebras of r x satisfying various properties we also give a sufficient codimension one criterion for a noetherian r subalgebra of r x to be finitely generated over r when r is locally factorial

rank regularization and bayesian inference for tensor completion and extrapolation a novel regularizer of the parafac decomposition factors capturing the tensor s rank is proposed in this paper as the key enabler for completion of three way data arrays with missing entries set in a bayesian framework the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities this probabilistic approach can naturally accommodate general models for the data distribution lending itself to various fitting criteria that yield optimum estimates in the maximum a posteriori sense in particular two algorithms are devised for gaussian and poisson distributed data that minimize the rank regularized least squares error and kullback leibler divergence respectively the proposed technique is able to recover the ground truth tensor rank when tested on synthetic data and to complete brain imaging and yeast gene expression datasets with 50 and 15 of missing entries respectively resulting in recovery errors at 11 db and 15 db

frequency domain blind mimo system identification based on second and higher order statistics we present a novel frequency domain framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs the system frequency response is obtained based on singular value decomposition svd of a matrix constructed based on the power spectrum and slices of polyspectra of the system output by appropriately selecting the polyspectra slices we can create a set of such matrices each of which could independently yield the solution of they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance the freedom to select the polyspectra slices allows us to bypass the frequency dependent permutation ambiguity that is usually associated with frequency domain svd while at the same time allows us compute and cancel the phase ambiguity an asymptotic consistency analysis of the system magnitude response estimate is performed

kernel of locally nilpotent r derivations of r x y in this paper we study the kernel of a non zero locally nilpotent r derivation of the polynomial ring r x y over a noetherian integral domain r containing a field of characteristic zero we show that if r is normal then the kernel has a graded r algebra structure isomorphic to the symbolic rees algebra of an unmixed ideal of height one in r and conversely the symbolic rees algebra of any unmixed height one ideal in r can be embedded in r x y as the kernel of a locally nilpotent r derivation of r x y we also give a necessary and sufficient criterion for the kernel to be a polynomial ring in general

on the non existence of optimal solutions and the occurrence of degeneracy in the candecomp parafac model the candecomp parafac cp model decomposes a three way array into a prespecified number of r factors and a residual array by minimizing the sum of squares of the latter it is well known that an optimal solution for cp need not exist we show that if an optimal cp solution does not exist then any sequence of cp factors monotonically decreasing the cp criterion value to its infimum will exhibit the features of a so called degeneracy that is the parameter matrices become nearly rank deficient and the euclidean norm of some factors tends to infinity we also show that the cp criterion function does attain its infimum if one of the parameter matrices is constrained to be column wise orthonormal

parallel factor analysis in sensor array processing this paper links multiple invariance sensor array processing mi sap to parallel factor parafac analysis which is a tool rooted in psychometrics and chemometrics parafac is a common name for low rank decomposition of three and higher way arrays this link facilitates the derivation of powerful identifiability results for mi sap shows that the uniqueness of single and multiple invariance esprit stems from uniqueness of low rank decomposition of three way arrays and allows tapping on the available expertise for fitting the parafac model the results are applicable to both data domain and subspace mi sap formulations the paper also includes a constructive uniqueness proof for a special parafac model

a block component model based blind ds cdma receiver in this paper we consider the problem of blind multiuser separation equalization in the uplink of a wideband ds cdma system in a multipath propagation environment with intersymbol interference isi to solve this problem we propose a multilinear algebraic receiver that relies on a new third order tensor decomposition and generalizes the parallel factor parafac model our method is deterministic and exploits the temporal spatial and spectral diversities to collect the received data in a third order tensor the specific algebraic structure of this tensor is then used to decompose it in a sum of user s contributions the so called block component model bcm receiver does not require knowledge of the spreading codes the propagation parameters nor statistical independence of the sources but relies instead on a fundamental uniqueness condition of the decomposition that guarantees identifiability of every user s contribution the development of fast and reliable techniques to calculate this decomposition is important we propose a blind receiver based either on an alternating least squares als algorithm or on a levenberg marquardt lm algorithm simulations illustrate the performance of the algorithms

non linear vibration of initially stressed hybrid composite plates abstract non linear partial differential equations based on the reissner mindlin plate theory are derived for large amplitude vibration of a hybrid composite plate in a general state of non uniform initial stress the equations include the effects of transverse shear and rotary inertia using these derived governing equations the large amplitude vibration of an initially stressed hybrid composite plate is studied the initial stress is taken to be a combination of pure bending stress and a uniform normal stress in the plane of the plate the galerkin method is used to reduce the governing non linear partial differential equations to ordinary non linear differential equations and the runge kutta method is used to obtain the non linear frequencies the linear frequency can be obtained by neglecting the non linear terms in ordinary non linear differential equations the non linear vibration frequencies are sensitive to the vibration amplitude elastic modulus laminate stacking sequence and state of initial stresses the effects of various parameters on the large amplitude free vibrations are presented

blind identification and source separation in 2 spl times 3 under determined mixtures under determined mixtures are characterized by the fact that they have more inputs than outputs or with the antenna array processing terminology more sources than sensors the problem addressed is that of identifying and inverting the mixture which obviously does not admit a linear inverse identification is carried out with the help of tensor canonical decompositions on the other hand the discrete distribution of the sources is utilized for performing the source extraction the under determined mixture being either known or unknown the results presented in this paper are limited to two dimensional 2 d mixtures of three sources

nonlinear dynamic analysis of shells with the triangular element tric abstract tric is a facet triangular shell element which is based on the natural mode method it has been shown that the tric shell element satisfies the individual element test and in the framework of the nonconsistent formulation the convergence requirements are fulfilled while it has been proved to be very efficient in linear and nonlinear static problems moreover another major advantage in the formulation of this element is the incorporation of the transverse shear deformations in a way that defies the shear locking phenomenon in this work the derivation of the consistent and lumped mass matrices of the tric element is presented so that it can be used in linear and nonlinear dynamic problems both translational and rotational inertia are included in the consistent mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element all the kinematical and geometrical arguments that are invoked for the derivation of the consistent mass matrix are briefly presented moreover two formulations of the lumped mass matrix of tric are derived the first formulation is based entirely on geometrical considerations whereas the second is based on lumping the consistent mass matrix of tric finally the element s robustness and accuracy will be shown by applying it to properly selected benchmark examples of nonlinear shell dynamics while its computational efficiency will be demonstrated by comparing the cpu performance of the element with the other available shell elements

finite element theory for curved and twisted beams based on exact solutions for three dimensional solids part 2 anisotropic and advanced beam models consistent finite element formulations for beams made of anisotropic materials and taking into account non classic inhomogeneous torsion have been developed the formulations are based on a kinematical hypothesis that includes exact solutions for three dimensional solids under terminal loading they describe warping of the cross sections in and out of their planes as well as their rigid displacements and rotations their large deformation and geometrically exact description by finite rotations are considered for the cases of monoclinic orthotropic and transversely isotropic materials exact solutions for the solid made from a monoclinic material have been deduced c 1998 elsevier science s a all rights reserved

large displacement analysis of thin walled beams with generic open section a finite element formulation for geometric non linear analysis of elastic straight thin walled beams is presented the updated lagrangian procedure is used for a stiffness matrix derivation to analyse large displacements or buckling behaviour of space frames the stiffness matrix is developed for a generic cross section and is equally efficient for symmetric monosymmetric or asymmetric open sections some non linear strain terms usually neglected in the literature have been considered resulting in a formulation which also includes the initial bimoment and torsion effect for all cross sections analysed the proposed method has been implemented and the results of sample problems are presented

comparison of natural frequencies of laminates by 3 d theory part i rectangular plates abstract the three dimensional theory of laminated plates and shells has been developed by chao et al 10 13 62 63 with many applications to impact and shock modal analyses in this research a complete survey of the literature is made on the free vibration natural frequencies of simply supported rectangular plates various boundary conditions are composed of fixed pin hinge roller and sliding pin supported edges the lowest frequencies are obtained in the present study in comparison with those in earlier studies as a result of the close natural state reached in keeping with the three dimensional boundary and interlaminar continuity conditions via a 3 d augmented energy variational approach

structure of a fibrations over one dimensional seminormal semilocal domains abstract in this paper we give a structure theorem for an a fibration over a one dimensional noetherian seminormal semilocal domain and show that in this situation any a fibration whose spectrum occurs as an affine open subscheme of the spectrum of an a 1 fibration equivalently an affine line a 1 is actually a the structure theorem provides examples of a fibrations over one dimensional noetherian seminormal semilocal domains whose spectra are not affine open subschemes of any affine line a 1 over the base ring we also construct examples of nontrivial a fibrations over one dimensional noetherian non seminormal local domains whose spectra are open subschemes of a 1 fibrations over the base ring

functional parallel factor analysis for functions of one and two dimensional arguments parallel factor analysis parafac is a useful multivariate method for decomposing three way data that consist of three different types of entities simultaneously this method estimates trilinear components each of which is a low dimensional representation of a set of entities often called a mode to explain the maximum variance of the data functional parafac permits the entities in different modes to be smooth functions or curves varying over a continuum rather than a collection of unconnected responses the existing functional parafac methods handle functions of a one dimensional argument e g time only in this paper we propose a new extension of functional parafac for handling three way data whose responses are sequenced along both a two dimensional domain e g a plane with x and y axis coordinates and a one dimensional argument technically the proposed method combines parafac with basis function expansion approximations using a set of piecewise quadratic finite element basis functions for estimating two dimensional smooth functions and a set of one dimensional basis functions for estimating one dimensional smooth functions in a simulation study the proposed method appeared to outperform the conventional parafac we apply the method to eeg data to demonstrate its empirical usefulness

a corotational based geometrically nonlinear generalized beam theory buckling fe analysis abstract a geometrically nonlinear generalized beam theory is formulated and the results in the framework of buckling analyses are discussed the geometrically nonlinear model is recovered reusing the model available in the linear context this generalization to the nonlinear context is obtained exploiting the corotational based method called implicit corotational method starting from a mixed energy description of the continuum in terms of nonlinear biot stress strain tensors and using convenient assumptions for the linear stress strain tensors once obtained the nonlinear model has been implemented using a flexibility based finite element the results of buckling analyses for different and complex beam cross section geometries emphasizing distortional and local buckling behaviors are presented and comparisons with finite element shell models made

khatri rao space time codes space time st coding techniques exploit the spatial diversity afforded by multiple transmit and receive antennas to achieve reliable transmission in scattering rich environments st block codes are capable of realizing full diversity and spatial coding gains at relatively low rates st trellis codes can achieve better rate diversity tradeoffs at the cost of high complexity on the other hand v blast supports high rates but has no built in spatial coding and does not work well with fewer receive than transmit antennas we propose a novel linear block coding scheme based on the khatri rao matrix product the proposed scheme offers flexibility for achieving full rate or full diversity or a desired rate diversity tradeoff and it can handle any transmit receive antenna configuration or signal constellation the proposed codes are shown to have numerous desirable properties including guaranteed unique linear decodability built in blind channel identifiability and efficient near maximum likelihood decoding

parafac based blind estimation of possibly underdetermined convolutive mimo systems in this paper we consider the problem of blind identification of a convolutive multiple input multiple output mimo system with no outputs and ni inputs while many methods have been proposed to blindly identify convolutive mimo systems with no ges ni overdetermined very scarce results exist for the case of underdetermined all of which refer to systems that either have some special structure or special and values in this paper we show that as long as independent of whether the system is overdetermined or underdetermined we can always find the appropriate order of statistics that guarantees identifiability of the system response within trivial ambiguities we also propose an algorithm to reach the solution that consists of parallel factorization parafac of a way tensor containing th order statistics of the system outputs followed by an iterative scheme for a certain order of statistics we provide the description of the class of identifiable mimo systems we also show that this class can be expanded by applying parafac decomposition to a pair of tensors instead of one tensor the proposed approach constitutes a novel scheme for estimation of underdetermined systems and improves over existing approaches for overdetermined systems

thermomechanical response of solids at high strains natural approach abstract the paper develops in pursuance of 4 the theoretical framework appertaining to coupled thermomechanical deformations of solids subject to large as well as inelastic deformations the essential feature of the analysis is a consistent natural formulation which encompasses also all thermodynamic aspects on the other hand it must be admitted that current concepts on mechanical constitutive assumptions 5 6 are not sufficiently sophisticated to permit a precise generalisation for the purpose of incorporating thermomechanical effects and delivering a fully compatible theory of the coupled problem uniqueness and bifurcation of the solutions as well as stable postcritical deformation paths are also considered in this account furthermore algorithms for the solution of the nonlinear algebraic equations representing the discretised problem and in particular quasi newton techniques are discussed the paper concludes with a number of applications of technical relevance

on uniqueness in candecomp parafac one of the basic issues in the analysis of three way arrays by candecomp parafac cp has been the question of uniqueness of the decomposition kruskal 1977 has proved that uniqueness is guaranteed when the sum of thek ranks of the three component matrices involved is at least twice the rank of the solution plus 2 since then little has been achieved that might further qualify kruskal s sufficient condition attempts to prove that it is also necessary for uniqueness except for rank 1 or 2 have failed but counterexamples to necessity have not been detected the present paper gives a method for generating the class of all solutions or at least a subset of that class given a cp solution that satisfies certain conditions this offers the possibility to examine uniqueness for a great variety of specific cp solutions it will be shown that kruskal s condition is necessary and sufficient when the rank of the solution is three but that uniqueness may hold even if the condition is not satisfied when the rank is four or higher

static and dynamic analysis of space frames using simple timoshenko type elements in this paper a finite element method for geometrically and materially non linear analyses of space frames is described beams with both solid and thin walled open cross sections are considered the equations of equilibrium are formulated using an updated incremental lagrangian description the elements developed can undergo large displacements and rotations but the incremental rotations are assumed to be small the material behaviour is described by elastoplastic temperature dependent elastoplastic and viscoplastic models with special reference to metals computationally more economical formulations based on the relationship between stress resultants and generalized strain quantities are also presented in the case of thin walled beams the torsional behaviour is modelled using a two parameter warping model where the angle of twist and the axial variation of warping have independent approximations this approach yields average warping shear strains directly from the displacement assumptions and no discrepancy between stress and strain fields exists

on finite generation of noetherian algebras over two dimensional regular local rings abstract let r be a complete regular local ring with an algebraically closed residue field and let a be a noetherian r subalgebra of the polynomial ring r x it has been shown in 4 that if dim r 1 then a is necessarily finitely generated over r in this paper we give necessary and sufficient conditions for a to be finitely generated over r when dim r 2 and present an example of a noetherian normal non finitely generated r subalgebra of r x over r c u v

blind parafac receivers for ds cdma systems this paper links the direct sequence code division multiple access ds cdma multiuser separation equalization detection problem to the parallel factor parafac model which is an analysis tool rooted in psychometrics and chemometrics exploiting this link it derives a deterministic blind parafac ds cdma receiver with performance close to non blind minimum mean squared error mmse the proposed parafac receiver capitalizes on code spatial and temporal diversity combining thereby supporting small sample sizes more users than sensors and or less spreading than users interestingly parafac does not require knowledge of spreading codes the specifics of multipath interchip interference doa calibration information finite alphabet constant modulus or statistical independence whiteness to recover the information bearing signals instead parafac relies on a fundamental result regarding the uniqueness of low rank three way array decomposition due to kruskal 1977 1988 and generalized herein to the complex valued case that guarantees identifiability of all relevant signals and propagation parameters these and other issues are also demonstrated in pertinent simulation experiments

on algebras which are locally mathbb a 1 in codimension one let r be a noetherian normal domain call an r algebra a locally a1 in codimension one if rp r a is a polynomial ring in one variable over rp for every height one prime ideal p in r we shall describe a general structure for any faithfully flat r algebra a which is locally a1 in codimensionone and deduce results giving sufficient conditions for such an r algebra to be a locally polynomial algebra we also give a recipe for constructing r algebras which are locally a1 in codimension one when r is a normal affine spot i e a normal local domain obtained by a localisation of an affine domain we give criteria for a faithfully flat r algebra a which is locally a1 in codimensionone to be krull and a further condition for a to be noetherian the results are used to construct intricate examples of faithfully flat r algebras locally a1 in codimension one which are noetherian normal but not finitely generated

kruskal s permutation lemma and the identification of candecomp parafac and bilinear models with constant modulus constraints candecomp parafac cp analysis is an extension of low rank matrix decomposition to higher way arrays which are also referred to as tensors cp extends and unifies several array signal processing tools and has found applications ranging from multidimensional harmonic retrieval and angle carrier estimation to blind multiuser detection the uniqueness of cp decomposition is not fully understood yet despite its theoretical and practical significance toward this end we first revisit kruskal s permutation lemma which is a cornerstone result in the area using an accessible basic linear algebra and induction approach the new proof highlights the nature and limits of the identification process we then derive two equivalent necessary and sufficient uniqueness conditions for the case where one of the component matrices involved in the decomposition is full column rank these new conditions explain a curious example provided recently in a previous paper by sidiropoulos who showed that kruskal s condition is in general sufficient but not necessary for uniqueness and that uniqueness depends on the particular joint pattern of zeros in the possibly pretransformed component matrices as another interesting application of the permutation lemma we derive a similar necessary and sufficient condition for unique bilinear factorization under constant modulus cm constraints thus providing an interesting link to and unification with cp

semi analytical finite elements in the higher order theory of beams abstract the paper presents semi analytical finite elements leading to the development of a higher order theory for beams an analysis of existing beam theories reveals their semi analytical character the semi analytical finite element sfe method proposed assumes the cross section of a solid beam to be an assemblage of certain semi analytical elements the sfe method is based on independent approximations of three dimensional fields of displacements and stresses the method reflects the multi level nature of beams where conventional finite elements are transferred to the level of beam equations for heuristic considerations a mathematical formulation of the linear theory of a solid beam involves the equations of compatibility equilibrium and constitutive relationships i e the elastic law as well as static and kinematic boundary conditions compatibility conditions are derived directly by using finite element approximations while equilibrium equations constitutive equations and boundary conditions may be derived by applying stationarity of a modified hellinger reissner functional this derivation may be also defined by straightforward application of a generalised virtual work formulation the equations of a beam are formulated in terms of generalised variables integral resultants of stresses and strains as well as of nodal displacements the definition of generalised variables is assigned to the nodes of the finite element mesh bending warping and other higher order deformation modes are described automatically finally the set of governing equations includes mixed algebraic differential operators their explicit expressions depend on one of the element types isoparametric subparametric or superparametric the versatility of sfe is demonstrated in practical applications involving well known solutions the classical euler bernoulli and timoshenko theories are derived using a single one dimensional element the beams with a thin walled cross section are described as an assemblage of semi analytical elements on the basis of a higher order theory the conventional semi analytically based finite elements sabfe are derived their basic relations are also presented some numerical examples of the applications to thin walled beams illustrate the basic features possible extensions of sfe to dynamics geometric non linearity and shells are briefly discussed

blind mimo system estimation based on parafac decomposition of higher order output tensors we present a novel framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs samples of the system frequency response are obtained based on parallel factorization parafac of three or four way tensors constructed based on respectively third or fourth order cross spectra of the system outputs the main difficulties in frequency domain methods are frequency dependent permutation and filtering ambiguities we show that the information available in the higher order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation ambiguities and a linear phase ambiguity important features of the proposed approach are that it does not require channel length information needs no phase unwrapping and unlike the majority of existing methods needs no prewhitening of the system outputs

three mode factor analysis by means of candecomp parafac a three mode covariance matrix contains covariances of n observations e g subject scores on j variables for k different occasions or conditions we model such an jk jk covariance matrix as the sum of a common covariance matrix having candecomp parafac form and a diagonal matrix of unique variances the candecomp parafac form is a generalization of the two mode case under the assumption of parallel factors we estimate the unique variances by minimum rank factor analysis the factors can be chosen oblique or orthogonal our approach yields a model that is easy to estimate and easy to interpret moreover the unique variances the factor covariance matrix and the communalities are guaranteed to be proper a percentage of explained common variance can be obtained for each variable condition combination and the estimated model is rotationally unique under mild conditions we apply our model to several datasets in the literature and demonstrate our estimation procedure in a simulation study

blind identification of underdetermined mixtures based on the characteristic function the complex case blind identification of underdetermined mixtures can be addressed efficiently by using the second characteristic function caf of the observations our contribution is twofold first we propose the use of a levenberg marquardt algorithm herein called lemacaf as an alternative to an alternating least squares algorithm known as alescaf which has been used recently in the case of real mixtures of real sources second we extend the caf approach to the case of complex sources for which the previous algorithms are not suitable we show that the complex case involves an appropriate tensor stowage which is linked to a particular tensor decomposition an extension of the lemacaf algorithm called then proposed to blindly estimate the mixing matrix by exploiting this tensor decomposition in our simulation results we first provide performance comparisons between third and fourth order versions of alescaf and lemacaf in various situations involving bpsk sources then a performance study of is carried out considering 4 qam sources these results show that the proposed algorithm provides satisfying estimations especially in the case of a large underdeterminacy level

blind identification of underdetermined mixtures by simultaneous matrix diagonalization in this paper we study simultaneous matrix diagonalization based techniques for the estimation of the mixing matrix in underdetermined independent component analysis ica this includes a generalization to underdetermined mixtures of the well known sobi algorithm the problem is reformulated in terms of the parallel factor decomposition parafac of a higher order tensor we present conditions under which the mixing matrix is unique and discuss several algorithms for its computation

accelerated canonical polyadic decomposition using mode reduction canonical polyadic decomposition candecomp cpd also known as parallel factor analysis parafac is widely applied to nth order n 3 tensor analysis existing cpd methods mainly use alternating least squares iterations and hence need to unfold tensors to each of their n modes frequently which is one major performance bottleneck for large scale data especially when the order n is large to overcome this problem in this paper we propose a new cpd method in which the cpd of a high order tensor i e is realized by applying cpd to a mode reduced one typically third order tensor followed by a khatri rao product projection procedure this way is not only quite efficient as frequently unfolding to n modes is avoided but also promising to conquer the bottleneck problem caused by high collinearity of components we show that under mild conditions any nth order cpd can be converted to an equivalent third order one but without destroying essential uniqueness and theoretically they simply give consistent results besides once the cpd of any unfolded lower order tensor is essentially unique it is also true for the cpd of the original higher order tensor error bounds of truncated cpd are also analyzed in the presence of noise simulations show that compared with state of the art cpd methods the proposed method is more efficient and is able to escape from local solutions more easily

explanation and elimination of shear locking and membrane locking with field consistence approach abstract in this paper in the context of beam elements shear locking and membrane locking are explained and cured in a unified way with a field consistence approach in the view of field consistence approach when transverse displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are adopted shear locking will occur similarly when in plane displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are used membrane locking will happen the beam elements derived by field consistence approach are not only free of shear locking and membrane locking but also highly efficient compared with their isoparametric counterparts although theoretically the internal forces generalized strains in mixed variational principles can vary independently they are neither independent to each other nor independent of displacement fields from the point of view of the field consistence approach

a multilayer composite triangular element for steady state conduction convection radiation heat transfer in complex shells abstract our latest study presents the theoretical formulation and computer implementation of a three node six degrees of freedom multilayer flat triangular element intended for the study of the temperature fields in complex multilayer composite shells inherent in the formulation in this first introductory and self consistent systematic study are the three modes of heat transfer namely conduction convection and radiation the latter introducing in our theoretical model strong nonlinear effects in the present discourse all nonlinear terms are strictly due to radiation the material properties are assumed independent of temperature but this in no way restricts the generality of the basic theory the formulation is based on a first order thermal lamination theory which assumes a linear through the thickness temperature variation the following features are uniquely implemented in the computer model 1 1 exact integration of all matrices including the highly nonlinear radiation matrix 2 2 exact integration of all derivative jacobian matrices for efficient nonlinear analysis 3 3 geometrical generality achieved by an arbitrarily oriented inexpensive flat shell element 4 4 compatibility with structural elements 5 5 computational efficiency and simplicity a predictor corrector scheme in the form of the newton raphson method is adopted for the solution of the stead state nonlinear problem numerical examples ranging from simple panels to complex anisotropic shells substantiate the theoretical formulation and show the potential of the present laminated triangular element in the computer simulation of temperature effects in complex geometries

sufficient conditions for uniqueness in candecomp parafac and indscal with random component matrices a key feature of the analysis of three way arrays by candecomp parafac is the essential uniqueness of the trilinear decomposition we examine the uniqueness of the candecomp parafac and indscal decompositions in the latter the array to be decomposed has symmetric slices we consider the case where two component matrices are randomly sampled from a continuous distribution and the third component matrix has full column rank in this context we obtain almost sure sufficient uniqueness conditions for the candecomp parafac and indscal models separately involving only the order of the three way array and the number of components in the decomposition both uniqueness conditions are closer to necessity than the classical uniqueness condition by kruskal

adaptive algorithms to track the parafac decomposition of a third order tensor the parafac decomposition of a higher order tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines existing parafac algorithms are computationally demanding and operate in batch mode both serious drawbacks for on line applications when the data are serially acquired or the underlying model changes with time adaptive parafac algorithms that can track the sought decomposition at low complexity would be highly desirable this is a challenging task that has not been addressed in the literature and the topic of this paper given an estimate of the parafac decomposition of a tensor at instant t we propose two adaptive algorithms to update the decomposition at instant t 1 the new tensor being obtained from the old one after appending a new slice in the time dimension the proposed algorithms can yield estimation performance that is very close to that obtained via repeated application of state of art batch algorithms at orders of magnitude lower complexity the effectiveness of the proposed algorithms is illustrated using a mimo radar application tracking of directions of arrival and directions of departure as an example

constrained tensor modeling approach to blind multiple antenna cdma schemes in this paper we consider an uplink multiple antenna code division multiple access cdma system linking several multiple antenna mobile users to one multiple antenna base station for this system a constrained third order tensor decomposition is introduced for modeling the multiple antenna transmitter as well as the received signal the constrained structure of the proposed tensor decomposition is characterized by two constraint matrices that have a meaningful physical interpretation in our context they can be viewed as canonical allocation matrices that define the allocation of users data streams and spreading codes to the transmit antennas the distinguishing features of the proposed tensor modeling with respect to the already existing tensor based cdma models are i it copes with multiple transmit antennas and spreading codes per user and ii it models several spatial spreading multiplexing schemes with multiple spreading codes by controlling the constrained structure of the tensor signal model a systematic design procedure for the canonical allocation matrices leading to a unique blind symbol or joint blind symbol code recovery is proposed which allows us to derive a finite set of multiple antenna schemes for a fixed number of transmit antennas identifiability of the proposed tensor model is discussed and a blind multiuser detection receiver based on the alternating least squares algorithm is considered for performance evaluation of several multiple antenna cdma schemes derived from the constrained modeling approach

fourth order cumulant based blind identification of underdetermined mixtures in this paper we study two fourth order cumulant based techniques for the estimation of the mixing matrix in underdetermined independent component analysis the first method is based on a simultaneous matrix diagonalization the second is based on a simultaneous off diagonalization the number of sources that can be allowed is roughly quadratic in the number of observations for both methods explicit expressions for the maximum number of sources are given simulations illustrate the performance of the techniques

cramer rao lower bounds for low rank decomposition of multidimensional arrays unlike low rank matrix decomposition which is generically nonunique for rank greater than one low rank three and higher dimensional array decomposition is unique provided that the array rank is lower than a certain bound and the correct number of components equal to array rank is sought in the decomposition parallel factor parafac analysis is a common name for low rank decomposition of higher dimensional arrays this paper develops cramer rao bound crb results for low rank decomposition of three and four dimensional 3 d and 4 d arrays illustrates the behavior of the resulting bounds and compares alternating least squares algorithms that are commonly used to compute such decompositions with the respective crbs simple to check necessary conditions for a unique low rank decomposition are also provided

on kruskal s uniqueness condition for the candecomp parafac decomposition let x be a real valued three way array the candecomp parafac cp decomposition is written as x under bar y under bar 1 y under bar r e where y r are rank 1 arrays and e under bar is a rest term each rank 1 array is defined by the outer product of three vectors a r b r and c r i e y ijk r a i r b j r c k t these vectors make up the r columns of the component matrices a b and c if 2r 2 is less than or equal to the sum of the k ranks of a b and c then the fitted part of the decomposition is unique up to a change in the order of the rank 1 arrays and rescaling counterscaling of each triplet of vectors a r b r c r forming a rank 1 array this classical result was shown by kruskal his proof is however rather inaccessible and does not seem intuitive in order to contribute to a better understanding of cp uniqueness this paper provides an accessible and intuitive proof of kruskal s condition the proof is both self contained and compact and can easily be adapted for the complex valued cp decomposition c 2006 elsevier inc all rights reserved

effective modelling of spatial buckling of beam assemblages accounting for warping constraints and rotation dependency of moments a simple two noded finite element model for the three dimensional buckling analysis of beam assemblages is developed the underlying generalized beam theory employed accounts for all coupled significant modes of deformations including stretching bending shear and torsion as well as warping its mixed formulation is of the two field type utilizing linear and constant interpolants for displacements and strain fields due considerations are given to the effect off inite rotations in space on the non linear kinematic descriptions as well as the configuration dependent behaviour of externally applied moment vectors of the conservative and non conservative types the performance of the model and particularly the accuracy of its geometric and load correction stiffnesses is assessed in a fairly complete set of numerical simulations

the special sign indeterminacy of the direct fitting parafac2 model some implications cautions and recommendations for simultaneous component analysis parafac2 is the most flexible simultaneous component analysis sca model that produces an essentially unique solution in this paper we discuss how parafac2 s special sign indeterminacy affects applications of sca and we reveal how an external criterion variable can be used to ensure that estimated parafac2 weights are meaningfully signed across the levels of the nesting mode we present an example with real data from clinical psychology that illustrates the importance of parafac2 s special sign indeterminacy as well as the effectiveness of our proposed solution we also discuss the implications of our results for general applications of sca

blind multichannel deconvolution and convolutive extensions of canonical polyadic and block term decompositions tensor decompositions such as the canonical polyadic decomposition cpd or the block term decomposition btd are basic tools for blind signal separation most of the literature concerns instantaneous mixtures memoryless channels in this paper we focus on convolutive extensions more precisely we present a connection between convolutive cpd btd models and coupled but instantaneous cpd btd we derive a new identifiability condition dedicated to convolutive low rank factorization problems we explain that under this condition the convolutive extension of cpd btd can be computed by means of an algebraic method guaranteeing perfect source separation in the noiseless case in the inexact case the algorithm can be used as a cheap initialization for an optimization based method we explain that in contrast to the memoryless case convolutive signal separation is in certain cases possible despite only two way diversities e g space times time

simplicity and typical rank results for three way arrays matrices can be diagonalized by singular vectors or when they are symmetric by eigenvectors pairs of square matrices often admit simultaneous diagonalization and always admit block wise simultaneous diagonalization generalizing these possibilities to more than two non square matrices leads to methods of simplifying three way arrays by nonsingular transformations such transformations have direct applications in tucker pca for three way arrays where transforming the core array to simplicity is allowed without loss of fit simplifying arrays also facilitates the study of array rank the typical rank of a three way array is the smallest number of rank one arrays that have the array as their sum when the array is generated by random sampling from a continuous distribution in some applications the core array of tucker pca is constrained to have a vast majority of zero elements both simplicity and typical rank results can be applied to distinguish constrained tucker pca models from tautologies an update of typical rank results over the real number field is given in the form of two tables

geometrically exact thin walled beam including warping formulated on the special euclidean group se 3 abstract based on a formulation on the special euclidean group s e 3 a geometrically exact thin walled beam with an arbitrary open cross section is proposed to deal with the finite deformation and rotation issues the beam strains are based on a kinematic assumption where warping deformation and wagner effects are included such that the nonlinear behavior of a thin walled beam is predicted accurately particular under large torsion to reduce the nonlinearity of rigid motion static and dynamic equations are derived in the s e 3 framework based on the local frame approach as the value of the iteration matrix including the jacobian matrix of inertial and internal forces is invariable under arbitrary rigid motion the number of updates required during the computation process decreases sharply which drastically improves the computational efficiency furthermore the isogeometric analysis iga based on the non uniform rational b splines nurbs basis functions which promotes the integration of computer aided design cad and computer aided engineering cae is adopted to interpolate the displacement rotation and warping fields separately the interpolated strain measures satisfy the objectivity by removing the rigid motion of the reference point to obtain the symmetric jacobian matrix of internal forces the linearization operation is conducted based on the previously converged configuration a lie group s e 3 extension of the generalized time integration method is utilized to solve the equations of motion for thin walled beams finally the proposed formulation is successfully tested and validated in several static and dynamic numerical examples

confac decomposition approach to blind identification of underdetermined mixtures based on generating function derivatives this work proposes a new tensor based approach to solve the problem of blind identification of underdetermined mixtures of complex valued sources exploiting the cumulant generating function cgf of the observations we show that a collection of second order derivatives of the cgf of the observations can be stored in a third order tensor following a constrained factor confac decomposition with known constrained structure in order to increase the diversity we combine three derivative types into an extended third order confac decomposition a detailed uniqueness study of this decomposition is provided from which easy to check sufficient conditions ensuring the essential uniqueness of the mixing matrix are obtained from an algorithmic viewpoint we develop a confac based enhanced line search confac els method to be used with an alternating least squares estimation procedure for accelerated convergence and also analyze the numerical complexities of two confac based algorithms namely confac als and confac els in comparison with the levenberg marquardt lm based algorithm recently derived to solve the same problem simulation results compare the proposed approach with some higher order methods our results also corroborate the advantages of the confac based approach over the competing lm based approach in terms of performance and computational complexity

semi blind receivers for joint symbol and channel estimation in space time frequency mimo ofdm systems in wireless communications increased spectral efficiency and low error rates can be achieved by means of space time frequency coded mimo ofdm systems in this work we consider a mimo ofdm transmit signal design combining space frequency modulation with a time varying linear precoding technique which allows spreading and multiplexing the transmitted symbols in both space time and frequency domains for this system we propose two closed form semi blind receivers that exploit differently the multilinear structure of the received signal which is formulated as a nested parallel factor parafac model first we devise a least squares khatri rao factorization ls krf based receiver for joint channel and symbol estimation by making an efficient use of a short frame of pilot symbols the ls krf receiver provides the same performance at a lower computational complexity compared to the alternating least squares als based receiver for further reducing pilot overhead we develop a simplified closed form parafac s cfp receiver coupled with a pairing algorithm that yields an unambiguous estimation of the transmitted symbols without the need of a pilot frame the uniqueness conditions spectral efficiency and computational complexity of the ls krf and s cfp with pairing receivers are analyzed and compared with the als receiver it is shown that the s cfp with pairing receiver has the same order of computational complexity as the als receiver meanwhile simulation results show that our s cfp with pairing receiver achieves the same or very similar performance of the competing receivers with extra pilot overhead at sufficiently high signal to noise ratio snr conditions on the other hand it is slightly inferior to them in terms of channel estimation accuracy and bit error rate at lower snrs

a constrained factor decomposition with application to mimo antenna systems in this paper we formulate a new tensor decomposition herein called constrained factor confac decomposition it consists in decomposing a third order tensor into a triple sum of rank one tensor factors where interactions involving the components of different tensor factors are allowed the interaction pattern is controlled by three constraint matrices the columns of which are canonical vectors each constraint matrix is associated with a given dimension or mode of the tensor the explicit use of these constraint matrices provides degrees of freedom to the confac decomposition for modeling tensor signals with constrained structures which cannot be handled with the standard parallel factor parafac decomposition the uniqueness of this decomposition is discussed and an application to multiple input multiple output mimo antenna systems is presented a new transmission structure is proposed the core of which consists of a precoder tensor decomposed as a function of the confac constraint matrices by adjusting the precoder constraint matrices we can control the allocation of data streams and spreading codes to transmit antennas based on a confac model of the received signal blind symbol code channel recovery is possible using the alternating least squares algorithm for illustrating this application we evaluate the bit error rate ber performance for some configurations of the precoder constraint matrices

blind identification of overcomplete mixtures of sources biome the problem of blind identification of linear mixtures of independent random processes is known to be related to the diagonalization of some tensors this problem is posed here in terms of a non conventional joint approximate diagonalization of several matrices in fact a congruent transform is applied to each of these matrices the left transform being rectangular full rank and the right one being unitary the application in antenna signal processing is described and suboptimal numerical algorithms are proposed

blind deconvolution of ds cdma signals by means of decomposition in rank 1 l l terms in this paper we present a powerful technique for the blind extraction of direct sequence code division multiple access ds cdma signals from convolutive mixtures received by an antenna array the technique is based on a generalization of the canonical or parallel factor decomposition candecomp parafac in multilinear algebra we present a bound on the number of users under which blind separation and deconvolution is guaranteed the solution is computed by means of an alternating least squares als algorithm the excellent performance is illustrated by means of a number of simulations we include an explicit expression of the cramer rao bound crb of the transmitted symbols

linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method abstract in the present study we apply the natural mode method and formulate an appropriate linear and geometrically nonlinear theory which is implemented on a model three node multilayered triangular facet element which incorporates the effect of transverse shear deformation and is intended for the nonlinear analysis of large and complex isotropic and composite structures in this context we discuss the derivation of the elastic and geometrical elemental stiffnesses which are based on appropriate kinematic as well as physical idealizations which constitute basic elements of the method of intelligent physical lumping subsequently we present the ariban scheme accumulation of the rigid body and natural modes for geometrically nonlinear analysis it is emphasized that both the triangular facet element and the nonlinear algorithm are developed for the analysis of large and complex structures for which higher order formal finite elements cannot provide answers inexpensivelly in addition the structure of the algorithm and its matrix language are ideally suited for modern parallel computers we conclude our study with numerical examples for isotropic and composite plates all the numerical experiments show the accuracy and potential of the developed methodology for extensive structural engineering computations

free vibration analysis of multilayered composite plates and shells with the natural approach abstract natural curved triangular shell element natcop developed in 1 is employed to vibration mode analysis of multilayered composite plates and shells the shells can be either symmetric or unsymmetric the spectral transformation lanczos method with selective or full orthogonalization is used to solve the eigenvalue problem of a pencil k m proper shifting of the eigenvalues is essential for the success of this method certain problems associated with the shift are discussed several numerical examples including symmetric and unsymmetric composite plates and unsymmetric composite conical shells are tested and show that element natcop is also efficient and reliable for free vibration analysis

the structure of a laurent polynomial fibration in n variables abstract bass connell and wright have proved that any finitely presented locally polynomial algebra in n variables over an integral domain r is isomorphic to the symmetric algebra of a finitely generated projective r module of rank n in this paper we prove a corresponding structure theorem for a ring a which is a locally laurent polynomial algebra in n variables over an integral domain r viz we show that a is isomorphic to an r algebra of the form sym r q i 1 where q is a direct sum of n finitely generated projective r modules of rank one and i is a suitable invertible ideal of the symmetric algebra sym r q further we show that any faithfully flat algebra over a noetherian normal domain r whose generic and codimension one fibres are laurent polynomial algebras in n variables is a locally laurent polynomial algebra in n variables over r

finite element theory for curved and twisted beams based on exact solutions for three dimensional solids part 1 beam concept and geometrically exact nonlinear formulation a geometrically exact and completely consistent finite element theory for curved and twisted beams is proposed it is based on the kinematical hypothesis generally formulated for large deformation and accounts for all kinds of deformation of a three dimensional solid translational and rotational displacements of the cross sections warping of their plane and distortion of their contours the principle of virtual work is applied in a straightforward manner to all non zero six components of the strain and stress tensors expressions are given for tangent matrices of elastic inertia and external forces and specific techniques for discretization and updating are developed for the analysis of beams in inertial and non inertial frames finally the numerical properties of the finite element models are demonstrated through examples c 1998 elsevier science s a all rights reserved

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types

tensor decompositions for identifying directed graph topologies and tracking dynamic networks directed networks are pervasive both in nature and engineered systems often underlying the complex behavior observed in biological systems microblogs and social interactions over the web as well as global financial markets since their structures are often unobservable in order to facilitate network analytics one generally resorts to approaches capitalizing on measurable nodal processes to infer the unknown topology structural equation models sems are capable of incorporating exogenous inputs to resolve inherent directional ambiguities however conventional sems assume full knowledge of exogenous inputs which may not be readily available in some practical settings this paper advocates a novel sem based topology inference approach that entails factorization of a three way tensor constructed from the observed nodal data using the well known parallel factor parafac decomposition it turns out that second order piecewise stationary statistics of exogenous variables suffice to identify the hidden topology capitalizing on the uniqueness properties inherent to high order tensor factorizations it is shown that topology identification is possible under reasonably mild conditions in addition to facilitate real time operation and inference of time varying networks an adaptive parafac tensor decomposition scheme that tracks the topology revealing tensor factors is developed extensive tests on simulated and real stock quote data demonstrate the merits of the novel tensor based approach

weight adjusted tensor method for blind separation of underdetermined mixtures of nonstationary sources in this paper a novel algorithm to blindly separate an instantaneous linear underdetermined mixture of nonstationary sources is proposed it means that the number of sources exceeds the number of channels of the available data the separation is based on the working assumption that the sources are piecewise stationary with a different variance in each block it proceeds in two steps 1 estimating the mixing matrix and 2 computing the optimum beamformer in each block to maximize the signal to interference ratio of each separated signal with respect to the remaining signals estimating the mixing matrix is accomplished through a specialized tensor decomposition of the set of sample covariance matrices of the received mixture in each block it utilizes optimum weighting which allows statistically efficient crb attaining estimation provided that the data obey the assumed gaussian piecewise stationary model in simulations performance of the algorithm is successfully tested on blind separation of 16 speech signals from nine linear instantaneous mixtures of these signals