a consistent finite element formulation for linear buckling analysis of spatial beams a consistent co rotational finite element formulation and numerical procedure for the linear buckling analysis of three dimensional elastic euler beam is presented a mechanism for generating configuration dependent conservative moment is proposed and the corresponding load stiffness matrix is derived it is assumed that the prebuckling displacements and rotations of the structure and the corresponding deformations of the elements are linearly proportional to the external loading the prebuckling rotations of the structure are fixed axis rotations or small rotations and the effect of the prebuckling displacement on transformation matrix for the coordinates transformation can be ignored all coupling among bending twisting and stretching deformations for beam element is considered by consistent linearization of the fully geometrically nonlinear beam theory an inverse power method for the solution of the generalized eigenvalue problem is used to find the buckling load and buckling mode numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method

finite element analysis of smooth folded and multi shell structures the paper is concerned with the nonlinear theory and finite element analysis of shell structures with an arbitrary geometry loading and boundary conditions a complete set of shell field equations and side conditions boundary and jump conditions is derived from the basic laws of continuum mechanics the developed shell theory includes the so called drilling couples as well as the drilling rotation it is shown that this property is crucial in the analysis of irregular shell structures such as those containing folds branches column supports stiffeners etc the relevant variational principles with relaxed regularity requirements are also presented these principles provide the mathematical basis for the formulation of various classes of shell finite elements the developed finite elements include a displacement rotation based lagrange family a stress resultant based mixed and a semi mixed family as well as so called assumed strain elements all elements have six degrees of freedom at each node three translational and three rotational ones including the drilling rotation formulated on the foundation of an exact in defined sense shell theory as such they are equally applicable to smooth as well as to irregular shell structures the general applicability of the developed elements is illustrated through an extensive numerical analysis of the representative test examples in order to obtain a still deeper insight into the problem a lagrange family of standard degenerated shell elements with five degrees of freedom per node and an element with six degrees of freedom per node based on the von karman plate theory are considered as well the presented numerical results include complex plate and doubly curved shell structures linear and non linear solutions with a pre and post buckling analysis are discussed

on the hyers ulam rassias stability of approximately additive mappings abstract in this paper using an idea from the paper of p gvruta j math anal appl 184 1994 431 436 the results of th m rassias j math anal appl 158 1991 106 113 shall be generalized

multiple output regression with latent noise in high dimensional data structured noise caused by observed and unobserved factors affecting multiple target variables simultaneously imposes a serious challenge for modeling by masking the often weak signal therefore 1 explaining away the structured noise in multiple output regression is of paramount importance additionally 2 assumptions about the correlation structure of the regression weights are needed we note that both can be formulated in a natural way in a latent variable model in which both the interesting signal and the noise are mediated through the same latent factors under this assumption the signal model then borrows strength from the noise model by encouraging similar effects on correlated targets we introduce a hyperparameter for the latent signal to noise ratio which turns out to be important for modelling weak signals and an ordered infinite dimensional shrinkage prior that resolves the rotational unidentifiability in reduced rank regression models simulations and prediction experiments with metabolite gene expression fmri measurement and macroeconomic time series data show that our model equals or exceeds the state of the art performance and in particular outperforms the standard approach of assuming independent noise and signal models

a co rotational formulation for thin walled beams with monosymmetric open section abstract a consistent co rotational total lagrangian finite element formulation and numerical procedure for the geometric nonlinear buckling and postbuckling analysis of thin walled beams with monosymmetric open section is presented the element developed here has two nodes with seven degrees of freedom per node the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element and the shear center axis is chosen to be the reference axis the deformations of the beam element are described in the current element coordinate system which is constructed at the current configuration of the beam element in element nodal forces all coupling among bending twisting and stretching deformations of the beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however the third order term of the twist rate of the beam axis is considered in element nodal forces an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a parabolic interpolation method of the arc length is used to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method

predicting multivariate responses in multiple linear regression we look at the problem of predicting several response variables from the same set of explanatory variables the question is how to take advantage of correlations between the response variables to improve predictive accuracy compared with the usual procedure of doing individual regressions of each response variable on the common set of predictor variables a new procedure is introduced called the curds and whey method its use can substantially reduce prediction errors when there are correlations between responses while maintaining accuracy even if the responses are uncorrelated in extensive simulations the new procedure is compared with several previously proposed methods for predicting multiple responses including partial least squares and exhibits superior accuracy one version can be easily implemented in the context of standard statistical packages

co rotational finite element formulation for thin walled beams with generic open section a consistent co rotational total lagrangian finite element formulation for the geometric nonlinear buckling and postbuckling analysis of thin walled beams with generic open section is presented the element developed here has two nodes with seven degrees of freedom per node the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element and the shear center axis is chosen to be the reference axis the deformations of the beam element are described in the current element coordinate system constructed at the current configuration of the beam element the element nodal forces are derived using the virtual work principle the virtual rigid body motion corresponding to the virtual nodal displacements is excluded in the derivation of the element nodal forces a procedure is proposed to determine the virtual rigid body motion the way used to determine the element coordinate system and element nodal deformations corresponding to the virtual nodal displacements and that corresponding to the incremental nodal displacement are consistent in element nodal forces all coupling among bending twisting and stretching deformations of the beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory in the derivation of the element tangent stiffness matrix the change of element nodal forces induced by the element rigid body rotations should be considered for the present method thus a stability matrix is included in the element tangent stiffness matrix an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state numerical examples are presented to investigate the accuracy and efficiency of the proposed method the effect of the terms in the element nodal force and tangent stiffness matrix which will converge to zero with the decrease of element size on the convergence rate of solution and accuracy for the buckling load and nonlinear behavior of three dimensional beam structures are also investigated through numerical examples 2005 elsevier b v all rights reserved

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

the problem of s m ulam for approximately multiplicative mappings in the present paper we study the problem of s m ulam for approximately multiplicative mappings and we consider new open problems

variational bayesian approach to canonical correlation analysis as a dimension reduction algorithm canonical correlation analysis cca encounters the issue of selecting the number of canonical correlations in this letter we present a bayesian model selection algorithm for cca based on a probabilistic interpretation a hierarchical bayesian model is applied to probabilistic cca and learned by variational approximation this method not only estimates the model parameters but also automatically determines the number of canonical correlations and avoids overfitting experiments show that it performs better compared with maximum likelihood and some other model selection methods

a co rotational finite element formulation for buckling and postbuckling analyses of spatial beams abstract a consistent co rotational finite element formulation and numerical procedure for the buckling and postbuckling analyses of three dimensional elastic euler beam is presented all coupling among bending twisting and stretching deformations for a beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however the third order terms which are relevant to the twist rate and curvature of the beam axis are also considered an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a bisection method of the arc length is proposed to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method and to investigate the effect of third order terms on the buckling load and postbuckling behavior of three dimensional beams

generalized mixed finite element model for pre and post quasistatic buckling response of thin walled framed structures adopting an updated lagrangian approach the general framework for the fully non linear analysis of thin walled framed structures is developed using a simple two node c0 model hmb2 the governing equations are derived based on a consistent linearization of an incremental mixed variational principle of modified hellinger reissner type with independent assumptions for displacement and strain fields all coupled significant modes of deformations i e stretching bending shear torsion and warping are accounted for in the generalized beam theory employed emphasis is placed on devising effective solution procedures to deal with finite rotations in space particularly with regard to their effect on the derivations of load correction matrices corresponding to configuration dependent externally applied forces moments the effectiveness and practical usefulness of present model are demonstrated through a number of test problems involving beam assemblages undergoing large displacements and rotations in space

stability of a mixed functional equation in several variables on banach modules abstract in this paper we establish the general solution of the functional equation i 1 n f x i 1 n j 1 n x j i 1 n f x i n f 1 n i 1 n x i n 2 and use a fixed point method to prove its generalized hyers ulam stability in banach modules over a unital banach algebra

natural approach for geometric non linear analysis of thin walled frames a new stiffness matrix for geometrically non linear analysis of three dimensional beam columns with bisymmetrical thin walled i type cross sections is presented the displacement field is described in terms of natural and rigid body displacements and both cartesian and natural matrices are derived a novelty of the resulting method is the use of this dual description in all aspects of the analysis including the computer implementation a companion paper1 that introduces the plastic behaviour of the material also justifies the need for this dual approach as a means to separate nodal forces from stress resultants in the cross section of the 3d beam column element the current development uses the updated lagrangian formulation and corrections in the element matrix are made to properly consider the behaviour under finite rotation it is shown that accuracy and convergence of the solution process can be improved if the natural matrices derived here are used in a new force recovery process that is insensitive to rigid body displacements

group factor analysis factor analysis fa provides linear factors that describe the relationships between individual variables of a data set we extend this classical formulation into linear factors that describe the relationships between groups of variables where each group represents either a set of related variables or a data set the model also naturally extends canonical correlation analysis to more than two sets in a way that is more flexible than previous extensions our solution is formulated as a variational inference of a latent variable model with structural sparsity and it consists of two hierarchical levels 1 the higher level models the relationships between the groups and 2 the lower models the observed variables given the higher level we show that the resulting solution solves the group factor analysis gfa problem accurately outperforming alternative fa based solutions as well as more straightforward implementations of gfa the method is demonstrated on two life science data sets one on brain activation and the other on systems biology illustrating its applicability to the analysis of different types of high dimensional data sources

a fixed point method for perturbation of bimultipliers and jordan bimultipliers in c ternary algebras let a be a c ternary algebra a c bilinear t a a a is called a c ternary algebra bi multiplier if it satisfies t abc d t a b cd t a bcd abt c d for all a b c d a also the mapping t a a a is a called c ternary algebra jordan bimultiplier if it satisfies t aaa a t a a aa t a aaa aat a a for all a a using the fixed point method we investigate the generalized hyers ulam rassias stability of bimultipliers and jordan bimultipliers in c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias proc am math soc 72 297 1978

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

generalized additive mapping in banach modules and isomorphisms between c algebras abstract let x y be vector spaces it is shown that if an odd mapping f x y satisfies the functional equation 1 r f j 1 d x j r j 0 1 j 1 d j l r f j 1 d 1 j x j r c l d 1 c l 1 d 1 1 j 1 d f x j then the odd mapping f x y is additive and we prove the hyers ulam stability of the functional equation 1 in banach modules over a unital c algebra as an application we show that every almost linear bijection h a b of a unital c algebra a onto a unital c algebra b is a c algebra isomorphism when h 2 n r n u y h 2 n r n u h y for all unitaries u a all y a and n 0 1 2

on the stability of the linear mapping in banach modules abstract we prove the generalized hyers ulam rassias stability of the linear mapping in banach modules over a unital banach algebra

a kinematically exact space finite strain beam model finite element formulation by generalized virtual work principle the present paper presents a novel finite element formulation for static analysis of linear elastic spatial frame structures extending the formulation given by simo and vu quoc a geometrically exact rod model incorporating shear and torsion warping deformation int j solids structures 27 3 1991 371 3931 along the lines of the work on the planar beam theory presented by saje a variational principle for finite planar deformation of straight slender elastic beams internat j solids and structures 26 1990 887 9001 we apply exact non linear kinematic relationships of the space finite strain beam theory assuming the bernoulli hypothesis and neglecting the warping deformations of the cross section finite displacements and rotations as well as finite extensional shear torsional and bending strains are accounted for in the formulation a deformed configuration of the beam is described by the displacement vector of the deformed centroid axis and an orthonormal moving frame rigidly attached to the cross section of the beam the position of the moving frame relative to a fixed reference frame is specified by an orthogonal matrix parametrized by the rotational vector which rotates the moving frame from an arbitrary position into the deformed configuration in one step also the incremental rotational vector is introduced which rotates the moving frame from the configuration obtained at the previous iteration step into the current configuration of the beam its components relative to the fixed global coordinate system are taken to be the rotational degrees of freedom at nodal points because in 3 d space both the axial and the follower moments are non conservative not the variational principle but the principle of virtual work has been introduced as a basis for the finite element discretization here we have proposed the generalized form of the principle of virtual work by including exact kinematic equations by means of a procedure similar to that of lagrangian multipliers this makes possible the elimination of the displacement vector field from the principle so that the three components of the incremental rotational vector field remain the only functions to be approximated in the finite element implementation of the principle other researchers on the other hand employ the three components of the incremental rotational vector field and the three components of the incremental displacement vector field as a result more accurate and efficient family of beam finite elements for the non linear analysis of space frames has been obtained a one field formulation results in the fact that in the present finite elements the locking never occurs any combination of deformation states is described equally precisely this is in contrast with the elements developed in literature where in order to avoid the locking a reduced numerical integration has to be applied which unfortunately diminishes the accuracy of the solution polynomials have been chosen for the approximation of the components of the rotational vector in this case the order of the numerical integration can rationally be estimated and the computer program can be coded in such a way that the degree of polynomials need not be limited to a particular value the newton method is used for the iterative solution of the non linear equilibrium equations in an non equilibrium configuration the tangent stiffness matrix obtained by the linearization of governing equations using the directional derivative is non symmetric even for conservative loadings only upon achieving an equilibrium state the tangent stiffness matrix becomes symmetric thus obtained tangent stiffness matrix can be symmetrized without affecting the rate of convergence of the newton method for non conservative loadings however the tangent stiffness matrix is always non symmetric the numerical examples demonstrate capability of the present formulation to determine accurately the non linear behaviour of space frames in numerical examples the out of plane buckling loads are determined and the whole pre and post critical load displacement paths of a cantilever and a right angle frame are traced these in the analysis of space beams standard verification example problems show excellent accuracy of the solution even when employing only one element to describe the displacements of the size of the structure itself the rotations of 2n and extensional strains much beyond the realistic values of linear elastic material

co rotational formulation for geometric nonlinear analysis of doubly symmetric thin walled beams abstract a doubly symmetric thin walled beam element with open section is derived using co rotational cr total lagrangian tl formulation the effects of deformation dependent third order terms of element nodal forces on the buckling load and post buckling behavior are investigated all coupling among bending twisting and stretching deformations for beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however all third order terms of nodal forces which are relevant to the twist rate rate of twist rate and curvature of the beam axis are also considered an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a parabolic interpolation method of the arc length is used to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed element and to investigate the effect of third order terms of element nodal forces on the buckling load and post buckling behavior of doubly symmetric thin walled beams

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

a novel framework for parsimonious multivariate analysis abstract this paper proposes a framework in which a multivariate analysis method mva guides a selection of input variables that leads to a sparse feature extraction this framework called parsimonious mva is specially suited for high dimensional data such as gene arrays digital pictures etc the feature selection relies on the analysis of consistency in the behaviour of the input variables through the elements of an ensemble of mva projection matrices the ensemble is constructed following a bootstrap that builds on an efficient and generalized mva formulation that covers pca cca and opls moreover it allows the estimation of the relative relevance of each selected input variable experimental results point out that the features extracted by the parsimonious mva have excellent discrimination power comparing favorably with state of the art methods and are potentially useful to build interpretable features besides the parsimonious feature extractor is shown to be robust against to parameter selection as we all computationally efficient

nonlinear finite element analysis of elastic systems under nonconservative loading natural formulation part ii dynamic problems abstract the paper presents a nonlinear finite element analysis of elastic structures subject to nonconservative forces attention is focused on the stability behaviour of such systems this leads mathematically to non self adjoint boundary value problems which are of great theoretical and practical interest in particular in connection with alternative modes of instability like divergence of flutter only quasistatic effects are however considered in the present part the methodology of our theory is general but the specific thrust of the present research is directed towards the analysis of structures acted upon by displacement dependent nonconservative follower forces in a finite element formulation the analysis of geometrically nonlinear elastic systems subject to such forces gives in general rise to a contributory nonsymmetric stiffness matrix known as the load correction matrix as a result the total tangent stiffness matrix becomes unsymmetric an indication of the non self adjoint character of the problem our theory is based on the natural mode technique 1 2 3 and permits i a a simple but elegant derivation of the load correction matrix the application of the general theory as evolved in this paper is demonstrated on the beam element in space a number of numerical examples are considered including divergence and flutter types of instability for which exact analytic solutions are known the problems demonstrate the efficiency of the present finite element formulation the paper furnishes also a novel and concise formulation of finite rotations in space which may be considered as a conceptual generalization of the theory presented in 2 3

corotational total lagrangian formulation for three dimensional beamelement a corotational total lagrangian formulation of beam element is presented for the nonlinear analysis of three dimensional beam structures with large rotations but small strains the nonlinear coupling among the bending twisting and stretching deformations is considered all of the element deformations and equations are defined in body attached element coordinates three rotation parameters are proposed to determine the orientation of the element cross section two sets of element nodal parameters termed explicit nodal parameters and implicit nodal parameters are introduced the explicit nodal parameters are used in the assembly of the system equations from the element equations and chosen to be three components of the incremental translation vector and three components of the incremental rotation vector the implicit nodal parameters are used to determine the deformations of the beam element and chosen to be three components of the total displacement vector and nodal values of the three rotation parameters the element internal nodal forces corresponding to the implicit nodal parameters are obtained from the virtual work principle numerical examples are presented and compared with the numerical and experimental results reported in the literature to demonstrate the accuracy and efficiency of the proposed method hree dimensional beams are very important structural elements in all types of engineering systems in many applications these beam elements undergo finite rotations that require a nonlinear formulation to their structural analysis the development of new and efficient formulations for nonlinear analysis of beam structures has attracted the study of many researchers in recent years based on different kinematic assumptions different alternative formulation strategies and procedures to accommodate large rotation capability during the large deformation process have been presented 1 20 the kinematic assumptions used in refs 4 5 7 11 and 17 19 are based on timoshenko s hypothesis the effect of stretching bending torsion and transverse shear are taken into account

kernel independent component analysis we present a class of algorithms for independent component analysis ica which use contrast functions based on canonical correlations in a reproducing kernel hilbert space on the one hand we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence on the other hand building on recent developments in kernel methods we show that these criteria and their derivatives can be computed efficiently minimizing these criteria leads to flexible and robust algorithms for ica we illustrate with simulations involving a wide variety of source distributions showing that our algorithms outperform many of the presently known algorithms

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

bayesian group factor analysis with structured sparsity latent factor models are the canonical statistical tool for exploratory analyses of low dimensional linear structure for a matrix of p features across n samples we develop a structured bayesian group factor analysis model that extends the factor model to multiple coupled observation matrices in the case of two observations this reduces to a bayesian model of canonical correlation analysis here we carefully define a structured bayesian prior that encourages both element wise and column wise shrinkage and leads to desirable behavior on high dimensional data in particular our model puts a structured prior on the joint factor loading matrix regularizing at three levels which enables element wise sparsity and unsupervised recovery of latent factors corresponding to structured variance across arbitrary subsets of the observations in addition our structured prior allows for both dense and sparse latent factors so that covariation among either all features or only a subset of features can be recovered we use fast parameter expanded expectation maximization for parameter estimation in this model we validate our method on simulated data with substantial structure we show results of our method applied to three high dimensional data sets comparing results against a number of state of the art approaches these results illustrate useful properties of our model including i recovering sparse signal in the presence of dense effects ii the ability to scale naturally to large numbers of observations iii flexible observation and factor specific regularization to recover factors with a wide variety of sparsity levels and percentage of variance explained and iv tractable inference that scales to modern genomic and text data sizes

bayesian canonical correlation analysis canonical correlation analysis cca is a classical method for seeking correlations between two multivariate data sets during the last ten years it has received more and more attention in the machine learning community in the form of novel computational formulations and a plethora of applications we review recent developments in bayesian models and inference methods for cca which are attractive for their potential in hierarchical extensions and for coping with the combination of large dimensionalities and small sample sizes the existing methods have not been particularly successful in fulfilling the promise yet we introduce a novel efficient solution that imposes group wise sparsity to estimate the posterior of an extended model which not only extracts the statistical dependencies correlations between data sets but also decomposes the data into shared and data set specific components in statistics literature the model is known as inter battery factor analysis ibfa for which we now provide a bayesian treatment

isomorphisms between c ternary algebras abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following cauchy jensen additive mappings 0 1 f x y 2 z f x y 2 z f x 2 f z 0 2 f x y 2 z f x y 2 z f y 0 3 2 f x y 2 z f x f y 2 f z these are applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

inverse closedness of approximation algebras abstract we prove the inverse closedness of certain approximation algebras based on a quasi banach algebra x using two general theorems on the inverse closedness of subspaces of quasi banach algebras in the first theorem commutative algebras are considered while the second theorem can be applied to arbitrary x and to subspaces of x which can be obtained by a general k method of interpolation between x and an inversely closed subspace y of x having certain properties as application we present some inversely closed subalgebras of c t and c 1 1 in particular we generalize wiener s theorem i e we show that for many subalgebras s of l 1 z the property c k f s c k f being the fourier coefficients of f implies the same property for 1 f if f c t vanishes nowhere on t

on approximation of approximately linear mappings by linear mappings abstract assume a is a normed linear space b is a banach space and f a b is a mapping approximately linear we solve the following ulam problem give conditions in order for a linear mapping near an approximately linear mapping to exist

hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation this is applied to investigate homomorphisms between quasi banach algebras the concept of hyers ulam rassias stability originated from th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

isomorphisms between unital c algebras abstract it is shown that every almost linear bijection h a b of a unital c algebra a onto a unital c algebra b is a c algebra isomorphism when h 2 n u y h 2 n u h y for all unitaries u a all y a and n 0 1 2 and that almost linear continuous bijection h a b of a unital c algebra a of real rank zero onto a unital c algebra b is a c algebra isomorphism when h 2 n u y h 2 n u h y for all u v a v v v 1 v is invertible all y a and n 0 1 2 assume that x and y are left normed modules over a unital c algebra a it is shown that every surjective isometry t x y satisfying t 0 0 and t u x u t x for all x x and all unitaries u a is an a linear isomorphism this is applied to investigate c algebra isomorphisms between unital c algebras

the role of non linear theories in transient dynamic analysis of flexible structures abstract transient dynamic analysis of flexible structures undergoing large motions is considered for rotating structures it is explicitly shown that appropriate account of the influence of centrifugal force on the bending stiffness requires the use of a geometrically non linear at least second order beam theory use of a first order linearized linear beam theory results in a spurious loss of bending stiffness for a rotating plane beam a set of linear partial differential equations of motion that includes all inertia effects coriolis centrifugal acceleration of revolution and coupling between extensional and flexural deformations is derived from the fully non linear beam theory by consistent linearization the analysis is subsequently extended to the more general case of a plate accomodating shear deformation and undergoing a general three dimensional rotating motion the discretization process of the resulting linear equations of motion for the beam and the plate is also discussed

canonical correlation analysis for multilabel classification a least squares formulation extensions and analysis canonical correlation analysis cca is a well known technique for finding the correlations between two sets of multidimensional variables it projects both sets of variables onto a lower dimensional space in which they are maximally correlated cca is commonly applied for supervised dimensionality reduction in which the two sets of variables are derived from the data and the class labels respectively it is well known that cca can be formulated as a least squares problem in the binary class case however the extension to the more general setting remains unclear in this paper we show that under a mild condition which tends to hold for high dimensional data cca in the multilabel case can be formulated as a least squares problem based on this equivalence relationship efficient algorithms for solving least squares problems can be applied to scale cca to very large data sets in addition we propose several cca extensions including the sparse cca formulation based on the 1 norm regularization we further extend the least squares formulation to partial least squares in addition we show that the cca projection for one set of variables is independent of the regularization on the other set of multidimensional variables providing new insights on the effect of regularization on cca we have conducted experiments using benchmark data sets experiments on multilabel data sets confirm the established equivalence relationships results also demonstrate the effectiveness and efficiency of the proposed cca extensions

practical approaches to principal component analysis in the presence of missing values principal component analysis pca is a classical data analysis technique that finds linear transformations of data that retain the maximal amount of variance we study a case where some of the data values are missing and show that this problem has many features which are usually associated with nonlinear models such as overfitting and bad locally optimal solutions a probabilistic formulation of pca provides a good foundation for handling missing values and we provide formulas for doing that in case of high dimensional and very sparse data overfitting becomes a severe problem and traditional algorithms for pca are very slow we introduce a novel fast algorithm and extend it to variational bayesian learning different versions of pca are compared in artificial experiments demonstrating the effects of regularization and modeling of posterior variance the scalability of the proposed algorithm is demonstrated by applying it to the netflix problem