albanese maps and off diagonal long time asymptotics for the heat kernel we discuss long time asymptotic behaviors of the heat kernel on a non compact riemannian manifold which admits a discontinuous free action of an abelian isometry group with a compact quotient a local central limit theorem and the asymptotic power series expansion for the heat kernel as the time parameter goes to infinity are established by employing perturbation arguments on eigenvalues and eigenfunctions of twisted laplacians our ideas and techniques are motivated partly by analogy with floque bloch theory on periodic schrodinger operators for the asymptotic expansion we make careful use of the classical laplace method in the course of a discussion we observe that the notion of albanese maps associated with the abelian group action is closely related to the asymptotics a similar idea is available for asymptotics of the transition probability of a random walk on a lattice graph the results obtained in the present paper refine our previous ones 4 in the asymptotics the euclidean distance associated with the standard realization of the lattice graph which we call the albanese distance plays a crucial role

on sufficiency and duality for generalized quasiconvex programs abstract for a nonlinear programming problem under differentiability assumptions fritz john suffcient optimality conditions are stated also some duality theorems are proved for mond weir type duals all results are given under generalized convexity assumptions

optimality conditions for multiobjective programming with generalized i ρ θ convex set functions abstract necessary conditions for pareto optimality in multiobjective programming with subdifferentiable set functions are established in theorem 12 of h c lai and l j lin j math anal appl 132 1988 558 571 in this paper we establish some sufficient conditions under which a feasible solution of such a problem will be pareto optimal provided that a weaker convexity requirement is satisfied for instance i convexity is assumed for both objective and constraint set functions some duality models are also discussed wolfe type and mond weir type duality theorems are proved

weak convergence of symmetric diffusion processes in this paper we show the convergence of forms in the sense of mosco associated with the part form on relatively compact open set of dirichlet forms with locally uniform ellipticity and the locally uniform boundedness of ground states under regular dirichlet space setting we also get the same assertion under dirichlet space in infinite dimensional setting as a result of this we get the weak convergence under some conditions on initial distributions and the growth order of the volume of the balls defined by modified pseudo metric used in k th sturm

duality for nondifferentiable static multiobjective variational problems involving generalized f ϱ convex functions using the generalized schwarz inequality we establish some weak duality theorems for nondifferentiable static multiobjective variational problems involving generalized f convex functions later in the sequel we introduce three dual models for the nondifferentiable static multiobjective fractional variational problems and derive weak duality results for such programs

redundancy analysis for qualitative variables redundancy analysis also called principal components analysis of instrumental variables is a technique for two sets of variables one set being dependent of the other its aim is maximization of the explained variance of the dependent variables by a linear combination of the explanatory variables the technique is generalized to qualitative variables it then gives implicitly a simultaneous optimal scaling of the dependent qualitative variables examples are taken from the dutch life situation survey 1977 using satisfaction with life and happiness as dependent variables the analysis leads to one well being scale defined by the explanatory variables marital status schooling income and activity

identification in restricted factor models and the evaluation of rank conditions abstract this paper presents a rank condition for the local identification in restricted factor analysis models and it provides a method for the computation of the exact rank in the condition the method can be applied to evaluate the rank of rather general jacobian matrices

zur theorie der linearen und nichtlinearen integralgleichungen fredholm hat eine auflosungsformel der inhomogenen linearen integralgleichung f left s right varphi left s right lambda int limits a b k left s t right varphi left t right dt entdeckt welche das resultat enthielt das diese gleichung nach s stets aufgelost werden kann wenn nicht eine der nullstellen einer gewissen ganzen transzendenten ist fur diese werte von in hilbertscher bezeichnung die sogenannten eigenwerte des kernes k s t und nur fur diese last wie fredholm ferner zeigte die homogene gleichung 0 varphi left s right int limits a b k left s t right varphi left t right dt losungen zu die nach hilbert zum betreffenden eigenwert des kernes k s t gehorige eigenfunktionen genannt werden hilbert hat die in der theorie der partiellen und gewohnlichen differentialgleichungen so wichtigen fragen nach der existenz sogenannter normalfunktionen und der entwickelbarkeit willkurlicher funktionen nach ihnen durch einfuhrung der greenschen funktion auf das viel allgemeinere problem zuruckgefuhrt die existenz von eigenfunktionen eines in s und t symmetrischen kernes k s t zu beweisen und die gesetze der entwickelbarkeit willkurlicher funktionen nach ihnen aufzustellen die greensche funktion selbst wird durch eine integralgleichung mit unsymmetrischem kerne bestimmt wobei die fredholmschen formeln zur anwendung kommen

models and methods for the analysis of correlation coefficients abstract the normal distribution plays a very prominant role in statistics and in multivariate analysis the multinormal model is even more dominant than in the classical univariate or bivariate situations in this paper we show that the assumption of continuous multinormal observations can be relaxed in various ways for continuous multivariate analysis most of the existing large sample theory can be applied without assuming multivariate normality we also develop several discrete multinormal models the first one is the classical pearson model which results from discreticizing multinormal variables the second one is inspired by correspondence analysis and the third one by loglinear analysis the models are presented in terms of correlation coefficients and applied to the spearman model of factor analyses using an example from political science

duality for generalized fractional programs involving n set functions abstract making use of a strong duality theorem for nonlinear programs involving n set functions we first establish a gordan type transposition theorem which is then utilized to construct a dual problem for a class of generalized fractional programming problems with n set functions as special cases of the main result we also obtain dual problems for discrete minmax and fractional programming problems

on efficiency and duality for multiobjective programs abstract for a multiobjective nonlinear program which involved inequality and equality constraints wolfe mond weir and general mond weir type duals are formulated and the concept of efficiency pareto optimum is used to state some duality results under generalized f convexity assumptions

multivariate methods for quantitative and qualitative data abstract in this paper several multivariate analysis methods are analyzed by means of the errors in variables model two specifications viz the principal relations and the principal factors model for the set of unobserved latent variables are introduced and shown to be complementary for particular choices of the error covariance matrix the general model reduces to several well known multivariate techniques including ordinary least squares principal components orthogonal regression and canonical correlations the same apparatus is used to arrive at a set of multivariate techniques in case the data is qualitative instead of quantitative the relationship with optimal scaling techniques for qualitative data is shown an empirical example is given of a regression involving a dependent latent variable having two ordered categorical indicator variables

duality for a minimax programming problem containingn set functions abstract parameter necessary and sufficient optimality conditions for the discrete minimax programming problem with differentiable n set functions are established in zalmai optimization 20 1989 377 395 in this paper we establish nonparameter necessary and sufficient optimality conditions the nonparameter necessary optimality conditions suggest the establishment of two parameter free duality models for the discrete minimax programming problem with differentiable n set functions and the weak strong and strict converse duality theorems have been derived

loglinear models and categorical data analysis with psychometric and econometric applications revision abstract the past decade has seen the publication of a large number of books and papers on the analysis of multi way contingency tables using loglinear and logic models the present article presents a summary of the statistical theory that underlies much of this work and provides some linkage to models and methods of special interest to psychometricians and econometricians the discussion includes a review of recent and current research on the computation of maximum likelihood estimates for loglinear and logit models especially for large multi way contingency tables

on minimax fractional optimality conditions with f ρ convexity abstract we establish the sufficient conditions for generalized fractional programming in the framework of f convex functions when the sufficient conditions are utilized one parametric dual problem and two parametric free dual problems may be formulated and duality results are derived

limits of random differential equations on manifolds consider a family of random ordinary differential equations on a manifold driven by vector fields of the form sum ky k alpha k z t epsilon omega where y k are vector fields epsilon is a positive number z t epsilon is a 1 over epsilon mathcal l 0 diffusion process taking values in possibly a different manifold alpha k are annihilators of mathrm ker mathcal l 0 under hormander type conditions on mathcal l 0 we prove that as epsilon approaches zero the stochastic processes y t over epsilon epsilon converge weakly and in the wasserstein topologies we describe this limit and give an upper bound for the rate of the convergence

collapsing of riemannian manifolds and eigenvalues of laplace operator on etudie la perturbation des valeurs propres de l operateur de laplace sous des deformations des varietes qui ne conservent pas les dimensions

quantitative analysis of qualitative data this paper presents an overview of an approach to the quantitative analysis of qualitative data with theoretical and methodological explanations of the two cornerstones of the approach alternating least squares and optimal scaling using these two principles my colleagues and i have extended a variety of analysis procedures originally proposed for quantitative interval or ratio data to qualitative nominal or ordinal data including additivity analysis and analysis of variance multiple and canonical regression principal components common factor and three mode factor analysis and multidimensional scaling the approach has two advantages a if a least squares procedure is known for analyzing quantitative data it can be extended to qualitative data and b the resulting algorithm will be convergent three completely worked through examples of the additivity analysis procedure and the steps involved in the regression procedures are presented

optimality and duality for generalized fractional programming involving nonsmooth f ρ convex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing f r convex functions

weak convergence of laws of stochastic processes on riemannian manifolds weak convergence of the laws of discrete time re metrized stochastic processes derived from brownian motions on compact riemannian manifolds with heat kernels uniformly bounded by a constant on each compact set of the time parameter and bounded volumes to a stochastic process is given with a weak condition we also give weak convergence of those of brownian motions themselves on manifolds in the same class several examples are given which cover the cases when the manifolds collapse the cases when the original brownian motions converge to a non local markov process and the cases when the gromov hausdorff limit and the spectral limit by kasue and kumura are different

simultaneous equation systems as moment structure models with an introduction to latent variable models abstract an introduction to latent variable covariance structure models is provided estimation and testing of such models with normal and non normal variables is reviewed and a relatively inexpensive asymptotically distribution free estimator is introduced the traditional econometric simultaneous equation system is reconceptualized as a random vector structural equation model extensions of the model to deal with latent variables and a wider variety of structural phenomena are made via the joreskog keesling wiley lisrel approach and a simpler approach due to bentler and weeks these representation systems are extended via first and second moments about the origin of measured variables explained in terms of the structural coefficients and the moments of explanatory variables citations to further literature are provided

latent variable structural equation modeling with categorical data abstract structural equation modeling with latent variables is overviewed for situations involving a mixture of dichotomous ordered polytomous and continuous indicators of latent variables special emphasis is placed on categorical variables models in psychometrics econometrics and biometrics are interrelated via a general model due to muthen limited information least squares estimators and full information estimation are discussed an example is estimated with a model for a four wave longitudinal data set where dichotomous responses are related to each other and a set of independent variables via latent variables with a variance component structure

three types dual model for minimax fractional programming abstract we establish necessary and sufficient optimality conditions for minimax fractional programming involving nonsmooth generalized t convex functions three types dual model of 1 are considered and certain duality results have been derived in the framework of generalized t convex functions