integral equation theory for fluids ordered by an external field separable interactions the structural and thermodynamical properties of classical fluids orientationally ordered by an external field are investigated by means of integral equation theories a general theoretical framework for handling these theories is developed and detailed for the particular case of separable interactions between fluid particles this approach is then illustrated for the case of two off lattice models the ferromagnetic heisenberg model and a simple liquid crystal model for which the numerical solution of integral equations such as the percus yevick the hypernetted chain and the reference hypernetted chain closure equations are presented and compared with monte carlo simulation results and the analytical solution of the mean spherical approximation the zero field case is also examined and the spontaneous ordering is analyzed in detail mainly in what concerns the appearance of infinite wavelength singularity in the ornstein zernike equation and the relation with the one body closure equations and the long range orientational ordering that occurs in particular it is shown that the wertheim one body closure equation appears as a sum rule compatible with the ornstein zernike equation the relation between the elastic constant and the long range tail of the pair correlation function is made explicit in particular the long range behavior of the various terms in the expansion of the pair correlation function is depicted the numerical investigation of the two models shows that it is not possible to discriminate between the four integral equations as to which one would be the most accurate in all cases the general trends in the thermodynamical and structural properties seem to indicate that the percus yevick approximation is generally better in the strong ordering case whereas the reference hypernetted chain approximation might be better suited to the study of the isotropic phase and the low ordering regimes

orthogonal polynomial approach to fluids with internal degrees of freedom the case of nonpolar polarizable molecules the molecules of real liquids have internal degrees of freedom that may couple with the external ones of position and orientation so that they affect and are affected by the microscopic liquid structure for cases where the internal coordinates possess a boltzmann like distribution a procedure is described whereby such coordinates can be incorporated into the conventional formulation of classical liquid theory with no approximations beyond some reliable closure relation familiar from simple liquids the basis of the procedure is expansions in appropriate orthogonal polynomials of the internal coordinates this program is successfully carried out for a classical model of nonpolar polarizable molecules treated as drude oscillators generalizing published solutions of the mean spherical approximation for the same model

asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

integral equation and simulation studies of the heisenberg spin fluid in an external magnetic field we develop a general method to study inhomogeneous liquids in an external field using orthogonal polynomials tailored to the one body density the procedure makes integral equation calculations of these systems no more difficult than those of ordinary homogeneous molecular fluids we apply this method to the ferromagnetic heisenberg spin fluid in an external magnetic field using both the reference hypernetted chain closure and a reference version of the zerah hansen closure with no further approximations the calculation includes a mapping of the two phase region for several values of the external magnetic field comparison with monte carlo simulation data shows the integral equation procedure yielding nearly exact results in particular for nonzero external fields s1063 651x 98 15109 7

spherical functions on symmetric cones in this note we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real jordan algebra we use this formula as an inspiration for a similar recursive formula involving the jack polynomials

adjusted qmle for the spatial autoregressive parameter abstract one simple and often very effective way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter we apply this general principle to the quasi maximum likelihood estimator qmle of the autoregressive parameter in a spatial autoregression the resulting estimator for has better finite sample properties compared to the qmle for especially in the presence of a large number of covariates it can also solve the incidental parameter problem that arises for example in social interaction models with network fixed effects however spatial autoregressions present specific challenges for this type of adjustment because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for conditions for this to happen are given and implications are discussed for inference we propose confidence intervals based on a lugannani rice approximation to the distribution of the adjusted qmle of based on our simulations the coverage properties of these intervals are excellent even in models with a large number of covariates

finite sample properties of maximum likelihood estimator in spatial models we investigate the finite sample properties of the maximum likelihood estimator for the spatial autoregressive model a stochastic expansion of the score function is used to develop the second order bias and mean squared error of the maximum likelihood estimator we show that the results can be expressed in terms of the expectations of cross products of quadratic forms or ratios of quadratic forms in a normal vector which can be evaluated using the top order invariant polynomial our numerical calculations demonstrate that the second order behaviors of the maximum likelihood estimator depend on the degree of sparseness of the weights matrix

a remark on orthogonality and symmetry of operators in b h abstract if t and a are operators on a hilbert space such that t a t for all real numbers then t is said to be r orthogonal to a we obtain necessary and sufficient conditions for this to be the case as a consequence we characterize r left symmetric left symmetric and r right symmetric right symmetric operators in b h where h is a real or complex hilbert space

feasibility of multivariate density estimates summary the curse of dimensionality has been interpreted as suggesting that kernel methods have limited applicability in more than several dimensions in this note qualitative and quantitative performance measures for multivariate density estimates are examined optimal pointwise and global window widths for mean absolute and mean squared errors are compared for multivariate data one result is that the optimal pointwise absolute and squared error window widths are nearly equal for all dimensions we also show that sample size requirements predicted by absolute rather than squared error criterion are substantially less further reductions are realized by using a coefficient of variation criterion finally an example of a 10 dimensional kernel density estimate is given it is suggested that the true nature of the curse of dimensionality is as much the lack of full rank as sparseness of the data

the operator valued parallelism abstract in this paper we consider the characterization of norm parallelism problem for trace class and compact operators on a hilbert space h in particular for compact operators t s we show that t s if and only if there exists a unit vector h such that t s t s moreover for two trace class operators t s we prove that t s if and only if there exists a unit c such that tr t tr u s p ker t t s p ker t where t u t is the polar decomposition of t and t s in addition we introduce the concept of the absolute value parallelism for bounded linear operators we show that the relations norm parallelism and the absolute value parallelism are coincident for trace class operators

the ultimate estimate of the upper norm bound for the summation of operators abstract let a and b be bounded linear operators acting on a hilbert space h it is shown that the triangular inequality serves as the ultimate estimate of the upper norm bound for the sum of two operators in the sense that sup u au v bv u and v are unitaries min a i b i c consequences of the result related to spectral sets the von neumann inequality and normal dilations are discussed furthermore it is shown that the above equality can be used to characterize those unitarily invariant norms that are multiples of the operator norm in the finite dimensional case

operators preserving the strong birkhoff james orthogonality on b h abstract we characterize the class of surjective conjugate linear mappings b h b h that preserve the strong birkhoff james orthogonality in both directions we also give characterizations of rank one operators as well as coisometries in terms of the strong birkhoff james orthogonality

some inequalities for central moments of matrices abstract in this paper we shall study non commutative central moment inequalities with a focus on whether the commutative bounds are tight in the non commutative case as well we prove that the answer is affirmative for the fourth central moment and several particular results are given in the general case as an application we shall present some lower estimates of the spread of hermitian and normal matrices as well

analysis and finite element approximation of an optimal control problem for the oseen viscoelastic fluid flow in this article we study a boundary control problem for an oseen type model of viscoelastic fluid flow the existence of a unique optimal solution is proved and an optimality system is derived by the first order necessary condition we investigate finite element approximations to a solution of the optimality system and a solution algorithm for the system based on the gradient method

orthogonality to matrix subspaces and a distance formula abstract we obtain a necessary and sufficient condition for a matrix a to be birkhoff james orthogonal to any subspace w of m n c using this we obtain an expression for the distance of a from any unital c subalgebra of m n c

approximate birkhoff james orthogonality in the space of bounded linear operators there are two notions of approximate birkhoff james orthogonality in a normed space we characterize both the notions of approximate birkhoff james orthogonality in the space of bounded linear operators defined on a normed space a complete characterization of approximate birkhoff james orthogonality in the space of bounded linear operators defined on hilbert space of any dimension is obtained which improves on the recent result by chmielinski et al 2017 4 in which they characterized approximate birkhoff james orthogonality of linear operators on finite dimensional hilbert space and also of compact operators on any hilbert space c 2017 elsevier inc all rights reserved

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

numerical approximation of a quasi newtonian stokes flow problem with defective boundary conditions in this article we study the numerical approximation of a quasi newtonian stokes flow problem where only the flow rates are specified at the inflow and outflow boundaries a variational formulation of the problem using lagrange multipliers to enforce the stated flow rates is given the existence and the uniqueness to the continuous and discrete variational formulations of the solution are shown an error analysis for the numerical approximation is also given numerical computations are included which demonstrate the approximation scheme studied

complex bimatrix variate generalised beta distributions in this paper the study of bivariate generalised beta types i and ii distributions is extended to the complex matrix variate case for which the corresponding density functions are found in addition for complex bimatrix variate beta type i distributions several basic properties including the joint eigenvalue density and the maximum eigenvalue distribution are studied

exact and higher order properties of the mle in spatial autoregressive models with applications to inference abstract the quasi maximum likelihood estimator for the autoregressive parameter in a spatial autoregression usually cannot be written explicitly in terms of the data a rigorous analysis of the first order asymptotic properties of the estimator under some assumptions on the evolution of the spatial design matrix is available in lee 2004 but very little is known about its exact or higher order properties in this paper we first show that the exact cumulative distribution function of the estimator can under mild assumptions be written in terms of that of a particular quadratic form simple examples are used to illustrate important exact properties of the estimator that follow from this representation in general models a complete exact analysis is not possible but a higher order saddlepoint approximation is made available by the main result we use this approximation to construct confidence intervals for the autoregressive parameter coverage properties of the proposed confidence intervals are studied by monte carlo simulation and are found to be excellent in a variety of circumstances

a posteriori estimators for mixed finite element approximations of a fluid obeying the power law we study a posteriori error estimation in the approximation by the finite element method of a fluid which obeys the power law 2 d u r 2d u p f u 0 1 r 2 abstract and calculable a posteriori estimators are given in two fields and in a three fields version of this problem furthermore we give some examples of fe spaces satisfying the inf sup condition which relates the discrete space of tensors and the discrete space of velocities needed for this formulation

characterization of birkhoff james orthogonality the birkhoff james orthogonality is a generalization of hilbert space orthogonality to banach spaces we investigate this notion of orthogonality when the banach space has more structures we start by doing so for the banach space of square matrices moving gradually to all bounded operators on any hilbert space then to an arbitrary c algebra and finally a hilbert c module

the second order bias and mean squared error of nonlinear estimators abstract despite the now widespread use of nonlinear estimators their finite sample properties have received very little attention in either the statistics or econometrics literature we partially redress this problem by deriving and examining the second order bias and mean squared error of a fairly wide class of nonlinear estimators which includes nonlinear least squares maximum likelihood and many generalized method of moments estimators as special cases a number of examples are provided the results from a monte carlo exercise demonstrate how the results can be applied for improved inferences

special functions of matrix argument i algebraic induction zonal polynomials and hypergeometric functions hypergeometric functions of matrix argument arise in a diverse range of applications in harmonic analysis multivariate statistics quantum physics molecular chemistry and number theory this paper presents a general theory of such functions for real division algebras these functions which generalize the classical hypergeometric functions are defined by infinite series on the space s s n f of all n x n hermitian matrices over the division algebra f the theory depends intrinsically upon the representation theory of the general linear group g gl n f of invertible n x n matrices over f and the theme of this work is the full exploitation of the inherent group theory the main technique is the use of the method of algebraic induction to realize explicitly the appropriate representations of g to decompose the space of polynomial functions on s and to describe the zonal polynomials from which the hypergeometric functions are constructed detailed descriptions of the convergence properties of the series expansions are given and integral representations are provided future papers in this series will develop the fine structure of these functions 0 introduction we begin a series of articles in which we develop the fine structure of generalized hypergeometric functions of matrix argument by fine structure we allude to the analogues of such classical results as series expansions integral formulas asymptotics differential equations summation formulas addition theorems composition formulas and recurrence relations this first paper in which we simultaneously treat real complex and quaternionic analysis is the result of our desire to present a complete theory of hypergeometric functions of matrix argument over real division algebras not only as a framework for the body of detailed results to follow in later papers but also to clarify the representationtheoretic foundation for such a theory although these hypergeometric functions are of interest on purely analytic grounds they arise in a wide range of applications indeed various classes of received by the editors may 19 1986 1980 malhema1zics s ject claszficain 1985 ren primary 22e30 22e45 33a75 43a85 43a90 62h10 secondary 20g20 32a07 32m15 44a10 62e15 key w and phrases generalized hypergeometric functions zonal polynomials representation theory algebraic induction multivariate statistics general linear group generalized gamma functions pochhammer symbols laplace transforms maximal compact subgroup invariant polynomials positive cones symmetric spaces schur functions special functions of matrix argument the first author is on leave from the university of wyoming the second author was partially supported by the national science foundation under grant mcs 8403381 and by the research council of the university of north carolina b1987 american mathematical society 0002 9947 87 1 00 25 per page

analysis and finite element approximation of optimal control problems for a ladyzhenskaya model for stationary incompressible viscous flows we examine certain analytic and numerical aspects of optimal control problems for a ladyzhenskaya model for stationary incompressible viscous flows the control considered is of the distributed type the functionals minimized are the l2 distance of candidate flow to some desired flow and the viscous drag on bounding surfaces we show the existence of optimal solutions and justify the use of lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced we study the regularity of solutions of this system then we consider approximations by finite element methods of solutions of the optimality system and examine their convergence properties

birkhoff james orthogonality of linear operators on finite dimensional banach spaces abstract in this paper we characterize birkhoff james orthogonality of linear operators defined on a finite dimensional real banach space x we also explore the left symmetry of birkhoff james orthogonality of linear operators defined on x using some of the related results proved in this paper we finally prove that t l l p 2 p 2 p is left symmetric with respect to birkhoff james orthogonality if and only if t is the zero operator

a general method for third order bias and variance corrections on a nonlinear estimator motivated by a recent study of bao and ullah 2007a on finite sample properties of mle in the pure sar spatial autoregressive model a general method for third order bias and variance corrections on a nonlinear estimator is proposed based on stochastic expansion and bootstrap working with concentrated estimating equation simplifies greatly the high order expansions for bias and variance a simple bootstrap procedure overcomes a major difficulty in analytically evaluating expectations of various quantities in the expansions the method is then studied in detail using a more general sar model with its effectiveness in correcting bias and improving inference fully demonstrated by extensive monte carlo experiments compared with the analytical approach the proposed approach is much simpler and has a much wider applicability the validity of the bootstrap procedure is formally established the proposed method is then extended to the case of more than one nonlinear estimator

analysis and approximation of the cross model for quasi newtonian flows with defective boundary conditions a numerical method for a generalized newtonian fluid with flow rate boundary conditions is considered the defect boundary condition problem is formulated as a constrained optimal control problem where a flow balance is forced on the inflow and outflow boundaries using a neumann control the control problem is analyzed for an existence result and the lagrange multiplier rule a decoupling solution algorithm is presented and numerical experiments are provided to validate robustness of the algorithm

inverse wishart distributions based on singular elliptically contoured distribution abstract assuming that the random matrix x has a singular or non singular matrix variate elliptically contoured distribution the density function of the moore penrose inverse z x x is given with respect to the hausdorff measure the result is applied to bayesian inference for a general multivariate linear regression model with matrix variate elliptically distributed errors some results concerning the posterior joint and marginal distributions of the parameters are obtained

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

on operators preserving james orthogonality abstract we characterise isometries and coisometries in b h in terms of james orthogonality as a consequence we obtain a characterisation of surjective linear or conjugate linear mappings b h b h that preserve james orthogonality in both directions

orthogonality of matrices abstract let a and b be rectangular matrices then a is orthogonal to b if a b a for every scalar some approximation theory and convexity results on matrices are used to study orthogonality of matrices and answer an open problem of bhatia and semrl

operator norm attainment and birkhoff james orthogonality abstract recently in sain d paul k operator norm attainment and inner product spaces linear algebra appl 439 2013 2448 2452 it was proved that if t is a linear operator on a finite dimensional real normed linear space x such that t attains norm only on d where d is a connected closed subset of s x then t satisfies the bhatia semrl bs property bhatia r semrl p orthogonality of matrices and distance problem linear algebra appl 287 1999 77 85 i e for a l x t b a implies that there exists x d such that t x b a x here we explore the converse of the above result we prove that in a real normed linear space x of dimension 2 a linear operator t satisfies the bs property if and only if the set of unit vectors on which t attains norm is connected in the corresponding projective space r p 1 s x x x motivated by the result in 2 dimensions we conjecture that this characterization of bs property is true in general n dimensional real normed linear spaces we further prove that if the space x is strictly convex then the set of operators in l x which satisfy the bs property is dense in l x

continuum percolation of simple fluids energetic connectivity criteria abstract during the last few years a number of works in computer simulation have focused on the clustering and percolation properties of simple fluids based on an energetic connectivity criterion proposed long ago by t l hill j chem phys 23 1955 617 this connectivity criterion appears to be the most appropriate in the study of gas liquid phase transition so far integral equation theories have relayed on a velocity averaged version of this criterion we show by using molecular dynamics simulations that this average strongly overestimates percolation densities in the lennard jones fluid making unreliable any prediction based on it additionally we use a recently developed integral equation theory phys rev e 61 2000 r6067 to show how this velocity average can be overcome

a low order mixed finite element method for a class of quasi newtonian stokes flows part i a priori error analysis abstract this is the second part of a work dealing with a low order mixed finite element method for a class of nonlinear stokes models arising in quasi newtonian fluids in the first part we showed that the resulting variational formulation is given by a twofold saddle point operator equation and that the corresponding galerkin scheme becomes well posed with piecewise constant functions and raviart thomas spaces of lowest order as the associated finite element subspaces in this paper we develop a bank weiser type a posteriori error analysis yielding a reliable estimate and propose the corresponding adaptive algorithm to compute the mixed finite element solutions several numerical results illustrating the efficiency of the method are also provided

on zero trace matrices let a be an n n complex matrix and let 1 p it is shown that tr a 0 if and only if i za p nsol1p for all z c some related characterizations are also given

some inequalities for positive linear maps it has long been known that an analogue of jensen s inequality holds for positive unital linear maps on matrix algebras provided that instead of ordinary convex functions one restricts to matrix convex functions we show that this restriction is not necessary in the case of 2 2 matrices a noncommutative analogue of the variance is studied and a basic inequality with several applications is established

asymptotically optimal bandwidth selection for kernel density estimators from randomly right censored samples abstract this paper makes two important contributions to the theory of bandwidth selection for kernel density estimators under right censorship first an asymptotic representation of the integrated squared error into easily understood variance and squared bias components is given second it is shown that if the bandwidth is chosen by the data based method of least squares cross validation then it is asymptotically optimal in a compelling sense a by product of the first part is an interesting comparison of the two most popular kernel estimators keywords nonparametric density estimation smoothing parameter

residual a posteriori error estimator for a three field model of a non linear generalized stokes problem in this article we propose and analyze an a posteriori error estimator for a three field model of a generalized stokes problem the components of the a posteriori error estimator are defined via a non linear projection of the residues of the variational equations both upper and lower bounds for the approximation error are derived in terms of the components of the a posteriori error estimator the non linear projections do not need to be explicitly computed to construct the a posteriori error estimates

quantity of operators with bhatia semrl property abstract we study the bhatia semrl property which is related to birkhoff james orthogonality on operator spaces recently many authors obtained some conditions for operators to have bhatia semrl property using them we explore the denseness of operators with bhatia semrl property or without bhatia semrl property on some classes of banach spaces

optimal control for quasi newtonian flows with defective boundary conditions we consider a generalized newtonian fluid with defective boundary conditions where only flow rates or mean pressures are prescribed on parts of boundary the defect boundary condition problem is formulated as an optimal control problem in which a neumann or dirichlet boundary control is used for matching given flow rates or mean pressures for the constrained optimization problem an optimality system is derived from which a solution of the problem is obtained computational algorithms are discussed and numerical results are also presented

a new approach to numerical solution of defective boundary value problems in incompressible fluid dynamics we consider the incompressible navier stokes equations where on a part of the boundary flow rate and mean pressure boundary conditions are prescribed there are basically two strategies for solving these defective boundary problems the variational approach see j heywood r rannacher and s turek internat j numer methods fluids 22 1996 pp 325 352 and the augmented formulation see l formaggia j f gerbeau f nobile and a quarteroni siam j numer anal 40 2002 pp 376 401 and a veneziani and c vergara internat j numer methods fluids 47 2005 pp 803 816 however both of these approaches present some drawbacks for the flow rate problem the former resorts to nonstandard functional spaces which are quite difficult to discretize on the other hand for the mean pressure problem it yields exact solutions only in very special cases the latter is applicable only to the flow rate problem since for the mean pressure problem it provides unfeasible boundary conditions in this paper we propose a new strategy based on a reformulation of the problems at hand in terms of the minimization of an appropriate functional this approach allows us to treat the two kinds of problems flow rate and mean pressure successfully within the same framework which can be useful in view of a mixed problem where the two conditions are simultaneously prescribed on different artificial boundaries moreover it is more versatile being prone to be extended to other kinds of defective conditions we analyze the problems obtained with this approach and propose some algorithms for their numerical solution several numerical results are presented supporting the effectiveness of our approach

on symmetry of birkhoff orthogonality in the positive cones of c algebras with applications abstract in this paper local symmetry of birkhoff orthogonality is considered in the positive cones of c algebras for the positive cone a of a c algebra a the notion of a local left or right symmetric points for birkhoff orthogonality is introduced some simple characterizations of them are given as an application we determine the form of birkhoff orthogonality preservers between the positive cones of c algebras by using jordan isomorphisms

orthogonality of matrices and some distance problems abstract if a and b are matrices such that a zb a for all complex numbers z then a is said to be orthogonal to b we find necessary and sufficient conditions for this to be the case some applications and generalisations are also discussed

numerical treatment of defective boundary conditions for the navier stokes equations we present a formulation for accommodating defective boundary conditions for the incompressible navier stokes equations where only averaged values are prescribed on measurable portions of the boundary in particular we consider the case where the flow rate is imposed on several domain sections this methodology has an interesting application in the numerical simulation of flow in blood vessels when only a reduced set of boundary data are generally available for the upstream and downstream sections

approximate orthogonality in normed spaces and its applications abstract in a normed space we consider an approximate orthogonality relation related to the birkhoff orthogonality we give some properties of this relation as well as applications in particular we characterize the approximate orthogonality in the class of linear bounded operators on a hilbert space

unimodal models to relate species to environment to assess the impact of environmental change on biological communities knowledge about species environment relationships is indispensable ecologists attempt to uncover the relationships between species and environment from data obtained from field surveys in the survey species are scored on their presence or their abundance at each of several sampling sites and environmental variables that ecologists believe to be important are measured the research that led to this thesis aimed to unravel the assumptions required for the application of statistical methods that are popular among ecologists to analyse such data from a statistical point of view species data are difficult to analyse there are many species involved 10 500 many species occur at a few sites only so the data contain numerous zeroes relations between species and environmental variables are not linear but unimodal a plant for example preferably grows under for that species optimal moisture conditions and is encountered less frequently at drier or wetter sites a mathematical model for a unimodal relationship is the gaussian response model standard statistical methods such as linear regression principal components analysis and canonical correlation analysis are often inappropriate for analysing species data because they are based on linear relationships one of the methods that ecologists use instead is correspondence analysis this thesis contributes to the understanding of the underlying response model with correspondence analysis species and sites are arranged to discover the structure in the data ordination and the arrangement is subsequently related to environmental variables it is an indirect method to detect relations between species and environment hence r h whittaker s term indirect gradient analysis correspondence analysis has been invented around 1935 but did not receive interest from ecologists before 1973 when m o hill derived the technique once more as the repeated application of weighted averaging a method that was familiar to ecologists ever since 1930 weighted averaging has the advantage of being simple to apply the method can be used for two different aims 1 to estimate the optimum of a species for an environmental variable and 2 to estimate the value of an environmental variable at a site from known optima of the species present calibration in chapter 2 estimating optima by weighted averaging is compared with the results of non linear regression on the basis of the gaussian response model under particular conditions both methods agree precisely in other cases weighted averaging gives a biased estimate of the optimum and non linear regression is the method to be preferred an additional advantage of non linear regression is that it can also be used to fit response models with more than one environmental variable in chapter 3 weighted averaging to estimate the value of an environmental variable is compared with calibration on the basis of the gaussian response model also in this context the techniques are sometimes equivalent chapter 4 deals with correspondence analysis it is shown that under particular conditions correspondence analysis approximates ordination on the basis of the gaussian response model which is computationally much more complicated to detect relations indirect methods have an important disadvantage the impact of some environmental variables on the species composition can be so large that the impact of other interesting environmental variables may fail to be detected this problem can be overcome by using non linear regression but with many species and environmental variables this is laborious in chapter 5 a simpler direct method is proposed canonical correspondence analysis in chapter 6 canonical correspondence analysis turns out to be a multivariate extension of weighted averaging the results can be displayed graphically in chapter 7 an extension with covariables is discussed which leads to partial canonical correspondence analysis chapter 7 also shows that gaussian models and hence canonical correspondence analysis are relevant to the analysis of contingency tables chapter 8 describes a study to estimate ecological amplitudes of plant species with respect to ellenberg s moisture scale from species data alone the question that is addressed as well is how consequent ellenberg s moisture indicator values are finally chapter 9 cross tabulates various gradient analysis techniques by the type of problem regression calibration ordination etc and the response model linear or unimodal furthermore improvements are proposed for detrended correspondence analysis a computer program named mom is written which can perform most of the methods discussed

specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances this study develops a methodology of inference for a widely used cliff ord type spatial model containing spatial lags in the dependent variable exogenous variables and the disturbance terms while allowing for unknown heteroskedasticity in the innovations we first generalize the gmm estimator suggested in kelejian and prucha 1998 1999 for the spatial autoregressive parameter in the disturbance process we also define iv estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the gmm estimator much of the theory is kept general to cover a wide range of settings

orthogonality of matrices abstract let x be a real finite dimensional normed space with unit sphere sx and let l x be the space of linear operators from x into itself it is proved that x is an inner product space if and only if for a c l x a c u s x a au au cu where denotes birkhoff orthogonality

the birkhoff james orthogonality of operators on infinite dimensional banach spaces abstract we study the birkhoff james orthogonality on operator spaces in terms of the bhatia semrl property we first prove that every functional on a banach space x has the bhatia semrl property if and only if x is reflexive we also find some geometric conditions of banach space which ensure the denseness of operators with bhatia semrl property finally we investigate operators with the bhatia semrl property when a domain space is l 1 0 1 or c 0 1

birkhoff james orthogonality and smoothness of bounded linear operators abstract we present a sufficient condition for smoothness of bounded linear operators on banach spaces for the first time let t a b x y where x is a real banach space and y is a real normed linear space we find sufficient condition for t b a t x b a x for some x s x with t x t and use it to show that t is a smooth point in b x y if t attains its norm at unique upto multiplication by scalar vector x s x tx is a smooth point of y and sup y c t y t for all closed subsets c of s x with d x c 0 for operators on a hilbert space h we show that t b a t x b a x for some x s h with t x t if and only if the norm attaining set m t x s h t x t s h 0 for some finite dimensional subspace h 0 and t h o t we also characterize smoothness of compact operators on normed spaces and bounded linear operators on hilbert spaces

a kernel type estimator of a quantile function from right censored data abstract based on right censored data from a lifetime distribution f 0 a kernel type estimator of the quantile function qo p inf t f 0 t p 0 p 1 is proposed the estimator is defined by which is smoother than the usual product limit quantile function where denotes the product limit estimator of f 0 from the censored sample under the random censorship model and general conditions on hn k and f 0 it is shown that qn p is strongly consistent in addition an approximation to qn is shown to be asymptotically equivalent to qn with probability one a small monte carlo simulation study shows that for several values of the bandwidth hn qn performs better than in the sense of estimated mean squared errors an optimal bandwidth hn may be estimated by bootstrap methods in some cases the procedure is illustrated by an application to data from a mechanical switch life test

percolation of clusters with a residence time in the bond definition integral equation theory we consider the clustering and percolation of continuum systems whose particles interact via the lennard jones pair potential a cluster definition is used according to which two particles are considered directly connected bonded at time t if they remain within a distance d the connectivity distance during at least a time of duration tau the residence time an integral equation for the corresponding pair connectedness function recently proposed by two of the authors phys rev e 61 r6067 2000 is solved using the orthogonal polynomial approach developed by another of the authors phys rev e 55 426 1997 we compare our results with those obtained by molecular dynamics simulations

the birkhoff james orthogonality in hilbert c modules abstract in this paper we characterize the birkhoff james orthogonality for elements of a hilbert c module in terms of states of the underlying c algebra we also show that the birkhoff james orthogonality in a hilbert c module over a c algebra a and orthogonality with respect to the a valued inner product coincide if and only if a is isomorphic to c in addition some new results concerning the case of equality in the triangle inequality for elements of a hilbert c module are obtained

symmetric points for strong birkhoff orthogonality in von neumann algebras with applications to preserver problems abstract complete characterizations of left or right symmetric points for strong birkhoff orthogonality in von neumann algebras and abelian unital c algebras are given as an application we show that every linear strong birkhoff orthogonality preserver between von neumann algebras is an algebraic isomorphism

on wishart distribution some extensions this paper proposes a unified approach that enables the wishart distribution to be studied simultaneously in the real complex quaternion and octonion cases under elliptical models in particular the matrix multivariate elliptical distribution the noncentral generalised wishart distribution the joint density of the eigenvalues and the distribution of the maximum eigenvalue are obtained for real normed division algebras

integral equation theory of polydisperse colloidal suspensions using orthogonal polynomial expansions a procedure is described for the calculation of the generalized pair distribution function g r s s8 where s is a molecular random variable with distribution f s using generalized integral equations familiar from simple liquid theory the method is based on expansions of all s dependent functions in the orthogonal polynomials p j s associated with the weight f s and is computationally efficient to illustrate the procedure calculations are made for a charge stabilized polydisperse colloidal suspension with schulz distribution of diameters s the method can be immediately generalized to fluids with internal degrees of freedom for which f s must itself be self consistently determined s1063 651x 96 12610 6

numerical analysis of a three fields model for a quasi newtonian flow abstract we study a finite element approximation of a non linear three fields version of stokes system for incompressible fluids such a problem arises when one considers a white metzner type model for a viscoelastic fluid flow and sets the relaxation time to zero the non linear aspect comes from the fact that a fraction of the viscosity of the fluid depends on the second invariant of the rate of deformation tensor we give existence and unicity results for the continuous problem and its approximation and we prove the error bound

refinements in maximum likelihood inference on spatial autocorrelation in panel data in a panel data model with fixed effects possible cross sectional dependence is investigated in a spatial autoregressive setting an edgeworth expansion is developed for the maximum likelihood estimate of the spatial correlation coefficient the expansion is used to develop more accurate interval estimates for the coefficient and tests for cross sectional independence that have better size properties than corresponding rules of statistical inference based on first order asymptotic theory comparisons of finite sample performance are carried out using monte carlo simulations

on stochastic majorization of the eigenvalues of a wishart matrix abstract in multivariate statistical analysis orthogonally invariant sets of real positive definite p p matrices occur as acceptance regions for tests of invariant hypotheses concerning the covariance matrix of a multivariate normal distribution equivalently orthogonally invariant acceptance regions can be expressed in terms of the eigenvalues l 1 s l p s of a random wishart matrix s w p n with n degrees of freedom and expectation n the probabilities of such regions depend on only though 1 p the eigenvalues of in this paper the behavior of these probabilities is studied when some i increase while others decrease our results will be expressed in terms of the majorization ordering applied to the vector 1 p where i log i and have implications for the unbiasedness and monotonicity of the power functions of orthogonally invariant tests

generating pseudo random time series with specified marginal distributions abstract our goal is to generate a target time series with a specified marginal distribution and a specified lag one autocorrelation we consider an existing approach first transform a known autocorrelated reference series into the corresponding uniform autocorrelated series and then apply the specified inverse transformation to each observation producing the target series this approach is simple except that the lag one reference series autocorrelation must be determined in a set up step we propose a method for determining this autocorrelation

relative numerical ranges abstract relying on the ideas of stampfli 14 and magajna 12 we introduce for operators s and t on a separable complex hilbert space a new notion called the numerical range of s relative to t at r t some properties of these numerical ranges are proved in particular it is shown that the relative numerical ranges are non empty convex subsets of the closure of the ordinary numerical range of s we show that the position of zero with respect to the relative numerical range of s relative to t at t gives an information about the distance between the involved operators this result has many interesting corollaries for instance one can characterize those complex numbers which are in the closure of the numerical range of s but are not in the spectrum of s

strong uniform consistency for nonparametric survival curve estimators from randomly censored data let p x t f t p y t g t and p z t h t h t f t g t an important problem of survival analysis is the estimation of the distribution function f recently the properties of two types of estimators were investigated one of them is the product limit p l estimator of kaplan and meier 8 the other is the nonparametric bayesian estimator introduced by v susarla and j van ryzin 11 in an earlier paper 13 b b winter and the authors proved the uniform consistency of the p l in a second joint paper 6 there was proved the uniform consistency of the p l with rate of o log n l12 nll4 the results of the above two papers were proved without any continuity conditions on f and g in case of arbitrary f and discrete g having finitely many jump points the uniform consistency of the p l with rate factor 0 log nl t was proved in 5 in 10 susarla and van rjzin proved for the bayesian estimator the pointwise consistency with rate factor o log n and the pointwise mean square consistency with rate factor