asymptotic equivalence of nonparametric regression and white noise the principal result is that under conditions to any nonparametric regression problem there corresponds an asymptotically equivalent sequence of white noise with drift problems and conversely this asymptotic equivalence is in a global and uniform sense any normalized risk function attainable in one problem is asymptotically attainable in the other with the difference in normalized risks converging to zero uniformly over the entire parameter space the results are constructive a recipe is provided for producing these asymptotically equivalent procedures some implications and generalizations of the principal result are also discussed

the intrinsic distribution and selection bias of long period cometary orbits a question that arises in the study of cometary orbits is whether or not the directed normals to the orbits are uniformly distributed on the celestial sphere previous studies by statisticians have not taken selection effects into account and have tended to reject uniformity here a plausible selection mechanism is proposed that gives rise to a one parameter family of distributions on the sphere data on long period comets are analyzed using this one parameter family a nonzero selection effect is detected and its size is estimated subject to this selection effect uniformity of the directed normals can no longer be ruled out

projective fourier analysis for patterns abstract identifying psl 2 c as a projective group for patterns in the conformal camera model the projective harmonic analysis on its double covering group sl 2 c is presented in the noncompact and compact pictures the pictures used to study different aspects of irreducible unitary representations of semisimple lie groups bypassing technicalities of representation theory but stressing the motivation and similarities with euclidean fourier analysis each constructed picture of the projective fourier analysis includes the fourier transform plancherel s theorem and convolution property projectively covariant characteristics of the analysis in the noncompact picture allow rendering any of image projective transformations of a pattern after removing conformal distortions by using only one projective fourier transform of the original pattern what is demonstrated in a computer simulation the convolution properties in both pictures must by used to develop algorithms for projectively invariant matching of patterns work in progress on fast algorithms for computing with projective fourier transforms and for rendering image projective transformations is discussed efficient computations of the convolutions would follow from the both fast projective fourier transforms and their inverses

three positive solutions for a generalized laplacian boundary value problem with a parameter concerned is a generalized laplacian boundary value problem with a positive parameter first we apply the leggett williams fixed point theorem to establish sufficient conditions on the existence of at least three positive solutions for the parameter belonging to an explicit interval then under a little bit stronger assumptions we show that there are at least three positive symmetric solutions for the parameter in an open interval the obtained results are new even for laplacian boundary value problems and they are illustrated with an example

existence of positive solutions for non positive higher order bvps abstract we shall provide conditions on non positive function f t u 1 u n 1 so that the boundary value problem has at least one positive solution then we shall apply this result to establish several existence theorems which guarantee the multiple positive solutions

l espace symetrique de drinfeld et correspondance de langlands locale ii we study the geometry and the cohomology of the tamely ramified cover of drinfeld s p adic symmetric space over a p adic field k for this tame level we prove in a purely local way most of a conjecture of harris on the form of the ell adic cohomologies as well as the torsion freeness of the integral cohomology in this paper we also compute the ell adic cohomology of coxeter deligne lusztig variety associated to mathrm gl d and some results of independent interest on the coefficient systems over the bruhat tits building associated to mathrm gl d k have been established

bayesian aspects of some nonparametric problems we study the bayesian approach to nonparametric function estimation problems such as nonparametric regression and signal estimation we consider the asymptotic properties of bayes procedures for conjugate gaussian priors we show that so long as the prior puts nonzero measure on the very large parameter set of interest then the bayes estimators are not satisfactory more specifically we show that these estimators do not achieve the correct minimax rate over norm bounded sets in the parameter space thus all bayes estimators for proper gaussian priors have zero asymptotic efficiency in this minimax sense we then present a class of priors whose bayes procedures attain the optimal minimax rate of convergence these priors may be viewed as compound or hierarchical mixtures of suitable gaussian distributions

positive solutions of difference equations with two point right focal boundary conditions abstract we consider the following boundary value problem formula formula where 1 p n 1 is fixed using a fixed point theorem for operators on a cone we develop criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are established for special cases we also include several examples to dwell upon the importance of the results obtained

multivariate smoothing spline functions given data z i g t i varepsilon i 1 leqq i leqq n where g is the unknown function the t i are known d dimensional variables in a domain omega and the varepsilon i are i

an empirical bayes approach to directional data and efficient computation on the sphere this paper proposes a consistent nonparametric empirical bayes estimator of the prior density for directional data the methodology is to use fourier analysis on s 2 to adapt euclidean techniques to this non euclidean environment general consistency results are obtained in addition a discussion of efficient numerical computation of fourier transforms on s 2 is given and their applications to the methods suggested in this paper are sketched

singular nonlinear boundary value problems for second order ordinary differential equations abstract the boundary value problem y f x y 0 y 0 y 0 0 y 1 y 1 0 is studied under conditions which are modeled on the problem y a x y p 0y 0 y 1 0 or y 0 y 1 0 which occurs in a number of applications the technical arguments involve properties of solutions i e concavity and the use of iterative techniques a new fixed point theorem for cones for decreasing mappings is proved and used it is of interest in its own right since most such theorems are for monotone increasing mappings

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

fixed sign solutions of a system of higher order difference equations abstract we consider the following system m u i k f i k u 1 k u 2 k u n k 0 k 0 1 t j u i 0 0 0 j m 3 i m 2 u i 0 i m 1 u i 0 0 i m 2 u i t 1 i m 1 u i t 1 0 i 1 2 n where m 2 t m 1 and for each 1 i n i 0 i 0 i 0 i i and i i t 1 i i i i 0 criteria are offered for the existence of single and double fixed sign solutions of the system

deconvolution density estimation on so n this paper develops nonparametric deconvolution density estimation over so n the group of n x n orthogonal matrices of determinant 1 the methodology is to use the group and manifold structures to adapt the euclidean deconvolution techniques to this lie group environment this is achieved by employing the theory of group representations explicit to so n general consistency results are obtained with specific rates of convergence achieved under sufficient smoothness conditions application to empirical bayes prior estimation and inference is also discussed

existence of positive solutions of bvps for third order discrete nonlinear difference systems in this paper we consider the following boundary value problem of discrete email protected 3u 1 k f 1 k u 1 k u 2 k 0 email protected 0 t d 3u 2 k f 2 k u 1 k u 2 k 0 email protected 0 t with the dirichlet boundary conditionu 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 some new results of the existence nonexistence and multiplicity are obtained by using krasnosel skii s fixed point theorem in a cone in particular it is proved that the above boundary value problem has n positive solutions under suitable conditions where n is an arbitrary positive integer

singular k n k boundary value problems between conjugate and right focal abstract for 1 k n 1 and 0 q k 1 solutions are obtained for the boundary value problem 1 n k f x y y i 0 0 i k 1 and y i 0 q j n k q 1 where f x y is singular at y 0 an application is made of a fixed point theorem for operators that are decreasing with respect to a cone

spline interpolation and smoothing on hyperspheres the authors generalize wahba s theory siam j sci statist comput 2 1981 pp 5 16 on spline interpolation and smoothing on the surface of the two dimensional unit sphere to arbitrary dimensional hyperspheres as a consequence practical solutions to minimum norm interpolation and smoothing problems on hyperspheres are provided in terms of certain hyperspherical splines in addition wahba s results for powers of the laplace beltrami operator are extended to more general operators and wahba s hilbert space of constant functions is expanded to allow more than just constant functions extensive curve fitting calculations are made for some two and higher dimensional test problems using hyperspherical harmonics and hyperspherical splines it is found that hyperspherical splines yield better fits than hyperspherical harmonics for test functions that possess no symmetry and are not infinitely differentiable tests have been run using several continuous functions satisfactory absolute errors can be obt

approximation of method of regularization estimators la methode de tikhonov est une methode generale d estimation du parametre de regression non parametrique dans un modele lineaire abstrait avec un bruit discret on donne une analyse asymptotique dans laquelle le probleme d estimation discrete est approche par une estimation continue

singular boundary value problems for superlinear second order ordinary and delay differential equations abstract existence criteria are established for singular boundary value problems for nonlinear second order ordinary and delay differential equations the theorems obtained are very general and complement previous known results

focal boundary value problems for singular difference equations abstract solutions are shown to exist for the boundary value problem n u m f m u u n 2 u 0 m 0 t satisfying focal boundary conditions where f m y 1 y n 1 is singular at y i 0 1 i n the techniques involve concavity properties iterations and a fixed point theorem for mappings which are decreasing with respect to a cone in a banach space

positive solutions to singular multi point dynamic eigenvalue problems with mixed derivatives abstract this paper considers a singular m point dynamic eigenvalue problem on time scales t p t u t f t u t t 0 1 t u 0 i 1 m 2 a i u i u 1 p 1 u 1 i 1 m 2 b i p i u i we allow f t w to be singular at w 0 and t 0 by constructing the green s function and studying its positivity eigenvalue intervals in which there exist positive solutions of the above problem are obtained by making use of the fixed point index theory

lidstone polynomials and boundary value problems abstract we define lidstone polynomials provide their explicit representations give their relations with bernoulli polynomials obtain best possible error estimates in lidstone interpolation and establish several best possible sharp inequalities which compare favourably with the known results next we use these results to study even order differential equations together with lidstone boundary conditions

spectral theory of second order vector difference equations abstract this paper is concerned with spectral problems of second order vector difference equations with two point boundary value conditions where the matrix valued coefficient of the leading term may be singular a concept of self adjointness of the boundary value conditions is introduced the self adjointness of the corresponding difference operator is discussed on a suitable admissible function space and fundamental spectral results are obtained the dual orthogonality of eigenfunctions is shown in a special case rayleigh s principles and the minimax theorems in two linear spaces are given as an application a comparison theorem for eigenvalues of two sturm liouville problems is presented

positive solutions of bvps for third order nonlinear difference systems abstract in this paper we consider the following discrete system boundary value problems 3 u 1 k f 1 k u 1 k u 2 k 0 k o t 3 u 2 k f 2 k u 1 k u 2 k 0 k o t with the dirichlet boundary condition u 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 some sufficient conditions are obtained for the existence of one or two positive solutions to the above system by using a nonlinear alternative of leray schauder type and krasnosel skii s fixed point theorem in a cone

acyclicity of schneider and stuhler s coefficient systems another approach in the level 0 case let f be a non archimedean local field and g be the locally profinite group gl n f n 1 we denote by x the bruhat tits building of g for any smooth complex representation v of g and for any level n 1 schneider and stuhler have constructed a coefficient system c c v n on the simplicial complex x they proved that if v is generated by its fixed vectors under the principal congruence subgroup of level n then the augmented complex c or x c v of oriented chains of x with coefficients in c is a resolution of v in the category of smooth complex representations of g in this paper we give another proof of this result in the level 0 case and assuming moreover that v is generated by its fixed vectors under an iwahori subgroup i of g here level 0 refers to bushnell and kutzko s terminology that is to the case n 1 0 our approach is different we strongly use the fact that the trivial character of i is a type in the sense of bushnell and kutzko

on the breuil mezard conjecture we give a new local proof of the breuil mezard conjecture for 2 dimensional representations of the absolute galois group of qp when p 5 and the representation has scalar endomorphisms

asymptotics for spherical needlets we investigate invariant random fields on the sphere using a new type of spherical wavelets called needlets these are compactly supported in frequency and enjoy excellent localization properties in real space with quasi exponentially decaying tails we show that for random fields on the sphere the needlet coefficients are asymptotically uncorrelated for any fixed angular distance this property is used to derive clt and functional clt convergence results for polynomial functionals of the needlet coefficients here the asymptotictheory is considered in the high frequency sense our proposals emerge from strong empirical motivations especially in connection with the analysis of cosmological data sets 1 introduction over the last two decades wavelets have emerged as one of the most interesting tools of statistical investigation in this paper we give an application to the statistical analysis of data sets indexed by the unit sphere s 2 this is motivated mostly by the analysis of the cosmic

bifurcation techniques and positive solutions of discrete lidstone boundary value problems abstract let n 1 t n 5 be two positive integers and t n n n 1 t we consider the existence of solutions of the discrete lidstone boundary value problem 1 n 2 n u t n f t u t 2 u t 1 2 n 2 u t n 1 t t n 2 i u n i 1 2 i u t i 1 0 i 0 1 n 1 where f t n r n r is continuous

three positive solutions of boundary value problems for p laplacian difference equations in this paper existence criteria for three positive solutions of p laplacian difference equation f p u t 1 a t f u t 0 t 1 t 1 u 0 u t 2 0 oru 0 u t 1 0 are established by using the five functionals fixed point theorem as an application one example is given to illustrate the main result in this paper

triple positive solutions of conjugate boundary value problems ii we consider the following boundary value problems 1 n py n a t h y n 2 t 0 1 y i 0 0 0 i p 1 y i 1 0 0 i n p 1 and 1 n p ny f k y y n 1y n 2 0 k m iy 0 0 i p 1 iy m p 1 0 0 i n p 1 where 1 p n 1 is fixed by employing fixed point theorems for operators on a cone existence criteria are developed for multiple at least three positive solutions of the boundary value problems as an application we also establish the existence of radial solutions of certain partial difference equations several examples are included to dwell upon the importance of the results obtained

multiple positive solutions of bvps for third order discrete difference systems this paper is concerned with the following email protected 3u 1 k f 1 k u 1 k u 2 k 0 email protected 0 t d 3u 2 k f 2 k u 1 k u 2 k 0 email protected 0 t with the dirichlet boundary conditionu 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 by using leggett williams fixed point theorem sufficient conditions are obtained for the existence of three positive solutions to the above system

eigenvalues and eigenfunctions of discrete conjugate boundary value problems abstract we consider the following boundary value problem 1 n p n y f k y y n 1 y n 2 0 k m i y 0 0 0 i p 1 i y m n i 0 0 i n p 1 where 1 p n 1 is fixed and 0 a characterization of the values of is carried out so that the boundary value problem has a positive solution next for 1 criteria are developed for the existence of two positive solutions of the boundary value problem in addition for particular cases we also offer upper and lower bounds for these positive solutions several examples are included to dwell upon the importance of the results obtained

spline smoothing and optimal rates of convergence in nonparametric regression models linear estimation is considered in nonparametric regression models of the form yi f xi ei xi e a b where the zero mean errors are uncorrelated with common variance a2 and the response function f is assumed only to have a bounded square integrable qth derivative the linear estimator which minimizes the maximum mean squared error summed over the observation points is derived and the exact minimax rate of convergence is obtained for practical problems where bounds on 11 f2q 11 and a2 may be unknown generalized cross validation is shown to give an adaptive estimator which achieves the minimax optimal rate under the additional assumption of normality 1 the model consider the nonparametric regression model

on eigenvalue intervals and twin eigenfunctions of higher order boundary value problems abstract in this paper we shall consider the boundary value problem y n q t y y 1 y n 2 p t y y 1 y n 2 n 2 t 1 1 y i 0 0 0 i n 3 y n 2 0 y n 1 0 0 yy n 2 1 y n 1 1 0 where 0 and are constants satisfying 0 0 0 and 0 intervals of are determined to ensure the existence of a positive solution of the boundary value problem for 1 we shall also offer criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are obtained for special cases several examples are included to dwell upon the importance of the results obtained

backfitting in smoothing spline anova a computational scheme for fitting smoothing spline anova models to large data sets with a near tensor product design is proposed such data sets are common in spatial temporal analyses the proposed scheme uses the backfitting algorithm to take advantage of the tensor product design to save both computational memory and time several ways to further speed up the backfitting algorithm such as collapsing component functions and successive over relaxation are discussed an iterative imputation procedure is used to handle the cases of near tensor product designs an application to a global historical surface air temperature data set which motivated this work is used to illustrate the scheme proposed

a generalization of concavity for finite differences abstract the concept of concavity is generalized to discrete functions u satisfying the n th order difference inequality 1 n k n u m 0 m 0 1 n and the homogeneous boundary conditions u 0 u k 1 0 u n k 1 u n n 0 for some k 1 n 1 a piecewise polynomial is constructed which bounds u below the piecewise polynomial is employed to obtain a positive lower bound on u m for m k n k where the lower bound is proportional to the supremum of u an analogous bound is obtained for a related green s function

existence of positive solutions for 2nth order singular superlinear boundary value problems this paper investigates the existence of positive solutions for 2nth order n 1 singular superlinear boundary value problems a necessary and sufficient condition for the existence of c 2 n 2 0 1 as well as c 2 n 1 0 1 positive solutions is given by constructing a special cone and with the e norm

discrete polynomial interpolation green s functions maximum principles error bounds and boundary value problems abstract we construct discrete interpolating polynomials provide explicit representations of discrete green s functions give several identities and inequalities for these green s functions use the explicit forms of the interpolating polynomials and that of green s functions to establish several maximum principles further we obtain error bounds in discrete polynomial interpolation and use them to study existence and uniqueness of the discrete boundary value problems these bounds are also used to provide sufficient conditions for the convergence of the picard s method the approximate picard s method quasilinearization and the approximate quasilinearization the monotone convergence of the picard s iterative method is also analysed

intrinsic regression models for medial representation of subcortical structures the aim of this article is to develop a semiparametric model to describe the variability of the medial representation of subcortical structures which belongs to a riemannian manifold and establish its association with covariates of interest such as diagnostic status age and gender we develop a two stage estimation procedure to calculate the parameter estimates the first stage is to calculate an intrinsic least squares estimator of the parameter vector using the annealing evolutionary stochastic approximation monte carlo algorithm and then the second stage is to construct a set of estimating equations to obtain a more efficient estimate with the intrinsic least squares estimate as the starting point we use wald statistics to test linear hypotheses of unknown parameters and establish their limiting distributions simulation studies are used to evaluate the accuracy of our parameter estimates and the finite sample performance of the wald statistics we apply our methods to the detection of the diffe

existence of positive solutions of bvps for second order nonlinear difference systems this paper is concerned with the following system d 2u i k f i k u 1 k u 2 k u n k 0 k 0 t i 1 2 nwith the dirichlet boundary conditionu i 0 u i t 2 0 i 1 2 n some new results are obtained for the existence and multiplicity of positive solutions to the above system by using nonlinear alternative of leray schauder type krasnosel skii s fixed point theorem in a cone and leggett williams fixed point theorem in particular it proves that the above system has n positive solutions under suitable conditions where n is an arbitrary integer

thomas bayes walk on manifolds convergence of the bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold or more generally on a compact metric space verifying some conditions a natural geometric prior based on randomly rescaled solutions of the heat equation is considered upper and lower bound posterior contraction rates are derived

double positive solutions of n p boundary value problems for higher order difference equations abstract we shall provide existence criteria for double positive solutions of the n p boundary value problem n y f k y y n 2 y g k y y n 1 y n 1 k n i y 0 0 0 i n 2 p y n n p 0 where n 2 and 0 p n 1 is fixed upper and lower bounds for the two positive solutions are also established for a particular boundary value problem when n 2 several examples are included to dwell upon the importance of the results obtained

multiple positive solutions of a discrete difference system this paper is concerned with the following system d 2u 1 k f 1 k u 1 k u 2 k 0 k 0 t d 2u 2 k f 2 k u 1 k u 2 k 0 k 0 t u 1 0 u 1 t 2 0 u 2 0 u 2 t 2 by using leggett williams fixed point theorem sufficient conditions are obtained for the existence of three positive solutions to the above system

multivariate bayesian function estimation bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact riemannian manifold in terms of the latter the underlying geometry of the manifold induces certain symmetries on the multivariate nonparametric regression function the bayesian approach then allows one to incorporate hierarchical bayesian methods directly into the spectral structure thus providing a symmetry adaptive multivariate bayesian function estimator one can also diffuse away some prior information in which the limiting case is a smoothing spline on the manifold this together with the result that the smoothing spline solution obtains the minimax rate of convergence in the multivariate nonparametric regression problem provides good frequentist properties for the bayes estimators an application to astronomy is included

positive solutions and nonlinear eigenvalue problems for third order difference equations first solutions that lie in a cone intersected with an annular type region are obtained for the third order difference equation 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 in the cases that f is either superlinear or sublinear the second part is devoted to determining values of for which there exist positive solutions of 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 when both limx 0 f x x and limx f x x exist as positive real numbers

a singular nonlinear boundary value problem for a higher order ordinary differential equation and the nonlinear term f x y y is assumed to have singularities at yi 0 1 i i 5 n 1 and to satisfy the following conditions a f x y y 0 1 x 0 a l 0 co is continuous where 0 oo l denotes the first orthant in r b for each fixed x yl v r yi r y 1 5 i n 1 x y y is decreasing in yi c for each fixed yr y j sf 4 lim f x yl y l 03 uniformly on compact subsets of 0 1 x 0 a y to l i n 1 e l n f x y 1 y r 0 uniformly on compact subsets of 0 1 x 0 oo

numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures numerical methods for strongly oscillatory and singular functions are given in this paper beside a summary of standard methods and product integration rules we consider a class of complex integration methods several applications of quadrature processes in problems in telecom munications and physics are also presented 1998 elsevier science ltd all rights reserved integration oscillatory kernel singular kernel orthogonal polynomials product rules gaussian quaclratures error function bessel functions legendre functions

multiple positive solutions to second order neumann boundary value problems in this paper the existence of multiple positive solutions to the second order neumann bvps u mu f t u u 0 u 1 0andu mu f t u u 0 u 1 0are proved by a fixed point theorem in cone due to krasnoselskii

a second order singular boundary value problem abstract we study the second order boundary value problem t t f u t o satisfying u 0 u 0 0 u 1 u 1 0 where a t i 1n ai t and 0 0 we assume that each ai t lpi 0 1 for pi 1 and that each ai t has a singularity in 0 1 to show the existence of countably many positive solutions we apply holder s inequality and krasnosel ski i s fixed point theorem for operators on a cone

positive solutions for p n p conjugate boundary value problems a new existence result is presented for the p n p conjugate boundary value problem 1 n py n h t y 0 t 1 withy i 0 0 0 i p 1 andy i 1 0 0 i n p 1 our nonlinearityhmay be singular aty 0 t 0 and ort 1

nonparametric estimation of a probability density on a riemannian manifold using fourier expansions supposing a given collection y 1 cdots y n of i i d random points on a riemannian manifold we discuss how to estimate the underlying distribution from a differential geometric viewpoint the main hypothesis is that the manifold is closed and that the distribution is sufficiently smooth under such a hypothesis a convergence arbitrarily close to the n 1 2 rate is possible both in the l 2 and the l infty senses

tensor product space anova models to deal with the curse of dimensionality in high dimensional nonparametric problems we consider using tensor product space anova models which extend the popular additive models and are able to capture interactions of any order the multivariate function is given an anova decomposition that is it is expressed as a constant plus the sum of functions of one variable main effects plus the sum of functions of two variables two factor interactions and so on we assume the interactions to be in tensor product spaces we show in both regression and white noise settings the optimal rate of convergence for the tps anova model is within a log factor of the one dimensional optimal rate and that the penalized likelihood estimator in tps anova achieves this rate of convergence the quick optimal rate of the tps anova model makes it very preferable in high dimensional function estimation many properties of the tensor product space of sobolev hilbert spaces are also given

existence of positive solutions of boundary value problem for a discrete difference system in this paper we consider the following boundary value problem of discrete system d 2u 1 k f 1 k u 1 k u 2 k 0 k 0 t d 2u 2 k f 2 k u 1 k u 2 k 0 k 0 t with the dirichlet boundary value conditionu 1 0 u 1 t 2 0 u 2 0 u 2 t 2 some sufficient conditions are obtained for the existence of one or two positive solutions to the above system by using nonlinear alternative of leray schauder type and krasnosel skii s fixed point theorem in a cone

an application of topological transversality to non positive higher order difference equations in this paper we shall provide sufficient conditions on the non positive function i u 1 u n 1 so that the boundary value problem bvp given by e d nu i m i u i du i d n 2 i 0 and bc d mu 0 0 0 m n 3 a d n 2 0 b d n 1u 0 0 c d n 2u t 1 d d n 1u t 1 0 has at least one positive solution

semiparametric analysis of variance with tensor product thin plate splines we consider fitting multivariate models to response data based on analysis of variance anova like decompositions of functions of several variables f t 1 t d c f t f t t a theory for fitting some components of these models with polynomial smoothing splines exists when each t is in a subset of the real line in this case the various estimated components turn out to be certain tensor sums and products of polynomial splines this approach may not be natural when one or more of the variables are geographic in particular where nature does not know north from east

l espace symetrique de drinfeld et correspondance de langlands locale i we study the geometry and the cohomology of the tamely ramified cover of drinfeld s p adic symmetric space over a p adic field k for this tame level we prove in a purely local way most of a conjecture of harris on the form of the ell adic cohomologies as well as the torsion freeness of the integral cohomology in this paper we also compute the ell adic cohomology of coxeter deligne lusztig variety associated to mathrm gl d and some results of independent interest on the coefficient systems over the bruhat tits building associated to mathrm gl d k have been established

multiplicity of positive solutions of a class of nonlinear fractional differential equations this paper is concerned with the nonlinear fractional differential equation l d u f x u u 0 0 0 x 1 where l d dsn an 1dsn 1 a1ds11 0 j 1 2 n 1 some results are obtained for the existence nonexistence and multiplicity of positive solutions of the above equation by using krasnoselskii s fixed point theorem in a cone in particular it is proved that the above equation has n positive solutions under suitable conditions where n is an arbitrary positive integer

nonlinear superlinear singular and nonsingular second order boundary value problems abstract many new existence theorems are presented for singular and nonsingular second order boundary value problems singularities at y 0 t 0 and t 1 will be discussed