multiple positive solutions of conjugate boundary value problems with singularities the existence of one or several positive solutions for some nth order differential equations with conjugate boundary conditions is obtained the approach is to employ the well known results on the existence of positive solutions for hammerstein integral equations obtained recently by the author this avoids utilizing the theory of fixed point index for compact maps defined on cones directly new properties on the kernels corresponding to the boundary value problems are provided and then employed to prove new properties of nonzero positive solutions for these boundary value problems and new inequalities on functions satisfying the conjugate boundary conditions our results improve and generalize many recent results

the green s function for k n k conjugate boundary value problems and its applications abstract a new integral representation of the green s function for k n k conjugate boundary value problems is obtained its applications are also given

a sharp nonconvexity bound for partition ranges of vector measures with atoms a sharp upper bound is given for the degree of nonconvexity of the partition range of a finite dimensional vector measure in terms of the maximum one dimensional mass of the atoms of that measure this upper bound improves on a bound of hill and tong 1989 anal stat 17 1325 1334 by an order of magnitude n its proof uses several ideas from graph theory combinatorics and convex geometry applications are given to optimal partitioning and fair division problems

multiple solutions for 2mth order sturm liouville boundary value problems growth conditions are imposed on f such that the following boundary value problem 1 my 2m f t y i 1y 2i 0 i 1y 2i 1 0 i 1y 2i 1 i 1y 2i 1 1 0 0 i m 1 has an arbitrary number of positive solutions

existence of solutions to some singular initial value problems on etudie l existence des solutions et leurs domaines de definition pour des problemes aux valeurs initiales pour des equations differentielles d ordre 1 et 2 qui sont singulieres soit dans les variables dependantes soit dans les variables independantes

two point higher order bvps with singularities in phase variables the existence of solutions for singular higher order differential equations with the lidstone or the n p boundary conditions is proved the right hand sides of differential equations can have singularities in the zero value of their phase variables and so higher derivatives of solutions changing their signs can pass through these singularities proofs are based on the method of a priori estimates the degree theory arguments and on vitali s convergence theorem

3d head model retrieval in kernel feature space using hsom in this paper we propose a novel 3d head model retrieval framework specifically to facilitate better classification and retrieval the original 3d head model representations are embedded into another kernel feature space in which kernel principal component analysis kernel pca is then performed to search for the optimal basis representation based on the extracted nonlinear features a hierarchical indexing structure for 3d model retrieval is constructed using the hierarchical self organizing map hsom the proposed indexing structure clusters the database into a hierarchy so that head models are partitioned by coarse features initially and then by finer scale features at lower levels the main motivation of adopting this approach is that subspace technique like kernel pca provides an elegant mechanism to describe the 3d head models on multiple resolutions based on the choices for reconstruction error and the orthogonal property of the produced eigenvectors to further enhance the performance a fuzzy metric between the query and the feature vector associated with each node on the soms is adopted instead of the usual euclidean metric only nodes that possess high fuzzy measure values will be considered further for retrieval in this way the fuzzy measure approach is able to pick up potential relevant models even though they may be distributed across a number of neighbouring nodes in addition to model categorization the topology preserving property of hsom also facilitates the exploration of the model database with the possibility for further knowledge discovery the effectiveness of the proposed approach is verified by a set of simulation examples on a 3d head model database

solvability of some fourth and higher order singular boundary value problems abstract existence results for a variety of singular fourth order boundary value problems of the form yiv f t y y y are given here our nonlinear term f may be singular at t 0 t 1 y 0 and or y 0 for example some singularities of the type y a and y b are included also we discuss and treat the extension of these results to nth order boundary value problems

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

smoothly distributed fuzzy c means this paper presents a new self organizing map algorithm unlike the well known method of kohonen the new algorithm corresponds to the optimization of an unambiguously defined cost function it consists of a modified version of the widely used fuzzy c means functional where the code vectors are distributed on a regular low dimensional grid and a penalization term is added in order to guarantee a smooth distribution for the values of the code vectors on the grid the mapping properties of the new method similar to those of kohonen s algorithm are illustrated with several data sets computer programs source code and executables and data are available upon request to the authors

upper estimate for positive solutions of the p n p conjugate boundary value problem abstract we consider the p n p conjugate boundary value problem a new upper estimate for positive solutions of the problem is obtained at the end of the paper we discuss the sharpness of this new upper estimate and a lower estimate from the literature

green s function and positive solutions for higher order ode abstract green s function for k n k conjugate boundary value problem 1 n k x n t t f x t a x i a 0 0 i k 1 x j b 0 0 j n k 1 is obtained and its integral representation is given as applications we obtain sufficient conditions for the existence of one two or three positive solutions

positive solutions for singular second order neumann boundary value problems via a cone fixed point theorem in this paper we consider the existence of positive solutions for the singular second order neumann boundary value problem x k 2x f t g t x 0

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

singular differential equations with linear and nonlinear boundary conditions abstract existence results are established for the singular equation y f t y 0 where f is not a caratheodory function our nonlinearity f is allowed to change sign

positive solutions for higher order lidstone boundary value problems a new approach via sperner s lemma abstract consider the higher order nonlinear scalar differential equation where associated to the lidstone boundary conditions existence of a solution of boundary value problems bvp 1 2 such that are given under superlinear or sublinear growth in f similarly existence for the bvp 1 3 under the same assumptions is proved such that we further prove analogous results for the case when i e derivatives of the obtaining solution satisfy inverse inequalities the approach is based on an analysis of the corresponding vector field on the face plane and the well known from combinatorial analysis knaster kuratowski mazurkiewicz s principle or as it is known sperner s lemma

positive solutions to singular and non singular second order boundary value problems abstract the existence of positive solutions to second order singular boundary value problems is established our analysis is based on the topological transversality theorem of andrzej granas which relies on the notions of an essential map and a priori estimates on solutions

existence and uniqueness of solutions for singular k n k conjugate boundary value problems by mixed monotone method the existence and uniqueness are established for singular k n k conjugate boundary value problems the theorems obtained are very general and complement previous known results

positive solutions for k n k conjugate boundary value problems in banach spaces abstract the existence and multiplicity of positive solutions for a integral equation in banach spaces are obtained using these results we investigate the existence of multiple positive solutions for k n k conjugate boundary value problems the arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators this work gives an unified approach applicable to many boundary value problems

eigenvalues of a general class of boundary value problem with derivative dependent nonlinearity we consider a general class of boundary value problem bvp comprising the differential equation y m t f t y t y t y t y q t t 0 1 where 1 q m 1 and 0 together with multi point boundary conditions y 0 y 0 y 0 y q 1 0 0 a i y q t j y q 1 t j y m 1 t j 0 j r 0 1 i m q where 0 t 0 t 1 t r 1 particular cases of this general bvp include the well known abel gontscharoff focal m p sturm liouville and complementary lidstone bvps it is noted that bvps with derivative dependent nonlinear terms are less investigated in the literature due to technical difficulty in this paper a new technique is developed to characterize the eigenvalues so that the bvp has a positive solution explicit eigenvalue intervals are also established we include several well known examples in the literature to illustrate the results obtained

solvability of some nonlinear boundary value problems on etablit l existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme y f t y y o o t 1

existence of solutions to singular integral equations abstract nonnegative solutions are established for singular integral equations of the form y t h t t 0 k t s f s y s ds for t 0 t here f may be singular at y 0

optimal partitioning inequalities in classification and multi hypotheses testing optimal partitioning a dminimax risk inequalities are obtained for the classification and multi hypotheses t ting problems best possible bounds are derived for the minimax risk for location parameter families based on the tail concentrations and levy concentrations of the distributions special attention is given to continuous distributions with the maximum likelihood ratio property and to symmetric unimodal continuous distributions bounds for general including discontinuous distributions are also obtained

positive solutions to semipositone k n k conjugate eigenvalue problems abstract in this paper we consider the existence of positive solutions to the following semipositone k n k conjugate eigenvalue problems scep 1 n k u n t f t u t 0 t 1 u i 0 0 0 i k 1 u j 1 0 0 j n k 1 where n 2 1 k n 1 and 0 is positive parameter the nonlinear function f may change sign for 0 t 1 i e we allow that the nonlinear term f is both semipositone and lower unbounded without making any monotone type assumptions by using the fixed point index theory we derive an explicit interval of such that for any in this interval the existence of at least one positive solution to the boundary value problem is guaranteed and the existence of at least two solutions for in an appropriate interval is also discussed

singular nonlinear k n k conjugate boundary value problems abstract for 1 k n 1 solutions are obtained for the boundary value problem 1 n k y n f x y y i 0 0 0 i k 1 and y j 1 0 0 j n k 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

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

multiplicity results for singular conjugate focal and n p problems abstract a new technique is presented which enables us to discuss the existence of one or more solutions to singular conjugate focal and n p boundary value problems our nonlinearity f t y may be singular at y 0 t 0 and or t 1

multiple nonnegative solutions for second order impulsive differential equations we study the existence of single and multiple solutions to a second order impulsive equation with fixed moments our analysis relies on combining a nonlinear alternative of leray schauder type with krasnoselskii s fixed point theorem in a cone

positive solutions for 2p order and 2q order systems of singular boundary value problems with integral boundary conditions abstract in this paper we study the existence multiplicity and nonexistence of positive solutions for 2p order and 2q order systems of singular boundary value problems with integral boundary conditions the results are based upon the fixed point theorem of cone expansion and compression type due to krasnosel skill moreover it generalizes and includes some known results

the dubins spanier optimization problem in fair division theory abstract an optimality criterion for fair division theory introduced by dubins and spanier in 1961 is recalled with the purpose of analyzing its structure in relationship with other optimal solutions pareto and equi optimal partitions a geometric dual approach is also defined with the purpose of characterizing and identifying the dubins spanier optimal solutions