boundary behavior of solutions to some singular elliptic boundary value problems abstract let be a bounded domain with smooth boundary in r n n 1 for the more general weight b some nonlinearities f and singularities g by two kinds of nonlinear transformations a new perturbation method which was introduced by garcia melian in j garcia melian boundary behavior of large solutions to elliptic equations with singular weights nonlinear anal 67 2007 818 826 and comparison principles we show that the boundary behavior of solutions to a boundary blow up elliptic problem w b x f w w 0 x w and a singular dirichlet problem u b x g u u 0 x u 0 has the same form under the nonlinear transformations which can be determined in terms of the inverses of the transformations

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

asymptotic behavior of large solutions to p laplacian of bieberbach rademacher type abstract by the karamata regular variation theory and the method of lower and upper solutions we establish the asymptotic behavior of boundary blow up solutions of the quasilinear elliptic equation div u p 2 u b x f u in a bounded r n subject to the singular boundary condition u x where the weight b x is non negative and non trivial in which may be vanishing on the boundary or go to unbounded the nonlinear term f is a varying function at infinity whose variation at infinity is not regular

exact boundary behavior of positive large solutions of a nonlinear dirichlet problem abstract in this paper we investigate the exact asymptotic behavior of positive solution to the following singular boundary value problem u b x f u x u 0 in u where is a c 2 bounded domain in r n n 3 f c 1 0 0 is nondecreasing on 0 and b is a function in c l o c 0 1 such that there exist b 1 b 2 0 satisfying for each x 0 b 1 lim d x 0 inf b x h d x lim d x 0 sup b x h d x b 2 where d x d i s t x and h t c t exp t z s s d s d i a m 2 such that z is a continuous function on 0 with z 0 0

the existence and nonexistence of entire large solutions for a quasilinear schrodinger elliptic system by dual approach abstract in this paper we establish some new results on the existence and nonexistence of radial large positive solutions for a modified schrodinger system with a nonconvex diffusion term by a successive iteration technique and the dual approach the necessary and sufficient condition for the existence of radial large positive solutions is established our results improve and extend many previous work in this field of research

large solutions to semi linear elliptic systems with variable exponents abstract we consider the elliptic system u u a v b v u c v d where the exponents are non negative spherically symmetric functions we study positive solutions on balls of finite and infinite radius r which satisfy lim x r u x lim x r v x we give conditions on the exponents that either ensure existence or nonexistence of these large solutions

existence and nonexistence of blow up boundary solutions for sublinear elliptic equations abstract in this paper we consider the semilinear elliptic problem u a x f u u 0 in with the boundary blow up condition u where is a bounded domain in r n n 2 a x c may blow up on and f is assumed to satisfy f1 and f2 below which include the sublinear case f u u m m 0 1 for the radial case that b the unit ball and a x is radial we show that a solution exists if and only if 0 1 1 r a r d r for a general domain we obtain an optimal nonexistence result the existence for nonradial solutions is also studied by using sub supersolution method

on total variation minimization and surface evolution using parametric maximum flows in a recent paper boykov et al lncs vol 3953 pp 409 422 2006 propose an approach for computing curve and surface evolution using a variational approach and the geo cuts method of boykov and kolmogorov international conference on computer vision pp 26 33 2003 we recall in this paper how this is related to well known approaches for mean curvature motion introduced by almgren et al siam journal on control and optimization 31 2 387 438 1993 and luckhaus and sturzenhecker calculus of variations and partial differential equations 3 2 253 271 1995 and show how the corresponding problems can be solved with sub pixel accuracy using parametric maximum flow techniques this provides interesting algorithms for computing crystalline curvature motion possibly with a forcing term

existence of large solutions for a quasilinear elliptic problem via explosive sub supersolutions abstract we consider the boundary blow up quasilinear elliptic problems div u m 2 u u q m 1 k x g u in a c 2 bounded domain with boundary condition u where m 1 q 0 m m 1 and 0 under suitable growth assumptions on k near the boundary and on g both at zero and at infinity we show the existence of at least one solution in c 1 our proof is based on the method of explosive sub supersolutions which permits positive weights k x which are unbounded and or oscillatory near the boundary

boundary blow up solutions to elliptic systems of competitive type abstract we consider the elliptic system u u p v q v u r v s in where p s 1 q r 0 and r n is a smooth bounded domain subject to different types of dirichlet boundary conditions f u v i u v and sf u v on where 0 under several hypotheses on the parameters p q r s we show existence and nonexistence of positive solutions uniqueness and nonuniqueness we further provide the exact asymptotic behaviour of the solutions and their normal derivatives near some more general related problems are also studied

a remark on uniqueness of large solutions for elliptic systems of competitive type abstract we prove that the semilinear system u a x u p v q v b x u r v s in a smooth bounded domain r n has a unique positive solution with the boundary condition u v on provided that p s 1 q r 0 and p 1 s 1 q r 0 the main novelty is imposing a growth on the possibly singular weights a x b x near rather than requiring them to have a precise asymptotic behavior

on a singular elliptic system with quadratic growth in the gradient abstract in this paper we deal with the following singular elliptic system u u 2 u p p q a x v q u p 2 u f x r n v v 2 v q p q a x u p v q 2 v g x r n where n 3 n 2 4 p q 1 and p q n 2 n 2 we show through the sub and supersolutions method the existence of a nonnegative solution for an approximated system the limit of the approximated solution is a positive solution in the case 0 p q and f g we prove the uniqueness of a solution among others we prove some existence and uniqueness results for some auxiliary problems by using the comparison principle a minimization method and with the help of nehari manifold the proofs rely on the concentration compactness principle

supervised feature selection in graphs with path coding penalties and network flows we consider supervised learning problems where the features are embedded in a graph such as gene expressions in a gene network in this context it is of much interest to automatically select a subgraph with few connected components by exploiting prior knowledge one can indeed improve the prediction performance or obtain results that are easier to interpret regularization or penalty functions for selecting features in graphs have recently been proposed but they raise new algorithmic challenges for example they typically require solving a combinatorially hard selection problem among all connected subgraphs in this paper we propose computationally feasible strategies to select a sparse and well connected subset of features sitting on a directed acyclic graph dag we introduce structured sparsity penalties over paths on a dag called path coding penalties unlike existing regularization functions that model long range interactions between features in a graph path coding penalties are tractable the penalties and their proximal operators involve path selection problems which we efficiently solve by leveraging network flow optimization we experimentally show on synthetic image and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs

a remark on the existence of entire positive solutions for a class of semilinear elliptic systems abstract under the simple conditions on f and g we show that entire positive radial solutions exist for the semilinear elliptic system u p x f v v q x g u x r n n 3 where the functions p q 0 0 are continuous

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

large solution to nonlinear elliptic equation with nonlinear gradient terms abstract the aim of this paper is to study the qualitative behavior of large solutions to the following problem u a x u q b x f u x u x x here a x c is a positive function with 0 1 b x c is a non negative function and may be singular near the boundary or vanish on the boundary and the nonlinear term f is a varying function whose variation at infinity is not regular we focus our investigation on the existence and asymptotic behavior close to the boundary of large solutions by karamata regular variation theory and the method of upper and lower solution the main results of this paper emphasize the central role played by the gradient term u q and the weight functions a x and b x

boundary blow up for differential equations with indefinite weight we obtain results of existence and multiplicity of solutions for the second order equation x q t g x 0 with x t defined for all tis an element of 0 1 and such that x t infinity as t 0 and t 1 we assume g having superlinear growth at infinity and q t possibly changing sign on 0 1 c 2002 elsevier science usa all rights reserved

large solutions to non monotone semilinear elliptic systems abstract we present the existence of entire large positive radial solutions for the non monotonic system u p x g v v q x f u on r n where n 3 the functions f and g satisfy a keller osserman type condition while nonnegative functions p and q are required to satisfy the decay conditions 0 t p t d t and 0 t q t d t further p and q are such that min p q does not have compact support

entire large solutions to semilinear elliptic systems abstract we consider the problem of existence of positive solutions to the elliptic system u p x v v q x u on r n n 3 which satisfies lim x u x lim x v x the parameters and are positive and the nonnegative functions p and q are continuous and min p r q r does not have compact support we show that if 1 then such a solution exists if and only if the functions p and q satisfy 0 t p t t 2 n 0 t s n 3 q s d s d t 0 t q t t 2 n 0 t s n 3 p s d s d t with p r 0 r p d and q r 0 r q d for 1 we show that a solution exists if either of the above conditions fails to hold i e one of the integrals is finite these extend all known results for the given system

boundary blow up elliptic problems with nonlinear gradient terms by karamata regular variation theory and perturbation method we show the exact asymptotical behaviour of solutions near the boundary to nonlinear elliptic problems u u q b x g u u 0 in u where is a bounded domain with smooth boundary in rn q 0 g c1 0 g 0 0 g is regularly varying at infinity with index with 0 and b is nonnegative nontrivial in which may be vanishing on the boundary

on the coupling number and characteristic length of micropolar media of differing topology in planar micropolar elasticity theory the degree of micropolarity exhibited by a loaded heterogeneous material is quantified by a dimensionless constitutive parameter the coupling number theoretical predictions of this parameter derived by considering the mechanical behaviour of regular two dimensional lattices with straight connectors suggest that its value is dependent on the connectivity or topology of the lattice with the coupling number in a square lattice predicted to be notably higher than in its hexagonal counterpart a second constitutive parameter reflecting the intrinsic lattice size scale the characteristic length is also predicted to be topology dependent in this paper we compare the behaviour of alternative two dimensional heterogeneous materials in the context of micropolar elasticity these materials consist of periodic arrays of circular voids within a polymeric matrix rather than a lattice of straight connectors two material variants that differ only in their matrix topology are investigated in particular values of the additional micropolar constitutive parameters are obtained for each material from both experimental tests and finite element analyses the values determined for these parameters particularly the coupling number suggest that their topological dependence differs appreciably from the theoretical predictions of the lattice models

the existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term abstract we show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term u u p x f u v v v q x g u v on r n n 3 provided that nonlinearities f and g are positive and continuous the potentials p and q are continuous c positive and satisfy appropriate growth conditions at infinity we find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity while if f and g satisfy some growth conditions at infinity and p q are of slow decay or fast decay at infinity then the system has infinitely many entire solutions which are large or bounded

the asymptotic behaviour of solutions with boundary blow up for semilinear elliptic equations with nonlinear gradient terms abstract in this paper we show existence uniqueness and exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems u u q k x g u x u where is a bounded domain with smooth boundary in r n 0 q 0 2 lim d x 0 k x d x c 0 0 2 c 0 0 g c 1 0 g 0 0 g is increasing on 0 and is karamata regular variation function at infinity with index 1 and 0

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

existence uniqueness and asymptotic behavior of solutions for a singular parabolic equation abstract in this paper we are concerned with a singular parabolic equation v t v f x t v 2 v in a smooth bounded domain r n subject to zero dirichlet boundary condition and initial condition 0 under the assumptions on and f x t some existence and uniqueness results are obtained by applying parabolic regularization method and the sub supersolutions method we also discuss the asymptotic behaviors of solutions in the sense of l 2 0 t w 0 1 2 and l 0 t l 2 norms as 0 or as a byproduct we obtain the existence of solutions for some problems which blow up on the boundary

a necessary and sufficient condition for the existence of large solutions to sublinear elliptic systems abstract we prove that the elliptic system u p x v v q x u on r n n 3 where 0 1 0 1 and p and q are nonnegative continuous functions has a nonnegative entire radial solution satisfying lim x u x lim x v x if and only if the functions p and q satisfy 0 t p t t 2 n 0 t s n 3 q s d s d t 0 t q t t 2 n 0 t s n 3 p s d s d t with p r 0 r p d and q r 0 r q d this extends previous existence results for both the single equation and systems

is smaller always stiffer on size effects in supposedly generalised continua abstract heterogeneous materials having constitutive behaviour described by more generalised continuum theories incorporating additional degrees of freedom such as couple stress micropolar or micromorphic elasticity are expected to exhibit size effects in which there is an apparent increase in stiffness as the size scale reduces here we briefly demonstrate that for a simple heterogeneous material the size effect predicted when loaded in bending depends on the nature of the sample surface diverse size effects may thus be exhibited by the same material we then show by detailed finite element analysis of a more representative material with regular heterogeneity that this diversity of size effects might actually be observed in practice thereby providing an explanation for the contradictory size effects that have sometimes been reported for real materials

blow up rates of large solutions for elliptic equations in this paper we mainly study the boundary behavior of solutions to boundary blow up elliptic problems for more general nonlinearities f which may be rapidly varying at infinity u b x f u x u where is a bounded domain with smooth boundary in rn and b c which is positive in and may be vanishing on the boundary and rapidly varying near the boundary further when f s sp f1 s for s sufficiently large where p 1 and f1 is normalized regularly varying at infinity with index p1 0 p we show the influence of the geometry of on the boundary behavior for solutions to the problem we also give the existence and uniqueness of solutions

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

a necessary and sufficient condition for existence of large solutions to semilinear elliptic equations we consider the semilinear equation u p x f u on a domain rn n 3 where f is a nonnegative nondecreasing continuous function which vanishes at the origin and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary for bounded we show that a nonnegative solution u satisfying u x as x exists if and only if the function s s0 f t dt satisfies 1 s 1 2 ds for unbounded including rn we show that a similar result holds where u x as x within and u x as x if p x decays to zero rapidly as x

nondegeneracy and uniqueness for boundary blow up elliptic problems abstract in this paper we use for the first time linearization techniques to deal with boundary blow up elliptic problems after introducing a convenient functional setting we show that the problem u a x u p g x u in with u on has a unique positive solution for large enough and determine its asymptotic behavior as here p 1 a x is a continuous function which can be singular near and g x u is a perturbation term with potential growth near zero and infinity we also consider more general problems obtained by replacing u p by e u or a logistic type function f u

multiplicity of positive solutions to boundary blow up elliptic problems with sign changing weights in this paper we consider the elliptic boundary blow up problem u a x ea x upin u on where is a bounded smooth domain of rn a a are positive continuous functions supported in disjoint subdomains of respectively p 1 and e 0 is a parameter we show that there exists e 0 such that no positive solutions exist when e e while a minimal positive solution exists for every e 0 e under the additional hypotheses that and intersect along a smooth n 1 dimensional manifold and a a have a convenient decay near we show that a second positive solution exists for every e 0 e if p n n 2 n 2 our proofs are mainly based on continuation methods

a control volume based finite element method for plane micropolar elasticity this paper describes the development of a numerical procedure for predicting deformations and stresses in a loaded two dimensional membrane exhibiting micropolar or cosserat constitutive behaviour the procedure employs a conventional finite element fe mesh together with a dual mesh of interconnected control volumes each of which must satisfy equilibrium a series of patch tests covering a variety of simple strain states are used to validate the procedure that is then employed to predict the stress concentration in a membrane containing a small hole the predictions provided by the procedure are compared with those given previously by fes

existence and uniqueness of solutions for a singular semilinear elliptic system abstract in this paper we study the existence and the uniqueness of solutions for the singular semilinear elliptic system u f x u 2 g x u 1 p 2 p q a x u p v 1 q x r n v f x v 2 g x v 1 q 2 p q a x u 1 p v q x r n where 0 p 1 and 0 q 1 we show the existence of a solution for an approximated system by using a perturbation method which eliminates the singularity and via variational methods the limit of the approximated solutions is a positive solution in the case g 0 p q and 1 2 p 1 we prove the uniqueness of solution the proofs rely on the concentration compactness principle

entire large solutions for a class of schrodinger systems with a nonlinear random operator abstract in this paper we study the nonexistence and existence of radial large positive solutions for a class of schrodinger systems with a nonlinear random operator under certain growth conditions we also establish the necessary and sufficient conditions for the existence of radial large positive solutions by a successive iteration technique the results of the paper improve and extend many previous work in this field of research

existence of entire large positive solutions of a semilinear elliptic system we show that large positive radial solutions exist for the semilinear elliptic system du p x f v dv q x g u on r n n 3 for nonnegative nondecreasing continuous functions f and g provided the nonnegative functions p and q are continuous c positive and satisfy the decay conditions 0tp t dt and 0tq t dt and f g satisfy 1 s 0f t dt 1 2 ds 1 s 0g t dt 1 2 ds

the second expansion of large solutions for semilinear elliptic equations abstract in this paper we analyze the influence of the domain geometry in the second expansion of solutions to the boundary blow up elliptic problem u b x f u u 0 x u where is a bounded domain with c 4 smooth boundary in r n b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p p 1

finding minimum cost circulations by canceling negative cycles a classical algorithm for finding a minimum cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc we show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm this gives a very simple strongly polynomial algorithm that uses no scaling a variant of the algorithm that uses dynamic trees runs in o nm log n min log nc m log n time on a network of n vertices m arcs and arc costs of maximum absolute value c this bound is comparable to those of the fastest previously known algorithms

existence of entire large positive solutions of semilinear elliptic systems abstract we show that entire large positive radial solutions exist for the semilinear elliptic system u p x v v q x u on r n n 3 for positive and provided that the nonnegative functions p and q are continuous c positive and satisfy the decay conditions 0 tp t dt 0 tq t dt and greater than unity and 0 tp t dt and 0 tq t dt if neither nor is greater than one

existence and global behavior of positive solution for semilinear problems with boundary blow up using the sub supersolution method with karamata regular variation theory we study the existence and asymptotic behavior of a classical solution to the following boundary blow up semilinear dirichlet problem u a x f u x u 0in lim x 0 u x where is a c1 1c1 1 bounded domain in rnrn n 2n 2 and the function a belongs to cloc 0 1 0 1 such that for each x x c1 x 1exp x z1 s sds a x c2 x 2exp x z2 s sds where diam diam c1 0c1 0 c2 0c2 0 x dist x x dist x 1 2 2 1 2 2 and for i 1 2 i 1 2 zizi is a continuous function on 0 0 with zi 0 0zi 0 0 for the function f we assume that there exist constants k1k1 k2k2 p1p1 p2p2 with 0 k1 k20 k1 k2 1 p1 p21 p1 p2 such that f t k2tp2for t 0andf t k1tp1for t 1

solving the convex cost integer dual network flow problem in this paper 1 we consider an integer convex optimization problem where the objective function is the sum of separable convex functions that is of the form i j eq f ij w ij iep b i i the constraints are similar to those arising in the dual of a minimum cost flow problem that is of the form i j w ij i j q with lower and upper bounds on variables letn p m q andu be the largest magnitude in the lower and upper bounds of variables we call this problemthe convex cost integer dual network flow problem in this paper we describe several applications of the convex cost integer dual network flow problem arising in a dial a ride transit problem inverse spanning tree problem project management and regression analysis we develop network flow based algorithms to solve the convex cost integer dual network flow problem we show that using the lagrangian relaxation technique the convex cost integer dual network flow problem can be transformed into a convex cost primal network flow problem where each cost function is a piecewise linear convex function with integer slopes its special structure allows the convex cost primal network flow problem to be solved ino nmlog n2 m log nu time this time bound is the same time needed to solve the minimum cost flow problem using the cost scaling algorithm and is also is best available time bound to solve the convex cost integer dual network flow problem

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

a boundary blow up elliptic problem with an inhomogeneous term abstract by a perturbation method and constructing comparison functions we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem u b x g u h x u 0 in u where is a bounded domain with smooth boundary in r n 0 g c 1 0 is increasing on 0 g 0 0 g is regularly varying at infinity with positive index the weight b which is non trivial and non negative in may be vanishing on the boundary and the inhomogeneous term h is non negative in and may be singular on the boundary

boundary behavior for large solutions to elliptic equations with singular weights abstract in this paper we analyze the boundary behavior of large positive solutions to some semilinear elliptic equations which include a singular weight the most important point is that the growth of the solutions can be determined in terms of the solution to a one dimensional first order equation we also consider the questions of existence and uniqueness of positive solutions

simultaneous variable selection we propose a new method for selecting a common subset of explanatory variables where the aim is to model several response variables the idea is a natural extension of the lasso technique proposed by tibshirani 1996 and is based on the joint residual sum of squares while constraining the parameter estimates to lie within a suitable polyhedral region the properties of the resulting convex programming problem are analyzed for the special case of an orthonormal design for the general case we develop an efficient interior point algorithm the method is illustrated on a dataset with infrared spectrometry measurements on 14 qualitatively different but correlated responses using 770 wavelengths the aim is to select a subset of the wavelengths suitable for use as predictors for as many of the responses as possible

the minimum description length principle in coding and modeling we review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling stochastic complexity is formulated as the solution to optimum universal coding problems extending shannon s basic source coding theorem the normalized maximized likelihood mixture and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms we assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference context tree modeling density estimation and model selection in gaussian linear regression serve as examples

comparison of wave propagation characteristics of the cosserat continuum model and corresponding discrete lattice models a comparison is made between two dimensional elastic discrete lattices and a corresponding cosserat continuum firstly it is demonstrated how the equations of motion of the cosserat model can be retrieved from those of a lattice model for this purpose two lattice geometries are elaborated a 7 cell hexagonal lattice and a 9 cell square lattice for both lattices the individual cells have two translational spring interactions and a rotational spring interaction with their neighbouring cells secondly the dispersion relations for the lattice models and the cosserat continuum model are examined in order to determine up to which wavelength of the deformation field the cosserat model accurately represents the underlying discrete micro structure the effect of the lattice anisotropy and inhomogeneity on this accuracy is also discussed

symmetry results of large solutions for semilinear cooperative elliptic systems abstract in this paper we consider symmetry of large solutions of the semilinear cooperative elliptic system u i g i u 1 u m in b r u i on b r where u i c 2 b r g i r m r a c function b r is the open ball of center 0 and radius r 0 in r n n 3 m n i 1 2 m after introducing the weakly coupled fully coupled hypotheses and some assumptions for g we use the moving plane method to prove any large solution of the semilinear cooperative elliptic system is radially symmetric and radially increasing in order to use the moving plane method for our problem a strong maximum principle of the linear cooperative elliptic system is constructed furthermore we also get the symmetry result of large solutions of the semilinear cooperative elliptic system in an annulus

boundary blow up elliptic problems of bieberbach and rademacher type with nonlinear gradient terms abstract by a perturbation method and constructing comparison functions we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems u u q b x e u x u where is a bounded domain with smooth boundary in r n q 0 b is non negative and non trivial in which may be vanishing on the boundary

boundary blow up quasilinear elliptic problems of the bieberbach type with nonlinear gradient terms abstract by a perturbation method and by constructing comparison functions we show the exact asymptotic behaviour of solutions near the boundary of the quasilinear elliptic problem div u m 2 u u x q m 1 b x e u x x u where is a c 2 bounded domain with a smooth boundary in r n n 2 m 1 q 0 b is nonnegative and nontrivial in which may vanish on the boundary

the asymptotic behaviour of solutions with blow up at the boundary for semilinear elliptic problems abstract by constructing the comparison functions and the perturbed method it is showed that any solution u c 2 to the semilinear elliptic problems u k x g u x u satisfies lim d x 0 u x z d x 2 2 2 c 0 2 1 where is a bounded domain with smooth boundary in r n lim d x 0 k x d x c 0 2 c 0 0 2 2 g c 1 0 g 0 and g s s is increasing on 0 there exists 0 such that lim s g s g s 0 z s d t 2 g t s g t 0 t g s d s

on a k hessian equation with a weakly superlinear nonlinearity and singular weights abstract consider the existence nonexistence and global estimates of k convex solutions to the boundary blow up k hessian problem s k d 2 u x h x u x k ln u x 0 for x u x as dist x 0 here k 1 2 n s k d 2 u is the k hessian operator 0 is a smooth bounded strictly convex domain in r n n 2 and h x is a positive weight function which is singular near the boundary we first give the existence and nonexistence results of k convex solution to the above boundary blow up problem on a larger range of h and then we show that there is a k convex solution provided that h x grows fast near and u k ln u grows slow at it turns out that this case is more difficult to handle than the case in which h x grows slow near and u k ln u grows fast at this needs some new ingredients in the arguments

large solutions for an elliptic system of competitive type existence uniqueness and asymptotic behavior abstract this paper deals with the existence uniqueness and asymptotic behavior of boundary blow up solutions for an elliptic system of competitive type where the weight functions a x b x vanish on the boundary of the underlying domain at different rates according to the point of the boundary the proof relies on subsolutions and supersolutions and the localization method

second order expansion for blowup solutions of semilinear elliptic problems abstract in this paper we mainly study the second order expansion of solutions to the elliptic problems u b x f u u 0 x u where is a bounded domain with a smooth boundary in r n n 2 b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p 1 our analysis is based on the sub supersolution method and karamata regular variation theory