on the spaces lp x ω and wm p x ω in this paper we present some basic results on the generalized lebesgue spaces l p x omega and generalized lebesgue sobolev spaces w m w p x omega these results provide the necessary framework for the study of variational problems and elliptic equations with non standard p x growth conditions c 2001 academic press

boundary trace embedding theorems for variable exponent sobolev spaces we study boundary trace embedding theorems for variable exponent sobolev space w1 p let be an open bounded or unbounded domain in rn satisfying strong local lipschitz condition under the hypotheses that p l 1 infp x supp x n we prove that there is a continuous boundary trace embedding w1 p lq provided q a measurable function on satisfies condition p x q x n 1 p x n p x for x

the adaptive projected subgradient method constrained by families of quasi nonexpansive mappings and its application to online learning many online i e time adaptive inverse problems in signal processing and machine learning fall under the wide umbrella of the asymptotic minimization of a sequence of nonnegative convex and continuous functions to incorporate a priori knowledge into the design the asymptotic minimization task is usually constrained on a fixed closed convex set which is dictated by the available a priori information to increase versatility toward the usage of the available information the present manuscript extends the adaptive projected subgradient method by introducing an algorithmic scheme which incorporates a priori knowledge in the design via a sequence of strongly attracting quasi nonexpansive mappings in a real hilbert space in such a way the benefits offered to online learning tasks by the proposed method unfold in two ways 1 the rich class of quasi nonexpansive mappings provides a plethora of ways to cast a priori knowledge and 2 by introducing a sequence of such mappings the proposed scheme is

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

existence of solutions and boundary asymptotic behavior of p r laplacian equation multi point boundary value problems abstract this paper investigates the problem p r u r f r u 0 r 0 r u 0 i 1 m i u i e 0 u r as r r where p r u u p r 2 u is called the p r laplacian r is a singular coefficient the existence and nonexistence of solutions are discussed and the exact boundary blow up rate of solutions is given

subspace learning and imputation for streaming big data matrices and tensors extracting latent low dimensional structure from high dimensional data is of paramount importance in timely inference tasks encountered with big data analytics however increasingly noisy heterogeneous and incomplete datasets as well as the need for real time processing of streaming data pose major challenges to this end in this context the present paper permeates benefits from rank minimization to scalable imputation of missing data via tracking low dimensional subspaces and unraveling latent possibly multi way structure from incomplete streaming data for low rank matrix data a subspace estimator is proposed based on an exponentially weighted least squares criterion regularized with the nuclear norm after recasting the nonseparable nuclear norm into a form amenable to online optimization real time algorithms with complementary strengths are developed and their convergence is established under simplifying technical assumptions in a stationary setting the asymptotic estimates obtained offer the well documented performance guarantees of the batch nuclear norm regularized estimator under the same unifying framework a novel online adaptive algorithm is developed to obtain multi way decompositions of low rank tensors with missing entries and perform imputation as a byproduct simulated tests with both synthetic as well as real internet and cardiac magnetic resonance imagery mri data confirm the efficacy of the proposed algorithms and their superior performance relative to state of the art alternatives

existence of infinitely many solutions for a neumann problem involving the p x laplacian abstract in this paper we consider the neumann problem involving the p x laplacian of the type div u p x 2 u x u p x 2 u f x u g x u in u 0 on we prove the existence of infinitely many solutions of the problem under weaker hypotheses by applying a variational principle due to b ricceri and the theory of the variable exponent sobolev spaces our results are an improvement and generalization of the relative results obtained by b ricceri for the p laplacian case

eigenvalues of p x laplacian dirichlet problem abstract this paper studies the eigenvalues of the p x laplacian dirichlet problem div u p x 2 u u p x 2 u in u 0 on where is a bounded domain in rn and p x is a continuous function on such that p x 1 we show that the set of eigenvalues is a nonempty infinite set such that sup we present some sufficient conditions for inf 0 and for inf 0 respectively

hartman type results for p t laplacian systems consider the weighted p t laplacian ordinary system w t u t p t 2u t w t f t u t 0 in a b u a u b 0 where f c a b rn rn w c a b r p c a b r and p t 1 for t a b it is proved that if r 0 such that f t u u 0 t a b u rn with u r then the problem has a solution u such that u t r for t a b as a corollary of this result taking w t tn 1 we obtain the existence of the radial solutions for the elliptic systems our result generalized the corresponding results obtained by hartman and mawhin

adaptive multiregression in reproducing kernel hilbert spaces the multiaccess mimo channel case this paper introduces a wide framework for online i e time adaptive supervised multiregression tasks the problem is formulated in a general infinite dimensional reproducing kernel hilbert space rkhs in this context a fairly large number of nonlinear multiregression models fall as special cases including the linear case any convex continuous and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response the only requirement is the subgradient of the adopted loss function to be available in an analytic form to this end we demonstrate a way to calculate the subgradients of robust loss functions suitable for the multiregression task as it is by now well documented when dealing with online schemes in rkhs the memory keeps increasing with each iteration step to attack this problem a simple sparsification strategy is utilized which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters a convergence analysis of the technique based on arguments of convex analysis is also provided to demonstrate the capacity of the proposed method the multiregressor is applied to the multiaccess multiple input multiple output channel equalization task for a setting with poor resources and nonavailable channel information numerical results verify the potential of the method when its performance is compared with those of the state of the art linear techniques which in contrast use space time coding more antenna elements as well as full channel information

existence nonexistence and asymptotic behavior of boundary blow up solutions to p x laplacian problems with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u d i v u p x 2 u is called the p x laplacian and x is a singular coefficient the existence and nonexistence of boundary blow up solutions is discussed and the asymptotic behavior of boundary blow up solutions is given in particular we do not assume radial symmetric conditions and the pointwise different exact blow up rate of solutions has been discussed

a multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids the goal of this correction is to correct a mistake that appears in the proof of both lemma 3 9 and 3 10 in the article mih ilescu r dulescu 2006 1 the mistake in the proof of lemma 3 9 and 3 10 is mainly owing to the fact that we wrongly computed the expression of function g x t

existence and multiplicity results for a new p x kirchhoff problem abstract in this work we study the existence and multiplicity results for the following nonlocal p x kirchhoff problem 0 1 a b 1 p x u p x d x d i v u p x 2 u u p x 2 u g x u in u 0 on where a b 0 are constants r n is a bounded smooth domain p c with n p x 1 is a real parameter and g is a continuous function the analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties

singular solutions of the p laplace equation soit un sous ensemble ouvert de r n n 1 et p un nombre reel plus grand que 1 on suppose que 0 o et u est p harmonique dans on etudie le comportement de la solution faible u pres de o de l equation apu div u p 2 u 0

spectrally and inertially arbitrary sign patterns we introduce some n by n sign patterns which allow for arbitrary spectrum and hence also arbitrary inertia consequently we demonstrate that some known inertially arbitrary patterns are in fact spectrally arbitrary we demonstrate that all inertially arbitrary patterns of order 3 are spectrally arbitrary and classify all spectrally arbitrary patterns of order 3 we illustrate that in general the class of spectrally arbitrary patterns is distinct from the inertially arbitrary patterns and present some observations about inertially arbitrary patterns

on superlinear p x laplacian equations in rn abstract we consider the p x laplacian equations in r n the nonlinearity is superlinear but does not satisfy the ambrosetti rabinowitz type condition we obtain ground states of the equations improving a recent result of fan x l fan p x laplacian equations in r n with periodic data and nonperiodic perturbations j math anal appl 341 2008 103 119 we also establish a bartsch wang type compact embedding theorem for variable exponent spaces then a multiplicity result for the equations is proved for odd nonlinearity

eigenvalues of the p x laplacian steklov problem abstract consider steklov eigenvalue problem involving the p x laplacian on a bounded domain the open subset of r n with n 2 as follows p x u u p x 2 u in u p x 2 u u p x 2 u on where p x constant we prove that the existence of infinitely many eigenvalue sequences unlike the p laplacian case for a variable exponent p x constant there does not exist a principal eigenvalue and the set of all eigenvalues is not closed under some assumptions finally we present some sufficient conditions for the infimum of all eigenvalues is zero and positive respectively

spectrally arbitrary zero nonzero patterns and field extensions abstract an n n matrix pattern is said to be spectrally arbitrary over a field f provided for every monic polynomial p t of degree n with coefficients from f there exists a matrix with entries from f in the given pattern that has characteristic polynomial p t let e f k be an extension of fields it is natural to ask whether a pattern that is spectrally arbitrary over f must also be spectrally arbitrary over e or k in this article it is shown that if f is dense in k and k is a complete metric space then any spectrally arbitrary or relaxed spectrally arbitrary pattern over f is relaxed spectrally arbitrary over k it is also established that if e is an algebraically closed subfield of a field f then any spectrally arbitrary pattern over f is spectrally arbitrary over e the 2n conjecture and the superpattern conjecture are explored over fields other than the real numbers in particular examples are provided to show that the superpattern conjecture is false over the field with 3 elements

remarks on ricceri s variational principle and applications to the p x laplacian equations abstract in this paper we give some remarks on a variational principle of ricceri in the case of sequentially weakly lower semi continuous functionals defined on a reflexive real banach space in particular we introduce the notions of ricceri block and ricceri box which are more convenient in some applications than the weakly connected components using the variational principle of ricceri and a local mountain pass lemma we study the multiplicity of solutions of the p x laplacian equations with neumann dirichlet or no flux boundary condition and under appropriate hypotheses in which the integral functionals need not satisfy the ps condition on the global space we prove that the problem has at least seven solutions

spectrally arbitrary patterns over rings with unity abstract a zero nonzero pattern a is a matrix with entries from the set 0 a square pattern a is spectrally arbitrary over r a commutative ring with unity if for each n th degree monic polynomial f x r x there exists a matrix a over r with pattern a such that the characteristic polynomial p a x f x a pattern a is relaxed spectrally arbitrary over r if for each n th degree monic polynomial f x r x there exists a matrix a over r with either pattern a or a subpattern of a such that the characteristic polynomial p a x f x we evaluate how the structure of rings affects how we determine if a pattern is spectrally arbitrary we consider whether a pattern a that is spectrally arbitrary over r is spectrally arbitrary or relaxed spectrally arbitrary over another commutative ring s with unity in particular we establish that a pattern that is spectrally arbitrary over z is relaxed spectrally arbitrary over z m for all m z and spectrally arbitrary over q similarly a pattern that is spectrally arbitrary over the p adic integers is spectrally arbitrary over the p adic numbers

uni mode uniqueness conditions for candecomp parafac decomposition of n way arrays with linearly dependent loadings abstract guo miron brie and stegeman x guo s miron d brie a stegeman uni mode and partial uniqueness conditions for candecomp parafac of three way arrays with linearly dependent loadings siam j matrix anal appl 33 2012 111 129 give three sufficient conditions for the three way candecomp parafac cp model which ensure uniqueness in one of the three modes uni mode uniqueness in this paper we generalize these uniqueness conditions to n 3 based on these conditions a partial uniqueness condition is given which allows collinear loadings in only one mode

matrix completion by least square low rank and sparse self representations abstract conventional matrix completion methods are generally based on rank minimization these methods assume that the given matrix is of low rank and the data points are drawn from a single subspace of low dimensionality therefore they are not effective in completing matrices where the data are drawn from multiple subspaces in this paper we establish a novel matrix completion framework that is based on self representation specifically least square low rank and sparse self representations based matrix completion algorithms are provided the underlying idea is that one data point can be efficiently reconstructed by other data points belonging to a common subspace where the missing entries are recovered so as to fit the common subspace the proposed algorithms actually maximize the weighted correlations among the columns of a given matrix we prove that the proposed algorithms are approximations for rank minimization of the incomplete matrix in addition they are able to complete high rank or even full rank matrices when the data are drawn from multiple subspaces comparative studies are conducted on synthetic datasets natural image inpainting tasks temperature prediction task and collaborative filtering tasks the results show that the proposed algorithms often outperform other state of the art algorithms in various tasks

existence and asymptotic behavior of blow up solutions to a class of p x laplacian problems abstract this paper investigates the problem p x u f x u 0 in u x as d x 0 where p x u div u p x 2 u is called p x laplacian the existence of blow up solutions is discussed and the singularity of blow up solutions is given

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

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

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

robust subspace tracking with missing entries the set theoretic approach in this paper an adaptive projected subgradient method apsm based algorithm for robust subspace tracking is introduced a properly chosen cost function is constructed at each time instance and the goal is to seek for points which belong to the zero level set of this function i e the set of points which score a zero loss at each iteration an outlier detection mechanism is employed in order to conclude whether the current data vector contains outlier noise or not in the sequel a sparsity promoting greedy algorithm is employed for the outlier vector estimation allowing the purification of the corrupted data from the outlier noise prior to any further processing furthermore the case where the observation vectors are partially observed is attacked via a prediction procedure which estimates the values of the unobserved missing coefficients a theoretical analysis is carried out and the simulation experiments within the contexts of robust subspace estimation and robust matrix completion demonstrate the enhanced performance of the proposed scheme compared to recently developed state of the art algorithms

mountain pass and ekeland s principle for eigenvalue problem with variable exponent in this article we study the boundary value problem div u p x 2 u u x 2 u u q x 2 u in u 0 on where is a smooth bounded domain in n and p q are continuous functions on we show that for any 0 there exists infinitely many weak solutions respectively if 0 and small enough then there exists a non negative non trivial weak solution our approach relies on the variable exponent theory of generalized lebesgue sobolev spaces combined with a 2 symmetric version for even functionals of the mountain pass theorem respectively on simple variational arguments based on ekeland s variational principle this article is devoted to the special issue vaxjo conference 2008

on the discrete boundary value problem for anisotropic equation abstract in this paper we consider the discrete anisotropic boundary value problem using critical point theory firstly we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at least one nontrivial solution secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at least two nontrivial solutions

on the spectra of close to schwarz matrices several inverse eigenvalue problems for tridiagonal matrices are discussed in particular it is shown that for every set s of n complex numbers which is symmetric with respect to the real axis there exists a symmetric in modulus tridiagonal n n matrix a which has a nonnegative super diagonal a nonpositive subdiagonal all diagonal elements zero except for a11 which is nonnegative and ann which is nonpositive and with spectrum s 2002 elsevier science inc all rights reserved

spectrally arbitrary patterns abstract an n n sign pattern matrix s is an inertially arbitrary pattern iap if each nonnegative triple n 1 n 2 n 3 with n 1 n 2 n 3 n is the inertia of a matrix with sign pattern s analogously s is a spectrally arbitrary pattern sap if for any given real monic polynomial r x of order n there is a matrix with sign pattern s and characteristic polynomial r x focusing on tree sign patterns consider the n n tridiagonal sign pattern t n with each superdiagonal entry positive each subdiagonal entry negative the 1 1 entry negative the n n entry positive and every other entry zero it is conjectured that t n is an iap by constructing matrices a n with pattern t n it is proved that t n allows any inertia with n 3 0 1 2 n 1 n for all n 2 this leads to a proof of the conjecture for n 5 the truth of the conjecture is extended to n 7 by showing the stronger result that t n is a sap the proof of this latter statement involves finding a matrix a n with pattern t n that is nilpotent further questions about patterns that are saps and iaps are considered

a strong maximum principle for differential equations with nonstandard p x growth conditions abstract in this paper with some special technics we give a strong maximum principle for the equations with nonstandard p x growth conditions div x u u d x f x u 0 in where x s d x f x u satisfy some conditions

existence of periodic solutions for p t laplacian systems abstract in this paper by using minimax methods in critical point theory we obtain some existence theorems for periodic solutions of p t laplacian system u t p t 2 u t f t u t 0 u 0 u t u 0 u t 0 and our results generalize some existed theorems

low rank perturbations and the spectrum of a tridiagonal sign pattern abstract the n by n tridiagonal sign pattern t n has every superdiagonal entry positive every subdiagonal entry negative the 1 1 entry negative the n n entry positive and every other diagonal entry zero inertia and spectral results for matrices a n having the sign pattern t n are proved using new techniques on low rank perturbations it is also shown by using maple that for 8 n 16 t n allows any spectrum these results extend those previously in the literature and strengthen the conjecture that t n allows any spectrum for all values of n in addition bounds on the algebraic multiplicity of an eigenvalue of a low rank perturbation of a general matrix are obtained

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

distributed source localization using esprit algorithm a new algorithm based on esprit is proposed for the estimation of the central angle and angular extension of distributed sources the central angles are estimated using tls esprit for both incoherently distributed id and coherently distributed cd sources for cd sources the extension width is estimated by constructing a one dimensional 1 d distributed source parameter estimator dspe spectrum for each source for id sources the extension widths are estimated using the central moments of the distribution the algorithm can be used for sources with different angular distributions

on a dirichlet problem with p x laplacian abstract we show the existence and stability of solutions for a family of dirichlet problems div v z 1 x u v z n x u l u x u f u k x u u w 0 1 p x in a bounded domain and with nonconvex nonlinearity satisfying some local growth conditions the conditions upon v and l allow for considering the p x laplacian equation we use the relations between critical points and critical values to the primal and a suitable dual action functional to get the existence stability and some properties of the solutions

allow problems concerning spectral properties of sign pattern matrices a survey abstract an n n sign pattern matrix has entries in 0 this paper surveys the following problems concerning spectral properties of sign pattern matrices sign patterns that allow all possible spectra spectrally arbitrary sign patterns sign patterns that allow all inertias inertially arbitrary sign patterns sign patterns that allow nilpotency potentially nilpotent sign patterns and sign patterns that allow stability potentially stable sign patterns relationships between these four classes of sign patterns are given and several open problems are identified

on the boundary blow up solutions of p x laplacian equations with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u div u p x 2 u is called the p x laplacian x is a singular coefficient the existence and nonexistence of boundary blow up solutions are discussed and the singularity of the boundary blow up solution is given

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed