conditional gauge and potential theory for the schrodinger operator on etend le theoreme de jauge conditionnelle a des operateurs plus generaux et a des domaines moins reguliers on obtient des resultats de theorie du potentiel pour l equation de schrodinger

camera calibration from images of spheres this paper introduces a novel approach for solving the problem of camera calibration from spheres by exploiting the relationship between the dual images of spheres and the dual image of the absolute conic iac it is shown that the common pole and polar with regard to the conic images of two spheres are also the pole and polar with regard to the iac this provides two constraints for estimating the iac and hence allows a camera to be calibrated from an image of at least three spheres experimental results show the feasibility of the proposed approach

optimal control of harvesting in a nonlinear elliptic system arising from population dynamics the aim of this article is to study an optimal control problem for a system of nonlinear elliptic equations with dirichlet boundary conditions u x a x x c x u x eu x u x x x 1 1 x b x u x d x x f x u x x x u x x 0 on 1 2 the authors were supported in part by cicyt ministry of education and culture spain under grant pb98 1343 by junta de andalucia fqm116 and by eec contract human capital and mobility program erbchrxct 940494 also they thank o arino for suggesting the study of this control problem

diffraction problems for quasilinear reaction diffusion systems abstract the aim of this paper is to investigate existence uniqueness and qualitative properties of the weak and piecewise classical solutions of the diffraction problem for weakly coupled reaction diffusion systems monotony and stability with respect to the time variable of the weak solutions is proved as an application is considered a model reaction diffusion system describing an enzyme sensor for concentration of phenol in the chemical industry

asymptotic behaviour of principal eigenvalues for a class of cooperative systems this paper analyzes the asymptotic behaviour as of the principal eigenvalue of the cooperative operator l l1 a x b cl2 d x in a bounded smooth domain of rn n 1 under homogeneous dirichlet boundary conditions on where a 0 d 0 and b x 0 c x 0 for all x precisely our main result establishes that if int a d 1 0 consists of two components 0 1 and 0 2 then lim 1 l mini 1 2 1 l 0 0 i where for any d and r 1 l d stands for the principal eigenvalue of l in d moreover if we denote by the principal eigenfunction associated to l normalized so that 2 2 1 and for instance 1 l 0 0 1 1 l 0 0 2 then the limit lim is well defined in h01 h01 0 in 0 1 and 0 1 provides us with the principal eigenfunction of l 0 0 1 this is a rather striking result for as according to it the principal eigenfunction must approximate zero as if a d 0 in spite of the cooperative structure of the operator

positivity for equations involving polyharmonic operators with dirichlet boundary conditions cranston fabes and zhao 26 5 established the uniform bound sup x y 2 x 6 y r g1 n x z g1 n z y dz g1 n x y m 1 1 where g1 n x y is the green function for the laplacian with dirichlet boundary conditions on a lipschitz domain rn with n 3 see 27 for n 2 this estimate was used in 23 and 18 to obtain positivity uniformly with respect to f 0 for noncooperative elliptic systems as

a paley wiener theorem for real reductive groups le groupe sl 3 r prequantification des orbites de dimension minimale parmi celles non triviales dans la representation co adjointe de sl 3 r noyaux de blattner kostant steinberg irreductibilite et unicite du prolongement de certaines representations de p 3 a sl 3 r etude du prolongement des representations e a sl 3 r la representation type s s 2 minimal parametres de langlands et operateur d entrelacement avec la serie principale pour les representations e et

sur le theoreme de paley wiener d arthur the fourier transform of a c function f with compact support on a real reductive lie group g is given by a collection of operators o p e ip e f for a suitable family of representations of g which depends on a family indexed by p in a finite set of parabolic subgroups of g of pairs of parameters e varying in a set of discrete series e lying in a complex finite dimensional vector space the ip e are generalized principal series induced from p it is easy to verify the holomorphy of the fourier transform in the complex parameters also it satisfies some growth properties moreover an intertwining operator between two representations ip e ip e of the family implies an intertwining property for o p e and o p e there is also a way to introduce hsuccessive partial derivatives h of the family of representations ip e along the parameter e and intertwining operators between subquotients of these successive derivatives imply the intertwining property for the successive derivatives of the fourier transform o we show that these properties characterize the collections of operators p e o p e which are fourier transforms of a c function with compact support for g linear the proof which uses harish chandra fs plancherel formula rests on a similar result for left and right k finite functions which is due to j arthur we give also a proof of arthur fs result purely in term of representations involving the work of a knapp and e stein on intertwining integrals and langlands and vogan fs classifications of irreducible representations of g

harnack principle for weakly coupled elliptic systems abstract we prove the harnack inequality for the weakly coupled elliptic system s where su big begin align l 1 cdots l n end align big u qu and u big begin align u 1 cdot cdot cdot u n end align big l k k 1 n are second order elliptic operators with holder continuous coefficients and q is a matrix valued function with singular entries in the case that q is irreducible a full harnack principle is proved

sign definite solutions in some linear elliptic systems on considere un ensemble faiblement couple de deux equations aux derivees partielles ou la matrice de couplage a des elements variables et la partie principale de chaque equation est le meme operateur uniformement elliptique on obtient des conditions necessaires pour le decouplage on determine le signe algebrique des composantes de solution

on the least point of the spectrum of certain cooperative linear systems with a large parameter abstract we obtain the asymptotic limit of the principal eigenvalue of a cooperative system of linear elliptic equations as a parameter tends to infinity our results are much more general than those in the work of caudevilla and lopez gomez 2008 2 we obtain an unusual limit problem

theoreme de type paley wiener pour les groupes de lie semi simples reels avec une seule classe de conjugaison de sous groupes de cartan abstract in this article we characterize the space of fourier transforms of the smooth compactly supported functions on a semisimple lie group with one conjugacy class of cartan subgroups cf th 6 we get also results on the space of fourier transforms of the elements of the enveloping algebra of the lie algebra of such a group cf th 1 2 and 3

on invariant probability measures of regime switching diffusion processes with singular drifts abstract under integrability conditions of the coefficients the existence uniqueness and regularity estimates are derived for the invariant probability measure of regime switching diffusion processes moreover we study the l 1 uniqueness of the semigroup generated by regime switching diffusion processes as an application the l 1 uniqueness of the extension of weakly coupled elliptic systems is obtained

the absolute line quadric and camera autocalibration we introduce a geometrical object providing the same information as the absolute conic the absolute line quadric alq after the introduction of the necessary exterior algebra and grassmannian geometry tools we analyze the grassmannian of lines of p from both the projective and euclidean points of view the exterior algebra setting allows then to introduce the alq as a quadric arising very naturally from the dual absolute quadric we fully characterize the alq and provide clean relationships to solve the inverse problem i e recovering the euclidean structure of space from the alq finally we show how the alq turns out to be particularly suitable to address the euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters providing new linear and non linear algorithms for this problem we also provide experimental results showing the good performance of the techniques

a geometric approach for the analysis and computation of the intrinsic camera parameters the authors of this paper adopted the projected characteristics of the absolute conic in terms of the pascal s theorem to propose an entirely new camera calibration method based on purely geometric thoughts the use of this theorem in the geometric algebra framework allows us to compute a projective invariant using the conics of only two images which expressed using brackets helps us to set enough equations to solve the calibration problem the method requires restricted controlled camera movements our method is less sensitive to noise as the kruppa s equation based methods experiments with simulated and real images con rm that the performance of the algorithm is reliable 2001pattern recognition society published by elsevier science ltd all rights reserved

green function for schrodinger operator and conditioned feynman kac gauge consider the schrodinger operator h 2 q in a bounded c1 1 domain d with q klocd d q satisfies the condition sup spec 2 q d v x y g x y e y x exp 0 t q x t d t x y d where xt is the conditioned brownian motion starting at x and ending at y with the life time t and v g can be extended to a continuous and positive function on d d specifically we give the comparison theorem there exists a constant c c d q 0 such that 1 c g x y v x y c g x y x y d another result is that v nz x z x d z d exists and represents the poisson kernel for the dirichlet problem corresponding to schrodinger operator h

on the ambrosetti prodi problem for non variational elliptic systems we study the ambrosetti prodi problem for nonlinear elliptic equations and systems with uniformly elliptic operators in non divergence form and non smooth coefficients and with non linearities with linear or power growth

global dynamics of a classical lotka volterra competition diffusion advection system abstract in this paper we study a classical two species lotka volterra competition diffusion advection system where the diffusion and advection rates of two competitors are supposed to be proportional by employing the principal spectral theory we first establish a key a priori estimate on the co existence positive steady state which is a powerful tool to link the local and global dynamics we then further present a complete classification on all possible long time dynamical behaviors by appealing to the theory of monotone dynamical systems lastly we apply these results to a special situation where two species are competing for the same resources and obtain a sharp criteria in term of certain variable parameters for all kinds of global dynamics this work gives a positive answer to the conjecture proposed by lou et al in 34 by considering a more general model under certain conditions and also can be seen as a further development of he and ni 19 for competition diffusion system where we bring new ingredients in the arguments to overcome the difficulty caused by the involvement of advection

feynman kac functionals and positive solutions of 1 2δu qu 0 let d be a bounded c 2 domain in d and let q be a bounded borel function in d for x d and z d suppose x t under the law p x z is brownian motion in d starting at x and conditioned to converge to z let be the lifetime of x t we show that if the quantity e x z left exp left int limits 0 t q x s ds right right is finite for one x d and one z d then this quantity remains bounded as x varies over d and z varies over d this may be considered one quantitative expression of the qualitative statement that no matter where brownian motion in d eventually hits d it goes all over d before it gets there we apply this result to show that if the equation 1 2 u qu 0 admits a non negative solution in d which is strictly positive on a subset of d of positive harmonic measure then for any non negative bounded borel function f on d it admits a unique bounded solution u satisfying u f on d and this solution u is non negative

coexistence states of an elliptic system modeling a population with two age groups in this work an elliptic system with nonlinear boundary conditions describing two subpopulations of the same species competing for resources is studied under some natural assumptions we find the sufficient conditions for the existence of positive solutions of the system by using bifurcation techniques

camera calibration from surfaces of revolution this paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution camera calibration is the process of determining the intrinsic or internal parameters i e aspect ratio focal length and principal point of a camera and it is important for both motion estimation and metric reconstruction of 3d models in this paper a novel and simple calibration technique is introduced which is based on exploiting the symmetry of images of surfaces of revolution traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern such as a calibration grid the use of surfaces of revolution which are commonly found in daily life e g bowls and vases makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects in this paper it is shown that two images of a surface of revolution will provide enough information for determining the aspect ratio focal length and principal point of a camera with fixed intrinsic parameters the algorithms presented in this paper have been implemented and tested with both synthetic and real data experimental results show that the camera calibration method presented is both practical and accurate

maximum and antimaximum principles for some nonlocal diffusion operators abstract in this work we consider the maximum and antimaximum principles for the nonlocal dirichlet problem j u u u h r n j x y u y d y u x u x h x 0 in a bounded domain with u x 0 in r n the kernel j in the convolution is assumed to be a continuous compactly supported nonnegative function with unit integral we prove that for 1 the solution verifies u 0 in if h l 2 h 0 while for 1 and close to 1 the solution verifies u 0 in provided h x x d x 0 h l this last assumption is also shown to be optimal the neumann version of the problem is also analyzed

maximum principles for a coupled system of second and fourth order elliptic equations and an application in this paper we obtain a maximum principle for the coupled system of second and fourth order elliptic equations using an abstract result in a recent paper by correa and souto nonlinear anal 26 1996 and an application of the maximum principle is given

comparison principle for non cooperative elliptic systems this paper presents some sufficient conditions for the validity of the comparison principle for weak and classical solutions of non cooperative weakly coupled systems of elliptic second order pde

switched diffusion processes and systems of elliptic equations a dirichlet space approach the switched diffusion process associated with a weakly coupled system of elliptic equations is studied via a dirichlet space approach and is applied to prove the existence theorem of the cauchy initial problem for the system a representation theorem for the solution of the dirichlet boundary value problem and a generalised skorohod decomposition for the reflecting switched diffusion process are obtained

on the existence of coexistence states for an advection cooperative system with spatial heterogeneities abstract this paper is devoted to the analysis of the existence of coexistence states for cooperative systems under homogeneous dirichlet boundary conditions we assume rather general spatial heterogeneities for the coefficients of the non linearities and the cooperative terms in order to obtain sharp existence results we add advection terms related to the cooperative terms so that the system can be transformed into a variational one applying then several variational methods and bifurcation theory we arrive at necessary and sufficient condition on the parameter for the existence and the uniqueness of coexistence states we also compare the conditions for the heterogeneous case and the constant case

existence uniqueness and stability of positive solutions to sublinear elliptic systems reaction diffusion systems are used to model many chemical and biological phenomena in the natural world 25 26 and systems of coupled partial differential equations are also used in other physical models such as nonlinear schrodinger systems in multi component bose einstein condensates and nonlinear optics 19 23 the steady state solutions or standing wave solutions of such systems of nonlinear partial differential equations satisfy a nonlinear elliptic system with more than one equation much effort has been devoted to the existence of solutions of such systems see for example 4 8 10 11 13 15 17 24 30 33 34 but it is usually difficult to determine whether or not the solution is unique we consider the positive solutions of a semilinear elliptic system of the form

on a system of reaction diffusion equations describing a population with two age groups abstract a system of reaction diffusion equations modelling a population divided into juvenile and adult age groups is studied the system is not co operative but its linear part is and this makes it possible to establish existence non existence and stability results for non negative solutions of the system in terms of the principal eigenvalue of the corresponding linearized system

irreducible compact operators the purpose of the present paper is to show that a positive compact ideal irreducible operator t in a banach lattice of dimension greater than one has spectral radius r t 0 i e t is not quasi nilpotent it was shown in 6 that there exist positive irreducible operators which are quasi nilpotent and the question under what conditions a positive irreducible operator t satisfies r t 0 has been studied extensively see e g 6 and 7 sect v 6 in particular we mention the ando krieger theorem see e g 9 theorem 136 9 which states that a positive irreducible kernel operator t in a banach function space has r t 0 recently in 8 some special situations are discussed in which a compact positive irreducible operator has a strictly positive spectral radius let l be a real or complex banach lattice by 2 we denote the banach space of all bounded linear operators in l as usual we write s t in l whenever su tu for all o uel given 0 t l the closed ideal j in l is called t invariant if t j j and t is called ideal irreducible if the only closed t invariant ideals are 0 and l see 7 iii 8 for the general theory of banach lattices and positive operators we refer to the books 7 and 9 in the proof of the main result of the paper we will use some properties of the center of a banach lattice we recall some elementary facts let l be a real banach lattice the center z l of l is the subspace of 5 l consisting of all operators z for which there exists 0 2 ir such that f l 2 f for all f l the center has the structure of a vector lattice with nl v n2 u n l u v n2u and ozla zz u lu a nzu for all o u l and all l n2ez l moreover z l is a commutative algebra with respect to composition as multiplication and the identity operator i in l is a strong unit i e for any rc z l there exists 0 2eir such that zi 2i see 9 chap 20 note that if l c k for some compact hausdorff space k then z l can be identified with c k acting on itself by multiplication if l is a dedekind complete banach lattice and 0 u v in l then it is an easy consequence of the freudenthal spectral theorem 4 theorem 40 2 that there exists n z l such that zcv u and o n i however in an arbitrary banach lattice such a 7z need not exist as is shown by the banach lattice l c 0 1 the next lemma shows that under rather mild conditions we can

unipotent representations of complex semisimple groups algebraic group over r or c in this paper we restrict attention to c we generalize arthur s definition slightly or perhaps simply make it more precise all of the resulting representations except for a finite set are then unitarily induced from representations of the same kind on proper parabolic subgroups we call the finite set remaining special unipotent representations a precise definition will be given later definition 1 17 our main result theorem iii of this introduction is a character formula for any special unipotent representation of course such a formula can be deduced from the kazhdan lusztig conjecture cf v3 the advantages of theorem iii are that it is in closed form and that it lends itself to verification of some conjectures of arthur in a so let g be a connected complex semisimple lie group and q its lie algebra choose

variational approach for a class of cooperative systems abstract the aim of this work is to ascertain the characterization of the existence of coexistence states for a class of cooperative systems supported by the study of an associated non local equation through classical variational methods thanks to those results we are able to obtain the blow up behavior of the solutions in the whole domain for certain values of the main continuation parameter

ground state positivity negativity and compactness for a schrodinger operator in rn abstract we treat the schrodinger operator a q x on l 2 r n with the potential q r n q 0 bounded below and satisfying some reasonable hypotheses on the growth at infinity faster than x 2 as x we are concerned primarily with the compactness of the resolvent a i 1 of a as an operator on the banach space x x f l 2 r n f l r n f x ess sup r n f where denotes the ground state for a if is the ground state energy for a we show that the restricted operator a i 1 x x is not only bounded but also compact for in particular the spectra of a in l 2 r n and x coincide each eigenfunction belongs to x as another consequence we obtain a maximum and an anti maximum principles

a spatial seirs reaction diffusion model in heterogeneous environment abstract we propose a susceptible exposed infected recovered susceptible seirs reaction diffusion model where the disease transmission and recovery rates can be spatially heterogeneous the basic reproduction number r 0 is connected with the principal eigenvalue of a linear cooperative elliptic system threshold type results on the global dynamics in terms of r 0 are established the monotonicity of r 0 with respect to the diffusion rates of the exposed and infected individuals which does not hold in general is established in several cases finally the asymptotic profile of the endemic equilibrium is investigated when the diffusion rate of the susceptible individuals is small our results reveal the importance of the movement of the exposed and recovered individuals in disease dynamics as opposed to most of previous works which solely focused on the movement of the susceptible and infected individuals

an extension of maximum and anti maximum principles to a schrodinger equation in r2 abstract strong maximum and anti maximum principles are extended to weak l2 r 2 solutions u of the schrodinger equation u q x u u f x in l2 r 2 in the following form let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the schrodinger operator a q x in l2 r 2 assume that q x q x f is a sufficiently smooth perturbation of a radially symmetric function f 0 and 0 f 1 c const a e in r 2 then there exists a positive number depending upon f such that for every 1 with 1 the inequality 1 u c 1 holds a e in r 2 where c is a positive constant depending upon f and it is shown that such an inequality is valid if and only if the potential q x which is assumed to be strictly positive and locally bounded has a superquadratic growth as x this result is applied to linear and nonlinear elliptic boundary value problems in strongly ordered banach spaces whose positive cone is generated by the eigenfunction 1 in particular problems of existence and uniqueness are addressed

a theory of self calibration of a moving camera there is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement the epipolar transformation imposes two algebraic constraints on the camera calibration if two epipolar transformations arising from different camera displacements are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four the curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces or by a curve of degree six in the dual of the image plane the curve in the dual plane has one singular point of order three and three singular points of order two if three epipolar transformations are available then two curves of degree six can be obtained in the dual plane such that one of the real intersections of the two yields the correct camera calibration the two curves have a common singular point of order three experimental results are given to demonstrate the feasibility of camera calibration based on the epipolar transformation the real intersections of the two dual curves are found by locating the zeros of a function defined on the interval 0 2 the intersection yielding the correct camera calibration is picked out by referring back to the three epipolar transformations

liouville type theorems monotonicity results and a priori bounds for positive solutions of elliptic systems this paper is a contribution to the study of boundary value problems for systems of elliptic partial differential equations

principal eigenvalue and maximum principle for cooperative periodic parabolic systems abstract this paper classifies the set of supersolutions of a general class of periodic parabolic problems in the presence of a positive supersolution from this result we characterize the positivity of the underlying resolvent operator through the positivity of the associated principal eigenvalue and the existence of a positive strict supersolution lastly this scalar characterization is used to characterize the strong maximum principle for a class of periodic parabolic systems of cooperative type under arbitrary boundary conditions of mixed type

positive solutions of an elliptic system modeling a population with two age groups we study the existence of positive solutions for an elliptic system modeling two subpopulations of the same species competing for resources under some suitable assumptions we find the necessary and sufficient conditions for the existence of positive solutions of the system by using bifurcation techniques moreover an open problem proposed by bouguima et al 2008 is answered

asymptotic behavior of the principal eigenvalue for cooperative periodic parabolic systems and applications abstract the effects of spatial heterogeneity on population dynamics have been studied extensively however the effects of temporal periodicity on the dynamics of general periodic parabolic reaction diffusion systems remain largely unexplored as a first attempt to understand such effects we analyze the asymptotic behavior of the principal eigenvalue for linear cooperative periodic parabolic systems with small diffusion rates as an application we show that if a cooperative system of periodic ordinary differential equations has a unique positive periodic solution which is globally asymptotically stable then the corresponding reaction diffusion system with either the neumann or regular oblique derivative boundary condition also has a unique positive periodic solution which is globally asymptotically stable provided that the diffusion coefficients are sufficiently small the role of temporal periodicity spatial heterogeneity and their combined effects with diffusion will be studied in subsequent papers for further understanding and illustration

euclidean upgrading from segment lengths we address the problem of the recovery of euclidean structure of a projectively distorted n dimensional space from the knowledge of the possibly diverse lengths of a set of segments this problem is relevant in particular for euclidean reconstruction with uncalibrated cameras extending previously known results in the affine setting the key concept is the quadric of segments qos defined in a higher dimensional space by the set of segments of a fixed length from which euclidean structure can be obtained in closed form we have intended to make a thorough study of the properties of the qos including the determination of the minimum number of segments of arbitrary length that determine it and its relationship with the standard geometric objects associated to the euclidean structure of space explicit formulas are given to obtain the dual absolute quadric and the absolute quadratic complex from the qos experiments with real and synthetic images evaluate the performance of the techniques