finding fundamental cycles and bridges on a tree structured parallel computer we present parallel algorithms for finding fundamental cycles and bridges in a connected undirected graph g with n vertices the machine model that we are concerned with is a tree structured parallel computer which combines simd and systolic computers in a treelike manner under this model we have an o n2dp n log p time algorithm for finding fundamental cycles and an o n2p time algorithm for finding bridges where p 1 p n is the number of processing elements used and d is the depth of a breadth first spanning tree of g

strichartz estimates for the wave and schrodinger equations with the inverse square potential abstract we prove spacetime weighted l 2 estimates for the schrodinger and wave equation with an inverse square potential we then deduce strichartz estimates for these equations

gaussian heat kernel upper bounds via the phragmen lindelof theorem we prove that in presence of l gaussian estimates so called davies gaffney estimates on diagonal upper bounds imply precise off diagonal gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces

improved hardy and rellich inequalities on riemannian manifolds in this paper we establish improved hardy and rellich type inequalities on a riemannian manifold m furthermore we also obtain sharp constants for improved hardy and rellich type inequalities on the hyperbolic space n

existence and nonexistence of positive solutions of p kolmogorov equations perturbed by a hardy potential abstract in this article we establish the phenomenon of existence and nonexistence of positive weak solutions of parabolic quasi linear equations perturbed by a singular hardy potential on the whole euclidean space depending on the controllability of the given singular potential to control the singular potential we use a weighted hardy inequality with an optimal constant which was recently discovered in hauer and rhandi 2013 our results in this paper extend the ones in goldstein et al 2012 concerning a linear kolmogorov operator significantly in several ways firstly by establishing existence of positive global solutions of singular parabolic equations involving nonlinear operators of p laplace type with a nonlinear convection term for 1 p and secondly by establishing nonexistence locally in time of positive weak solutions of such equations without using any growth conditions

hardy and rellich type inequalities on metric measure spaces abstract in this paper some hardy and rellich type inequalities on complete non compact smooth metric measure spaces have been established moreover based on the main results about the hardy and rellich type inequalities several inequalities of the hardy poincare type or the heisenberg pauli weyl type can also be given as byproducts

best constants for higher order rellich inequalities in l p ω we obtain a series improvement to higher order lp rellich inequalities on a riemannian manifold m the improvement is shown to be sharp as each new term of the series is added

level set approach to mean curvature flow in arbitrary codimension we develop a level set theory for the mean curvature evolution of surfaces with arbitrary co dimension thus generalizing the previous work 8 15 on hypersurfaces the main idea is to surround the evolving surface of co dimension k in r by a family of hypersurfaces the level sets of a function evolving with normal velocity equal to the sum of the d k smallest principal curvatures the existence and the uniqueness of a weak level set solution is easily established using mainly the results of 8 and the theory of viscosity solutions for second order nonlinear parabolic equations the level set solutions coincide with the classical solutions whenever the latter exist the proof of this connection uses a careful analysis of the squared distance from the surfaces it is also shown that varifold solutions constructed by brakke 7 are included in the level set solutions the idea of surrounding the evolving surface by a family of hypersurfaces with a certain property is related to the barriers of de giorgi an introduction to the theory of barriers and his connection to the level set solutions is also provided

the effect of the hardy potential in some calderon zygmund properties for the fractional laplacian abstract the goal of this paper is to study the effect of the hardy potential on the existence and summability of solutions to a class of nonlocal elliptic problems s u u x 2 s f x u in u 0 in r n u 0 in where s s 0 1 is the fractional laplacian operator r n is a bounded domain with lipschitz boundary such that 0 and n 2 s we will mainly consider the solvability in two cases 1 the linear problem that is f x t f x where according to the summability of the datum f and the parameter we give the summability of the solution u 2 the problem with a nonlinear term f x t h x t for t 0 in this case existence and regularity will depend on the value of and on the summability of h looking for optimal results we will need a weak harnack inequality for elliptic operators with singular coefficients that seems to be new

second order sobolev type inequalities in the hyperbolic spaces abstract in this paper we establish several poincare sobolev type inequalities concerning to the laplace beltrami operator g in the hyperbolic space h n with n 5 these inequalities could be seen as the improved second order poincare inequality with remainder terms involving with the sharp rellich inequality or the sharp sobolev inequality in h n the novelty of these inequalities is that it combines both the sharp poincare inequality and the sharp rellich inequality or the sharp sobolev inequality for g in h n as a consequence we obtain the poincare sobolev inequality for the second order gjms operator p 2 in h n in dimension 4 we obtain an improvement of the sharp adams inequality and an adams inequality with exact growth for radial functions

de finetti s coherence and statistical inference on donne la definition d une inference coherente en conformite avec une theorie des probabilites conditionnelles derivee du principe de coherence de de finetti et on effectue une comparaison critique d une telle definition avec celle proposee par heath lane et sudderth

a new network topology with multiple meshes this paper introduces a new network topology called multi mesh mm which uses multiple meshes as the basic building blocks interconnected in a suitable manner the proposed network consists of n sup 4 processors and is 4 regular with a diameter of 2n the network also contains a hamiltonian cycle simple routing algorithms for point to point communication one to all broadcast and multicast have been described for this network it is shown that a simple n sup 2 spl times n sup 2 mesh can also be emulated on this network in o 1 time several application examples have been discussed for which this network is found to be more efficient with regard to computational time than the corresponding mesh with the same number of processors as examples o n time algorithms for finding the sum average minimum and maximum of n sup 4 data values located at n sup 4 different processors have been discussed time efficient implementations of algorithms for solving nontrivial problems e g lagrange s interpolation matrix transposition matrix multiplication and discrete fourier transform dft computation have also been discussed the time complexity of lagrange s interpolation on this network is o n for n sup 2 data points compared to o n sup 2 time on mesh of the same size matrix transpose requires o n sup 0 5 time for an n spl times n matrix the time for multiplying two n spl times n matrices is o n sup 0 6 with an at cost of o n sup 3 dft of n sample points can be computed in o n sup 0 6 time on this network the previous papers show that n sup 4 data elements can be sorted on this network in o n time

the hardy inequality and the asymptotic behaviour of the heat equation with an inverse square potential we study the well posedness and describe the asymptotic behavior of solutions of the heat equation with inverse square potentials for the cauchy dirichlet problem in a bounded domain and also for the cauchy problem in rn in the case of the bounded domain we use an improved form of the so called hardy poincare inequality and prove the exponential stabilization towards a solution in separated variables in rn we first establish a new weighted version of the hardy poincare inequality and then show the stabilization towards a radially symmetric solution in self similar variables with a polynomial decay rate this work complements and explains well known work by baras and goldstein on the existence of global solutions and blow up for these equations in the present article the sign restriction on the data and solutions is removed the functional framework for well posedness is described and the asymptotic rates calculated examples of non uniqueness are also given

sharp poincare hardy and poincare rellich inequalities on the hyperbolic space abstract we study hardy type inequalities associated to the quadratic form of the shifted laplacian h n n 1 2 4 on the hyperbolic space h n n 1 2 4 being as it is well known the bottom of the l 2 spectrum of h n we find the optimal constant in a resulting poincare hardy inequality which includes a further remainder term which makes it sharp also locally the resulting operator is in fact critical in the sense of 17 a related improved hardy inequality on more general manifolds under suitable curvature assumption and allowing for the curvature to be possibly unbounded below is also shown it involves an explicit curvature dependent and typically unbounded potential and is again optimal in a suitable sense furthermore with a different approach we prove rellich type inequalities associated with the shifted laplacian which are again sharp in suitable senses

continuation of blowup solutions of nonlinear heat equations in several space dimensions the possible continuation of solutions of the nonlinear heat equation in r n r ut u m u p with m 0 p 1 after the blowup time is studied and the different continuation modes are discussed in terms of the exponents m and p thus for m p 2 we find a phenomenon of nontrivial continuation where the regionfx u x t 1g is bounded and propagates with finite speed this we call incomplete blowup for n 3 and p m n 2 n 2 we find solutions that blow up at finite t t and then become bounded again for t t otherwise we find that blowup is complete for a wide class of initial data in the analysis of the behavior for large p a list of critical exponents appears whose role is described we also discuss a number of related problems and equations we apply the same technique of analysis to the problem of continuation after the onset of extinction for example for the equation ut u m u p m 0

on some strong poincare inequalities on riemannian models and their improvements abstract we prove second and fourth order improved poincare type inequalities on the hyperbolic space involving hardy type remainder terms since theirs l h s only involve the radial part of the gradient or of the laplacian they can be seen as stronger versions of the classical poincare inequality we show that such inequalities hold true on model manifolds as well under suitable curvature assumptions and sharpness of some constants is also discussed

fast efficient parallel algorithms for some graph problems algorithms for solving graph problems on an unbounded parallel model of computation are considered parallel algorithms of time complexity o log 2 n are described for finding biconnected components bridges minimum spanning trees and fundamental cycles in the algorithms for finding minimum spanning trees bridges and fundamental cycles the number of processors used is small enough that the parallel algorithm is efficient in comparison with the best sequential algorithms for these problems several other algorithms are presented which are especially suitable for processing sparse graphs

on nonexistence of baras goldstein type for higher order parabolic equations with singular potentials the celebrated result by baras and goldstein 1984 established that the heat equation with singular inverse square potential in a smooth bounded domain n n 3 such that 0 e u t u c x 2 u in 0 t u 0 in the supercritical range c c hardy 1 n 2 2 2 does not have a solution for any nontrivial l 1 initial data uo x 0 in or for a positive measure namely it was proved that a regular approximation of a possible solution by a sequence u n x t of classical solutions of uniformly parabolic equations with bounded truncated potentials given by v x c x 2 v n x min c x 2 n n 1 diverges and as n oo u n x t in x 0 t in the present paper we reveal the connection of this very singular evolution with a spectrum of some limiting operator the proposed approach allows us to consider more general higher order operators for which hardy s inequalities were known since rellich 1954 and initial data that are not necessarily positive in particular it is established that under some natural hypothesis the divergence result is valid for any 2mth order parabolic equation with singular potential u t m u c x 2m u in 0 t where c c h m m 1 with zero dirichlet conditions on and for a wide class of initial data in particular typically the divergence holds for any data satisfying u 0 x is continuous at x 0 and uo 0 0 similar nonexistence i e divergence as e 0 results are also derived for time dependent potentials e 2m q x e t e 2m and nonlinear reaction terms u p e 2m x 2m with p 1 applications to other linear and semilinear schrodinger and wave pdes are discussed

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

sure wins separating probabilities and the representation of linear functionals abstract we discuss conditions under which a convex cone k r admits a finitely additive probability m such that sup k k m k 0 based on these we characterise those linear functionals that are representable as finitely additive expectations a version of riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions

isoperimetric and sobolev inequalities for carnot caratheodory spaces and the existence of minimal surfaces after hormander s fundamental paper on hypoellipticity 54 the study of partial differential equations arising from families of noncommuting vector fields has developed significantly in this paper we study some basic functional and geometric properties of general families of vector fields that include the hormander type as a special case similar to their classical counterparts such properties play an important role in the analysis of the relevant differential operators both linear and nonlinear to motivate our results we recall some classical inequalities let e c r be a caccioppoli set a measurable set having a locally finite perimeter then one has the isoperimetric inequality

sharp uncertainty principles on general finsler manifolds the paper is devoted to sharp uncertainty principles heisenberg pauli weyl caffarelli kohn nirenberg and hardy inequalities on forward complete finsler manifolds endowed with an arbitrary measure under mild assumptions the existence of extremals corresponding to the sharp constants in the heisenberg pauli weyl and caffarelli kohn nirenberg inequalities fully textit characterizes the nature of the finsler manifold in terms of three non riemannian quantities namely its textit reversibility and the vanishing of the textit flag curvature and s textit curvature induced by the measure respectively it turns out in particular that the busemann hausdorff measure is the optimal one in the study of sharp uncertainty principles on finsler manifolds the optimality of our results are supported by randers type finslerian examples originating from the zermelo navigation problem

conditioning likelihood and coherence a review of some foundational concepts 2000 conditioning likelihood and coherence a review of some foundational concepts journal of the american statistical association vol 95 no 452 pp 1340 1346

finitely maxitive conditional possibilities bayesian like inference disintegrability and conglomerability the aim of the paper is to study bayesian like inference processes involving coherent finitely maxitive t conditional possibilities assessed on infinite sets of conditional events coherence of an assessment consisting of an arbitrary possibilistic prior and an arbitrary possibilistic likelihood function is proved thus a closed form expression for the envelopes of the relevant joint and posterior possibilities is given when t is the minimum or a strict t norm the notions of disintegrability and conglomerability are also studied and their relevance in the infinite version of the possibilistic bayes formula is highlighted

on birman s sequence of hardy rellich type inequalities abstract in 1961 birman proved a sequence of inequalities i n for n n valid for functions in c 0 n 0 l 2 0 in particular i 1 is the classical integral hardy inequality and i 2 is the well known rellich inequality in this paper we give a proof of this sequence of inequalities valid on a certain hilbert space h n 0 of functions defined on 0 moreover f h n 0 implies f h n 1 0 as a consequence of this inclusion we see that the classical hardy inequality implies each of the inequalities in birman s sequence we also show that for any finite b 0 these inequalities hold on the standard sobolev space h 0 n 0 b furthermore in all cases the birman constants 2 n 1 2 2 2 n in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in l 2 0 resp l 2 0 b we also show that these birman constants are related to the norm of a generalized continuous cesaro averaging operator whose spectral properties we determine in detail

nonlinear degenerate elliptic equation with hardy potential and critical parameter abstract some embedding inequalities in hardy sobolev spaces with general weight functions were proved and a positive answer to an open problem raised by brezis vazquez was given in the weighted hardy sobolev spaces the existence of nontrivial many solutions to the corresponding nonlinear degenerated elliptic equations with hardy potential and critical parameter under conditions weaker than ambrosetti rabinowitz condition was obtained

merging and testing opinions we study the merging and the testing of opinions in the context of a prediction model in the absence of incentive problems opinions can be tested and rejected regardless of whether or not data produces consensus among bayesian agents in contrast in the presence of incentive problems opinions can only be tested and rejected when data produces consensus among bayesian agents these results show a strong connection between the testing and the merging of opinions they also relate the literature on bayesian learning and the literature on testing strategic experts 1 introduction data can produce consensus among bayesian agents who initially disagree it can also test and reject opinions we relate these two critical uses of data in a model where agents may strategically misrepresent what they know in each period either 0 or 1 is observed let p and q be two probability measures on 0 1 1 such that q is absolutely continuous with respect to p if p and q are additive then as shown by blackwell and dubins 1962 the conditional probabilities of p and q merge in the sense that the two posteriors become uniformly close as the amount of observations increases q almost surely so repeated applications of bayes rule lead to consensus among bayesian agents provided that their opinions were initially compatible now consider savage s axiomatization of subjective probability he proposed postulates that characterize a preference relation over bets in terms of a nonatomic finitely additive probability p call such p for short an opinion savage s framework allows for finitely additive probabilities that are not additive in particular the conclusions of the blackwell and dubins theorem hold for some but not all opinions this flexibility makes savage s

on schrodinger operators with multipolar inverse square potentials abstract positivity essential self adjointness and spectral properties of a class of schrodinger operators with multipolar inverse square potentials are discussed in particular a necessary and sufficient condition on the masses of singularities for the existence of at least a configuration of poles ensuring the positivity of the associated quadratic form is established

group nearest neighbor queries in the l 1 plane let p be a set of n points in the plane the k nearest neighbor abbreviated as k nn query problem is to preprocess p into a data structure that quickly reports k closest points in p for a query point q this paper addresses a generalization of the k nn query problem to a query set q of points namely the group k nearest neighbor query problem in the l 1 plane more precisely a query is assigned with a set q of at most m points and a positive integer k with k n and the distance between a point p of p and a query set q is defined as the sum of l 1 distances from p to all q q the maximum number m of query points q is assumed to be known in advance and to be at most n in this paper we propose two algorithms one based on the range tree and the other based on a data structure for segment dragging queries and obtain the following complexity bounds 1 a group k nn query can be handled in o t min log n k m 2 log log n log m time after preprocessing p using o m 2 n log 2 n space where t min min k m m 2 or 2 a group k nn query can be handled in o k m log 2 n m 2 log n log m time after preprocessing p using o m 2 n space where 0 is an arbitrarily small constant we also show that our approach can be applied to the weighted group k nearest neighbor query problem and the group k farthest neighbor query problem

uniform resolvent estimates for schrodinger operator with an inverse square potential abstract we study the uniform resolvent estimates for schrodinger operator with a hardy type singular potential let l v v x where is the usual laplacian on r n and v x v 0 r 2 where r x x x and v 0 c 1 s n 1 is a real function such that the operator v 0 n 2 2 4 is a strictly positive operator on l 2 s n 1 we prove some new uniform weighted resolvent estimates and also obtain some uniform sobolev estimates associated with the operator l v

finding lowest common ancestors in parallel two parallel algorithms for finding the lowest common ancestors of a set of vertex pairs q the query set in a directed tree are presented with all the overheads taken into account these algorithms take o n qi p log2 n and o n2 p log2n time respectively with p 0 processors n is the size of the tree these results are better than the best known result in that the first achieves the o log2 n time bound with only n q processors while the second reduces the number of processors used by a factor of log2 n which is optimal for large query sets when 0 p n2 log2 n the computer model we use here is the pram which is an simd model allowing read but not write conflicts our results also imply the following improvements the processor bound for finding a set of fundamental cycles in an undirected graph is improved by a factor of log2 n and the result is optimal for dense graphs the implementations of some other sequential and parallel algorithms are also simplified

computing farthest neighbors on a convex polytope let n be a set of n points in convex position in r3 the farthest point voronoi diagram of n partitions r3 into n convex cells we consider the intersection g n of the diagram with the boundary of the convex hull of n we give an algorithm that computes an implicit representation of g n in expected o n log2 n time more precisely we compute the combinatorial structure of g n the coordinates of its vertices and the equation of the plane defining each edge of g n the algorithm allows us to solve the all pairs farthest neighbor problem for n in expected time o n log2 n and to perform farthest neighbor queries on n in o log2 n time with high probability

convergence in distribution of nonmeasurable random elements a notion of convergence in distribution for non necessarily measurable random elements due to hoffmann jorgensen is characterized in terms of weak convergence of finitely additive probability measures a similar characterization is given for a strengthened version of such a notion further it is shown that the empirical process for an exchangeable sequence can fail to converge due to the nonexistence of any measurable limit although it converges for an i i d sequence because of phenomena of this type hoffmann jorgensen s definition is extended to the case of a nonmeasurable limit in the extended definition naturally suggested by the main results the limit is a finitely additive probability measure

dirichlet problems with singular convection terms and applications abstract in this paper we study dirichlet problems with singular convection terms then applications to the study of some elliptic systems of two equations are given

bessel pairs and optimal hardy and hardy rellich inequalities we give necessary and sufficient conditions on a pair of positive radial functions v and w on a ball b of radius r in rn n 1 so that the following inequalities hold for all u in c 0 infty b label one int limits b v x nabla u 2 dx geq int limits b w x u 2dx label two int limits b v x delta u 2 dx geq int limits b w x nabla u 2 dx n 1 int limits b left frac v x x 2 frac v r x x right nabla u 2dx this characterization makes a very useful connection between hardy type inequalities and the oscillatory behaviour of certain ordinary differential equations and helps in the identification of a large number of such couples v w that we call bessel pairs as well as the best constants in the corresponding inequalities this allows us to improve extend and unify many results old and new about hardy and hardy rellich type inequalities such as those obtained by caffarelli et al compos math 53 259 275 1984 brezis and vazquez revista mat univ complutense madrid 10 443 469 1997 wang and willem j funct anal 203 550 568 2003 adimurthi et al proc am math soc 130 489 505 2002 and many others

stable foliations with respect to the fuglede p modulus and level sets of q harmonic functions abstract we consider the p modulus of a foliation on a riemannian manifold we study the second variation of the p modulus and we derive a stability condition for this variation which we formulate as a type of the hardy inequality with the weight depending on the geometry of the foliation in particular we show that foliations defined by the distance function are p stable for any p 2 we examine the critical points of the p modulus of the level sets of a smooth function this leads via a new approach to generalizations of the well known result that the q capacity of a condenser is the reciprocal of the p modulus of the family of all hyper surfaces separating the plates of the condenser

the hardy inequality and nonlinear parabolic equations on carnot groups abstract in this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation u t g p u v x u p 1 in 0 t 1 p 2 u x 0 u 0 x 0 in u x t 0 on 0 t where g p is the p sub laplacian on a carnot group g and v l loc 1

doubly nonlinear parabolic equations with singular lower order term abstract in this paper we are concerned with positive solutions of the doubly nonlinear parabolic equation u t div u m 1 u p 2 u vu m p 2 in a cylinder 0 t with initial condition u 0 u 0 0 and vanishing on the parabolic boundary 0 t here r n resp h n is a bounded domain with smooth boundary v l loc 1 m r 1 p n and m p 2 0 the critical exponents q are found and the nonexistence results are proved for q m p

the heat equation with a singular potential of concern is the singular problem du dt au c x 2 iz x tz x 0 u0 x and its generalizations here c 0 x g rn t 0 and and t 0 are nonnegative and not both identically zero there is a dimension dependent constant c n such that the problem has no solution for c ct n for c s ct a necessary and sufficient conditions are found for and u0 so that a nonnegative solution exists

on a class of rellich inequalities we prove the rellich and the improved rellich inequalities that involve the distance function from a hypersurface of codimension k under a certain geometric assumption in case the distance is taken from the boundary that assumption is the convexity of the domain we also discuss the best constant of these inequalities

isolated singularities of the solutions of the schrodinger equation with a radial potential we study the behavior near an isolated singularity say x 0 of solutions of the equation 1 u x v x u x defined in a neighborhood of 0 in terms of the potential v which we assume to be radially symmetric for a class of potentials p1 that we characterize completely there is a unique singularity with constant sign behaving like the fundamental solution of the laplace operator for a larger class p2 we obtain a unique type of nonnegative singularity that is radially symmetric if v r cr with c 0 e r the class p1 is characterized by 2 and the class p2 by 2 the results fail for 2

stability of optimal control of heat equation with singular potential abstract in this paper we study stability of an optimal control for a multi dimensional heat equation with a singular potential term a family of perturbed optimal control problems with lower power singular potentials are formulated it is shown that when the lower powers tend to the critical power two the optimal controls are convergent to the optimal control of the original system

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

proper posteriors from improper priors for an unidentified errors in variables model the problem considered is inference in a simple errors in variables model where consistent estimation is impossible without introducing additional exact prior information the probabilistic prior information required for bayesian analysis is found to be surprisingly light despirte the model s lack of identification a proper posterior is guaranteed for any bounded prior density including those representing improper priors this result is illustrated with the improper uniform prior which implies marginal posterior densities obtainable by integrating the likelihood function

hardy and rellich type inequalities on complete manifolds abstract we prove some hardy and rellich type inequalities on complete noncompact riemannian manifolds supporting a weight function which is not very far from the distance function in the euclidean space

improved lp poincare inequalities on the hyperbolic space abstract we investigate the possibility of improving the p poincare inequality h n u p p p u p p on the hyperbolic space where p 1 and p n 1 p p is the best constant for which such inequality holds we prove several different and independent improved inequalities one of which is a poincare hardy inequality namely an improvement of the best p poincare inequality in terms of the hardy weight r p r being geodesic distance from a given pole certain hardy maz ya type inequalities in the euclidean half space are also obtained

improved hardy and rellich inequalities on nonreversible finsler manifolds abstract in this paper we study the sharp constants of quantitative hardy and rellich inequalities on nonreversible finsler manifolds equipped with arbitrary measures in particular these inequalities can be globally refined by adding remainder terms like the brezis vazquez improvement if finsler manifolds are of strictly negative flag curvature vanishing s curvature and finite uniformity constant furthermore these results remain valid when finsler metrics are reversible

null controllability for the heat equation with singular inverse square potentials abstract we prove the null controllability of the heat equation perturbed by a singular inverse square potential arising in quantum mechanics and combustion theory this is done within the range of subcritical coefficients of the singular potential provided the control acts on an annular set around the singularity our proof uses a splitting argument on the domain decomposition in spherical harmonics new carleman inequalities and refined hardy inequalities

interpolation between brezis vazquez and poincare inequalities on nonnegatively curved spaces sharpness and rigidities abstract this paper is devoted to investigate an interpolation inequality between the brezis vazquez and poincare inequalities shortly bpv inequality on nonnegatively curved spaces as a model case we first prove that the bpv inequality holds on any minkowski space by fully characterizing the existence and shape of its extremals we then prove that if a complete finsler manifold with nonnegative ricci curvature supports the bpv inequality then its flag curvature is identically zero in particular we deduce that a berwald space of nonnegative ricci curvature supports the bpv inequality if and only if it is isometric to a minkowski space our arguments explore fine properties of bessel functions comparison principles and anisotropic symmetrization on minkowski spaces as an application we characterize the existence of nonzero solutions for a quasilinear pde involving the finsler laplace operator and a hardy type singularity on minkowski spaces where the sharp bpv inequality plays a crucial role the results are also new in the riemannian euclidean setting

a unified approach to improved l p hardy inequalities with best constants we present a unified approach to improved l p hardy inequalities in r n we consider hardy potentials that involve either the distance from a point or the distance from the boundary or even the intermediate case where the distance is taken from a surface of codimension 1 k n in our main result we add to the right hand side of the classical hardy inequality a weighted l p norm with optimal weight and best constant we also prove nonhomogeneous improved hardy inequalities where the right hand side involves weighted l q norms q p

on the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term we study questions of existence uniqueness and asymptotic behaviour for the solutions of u x t of the problem begin gathered text u t delta u lambda e u text lambda text 0 t 0 text x text varepsilon b hfill p text u x 0 u 0 x text x text varepsilon b hfill text u x t 0 text on text partial b times 0 infty hfill end gathered where b is the unit ball x varepsilon r n x text leqq text 1 text and n geqq 3 our interest is focused on the parameter 0 2 n 2 for which p admits a singular stationary solution of the form s x 2log x

on a degenerate heat equation with a singular potential using a new method we generalize the blow up and existence result from p baras and j a goldstein 1984 trans amer math soc 284 121 139 to heat equations on the heisenberg group in doing so we need to overcome the difficulty that the equation in this case is both degenerate and of variable coefficients comparing with the euclidean case an interesting new result is that solutions can blow up even when the singularity of the potential is weaker than the inverse square of the distance function

parametric models for an splitting processes and mixtures a class of parametric models called splitting processes is defined by using de finetti s concept of adherent mass such splitting processes give rise to complex mixtures of distributions it is proved that the nonparametric bayesian predictive procedure a n of hill holds exactly for a member of this class called a nested splitting process the connection between a n and the dirichlet process is stated and proved a multivariate version of a n based on splitting processes is proposed

variational problems related to self similar solutions of the heat equation on demontre la compacite de certains plongements de sobolev sous de bonnes conditions sur les poids k x exp x c 2 r n r on considere des methodes variationnelles pour la resolution d equations elliptiques

geometrical properties of the fermat weber problem abstract this paper is devoted to the fermat weber problem with mixed gauges in order to take into account nonsymmetric distances a geometrical description of the set of solutions is obtained then the concept of metric hull is defined general sufficient conditions are given such that the metric hull of existing facilities intersects the set of optimal locations particularly it is shown that an optimal location can be found in the metric hull in dimension two whatever the gauges are and in dimension n with the rectilinear norm the connection between metric hull convex hull and octagonal hull is studied

semilinear elliptic equations for the fractional laplacian with hardy potential abstract in this paper we study existence and nonexistence of nonnegative distributional solutions for a class of semilinear fractional elliptic equations involving the hardy potential

hardy and rellich inequalities for submanifolds in hadamard spaces abstract some of the most known integral inequalities are the sobolev hardy and rellich inequalities on regions in euclidean spaces in the context of submanifolds the sobolev inequality was proved by michael simon 13 and hoffman spruck 12 since then a sort of applications to the submanifold theory has been derived from those inequalities years later carron 6 obtained a hardy inequality for submanifolds in hadamard spaces in this paper we prove the general hardy and rellich inequalities for submanifolds in hadamard spaces some applications are given and we also analyse the equality cases

optimal graph algorithms on a fixed size linear array parallel algorithms for computing the minimum spanning tree of a weighted undirected graph and the bridges and articulation points of an undirected graphs on a fixed size linear array of processors are presented for a graph of n vertices the algorithms operate on a linear array of p processors and require o n2 p time for all p 1 p n in particular using n processors the algorithms require o n time which is optimal on this model the paper describes two approaches to limit the communication requirements for solving the problems the first is a divide and conquer strategy applied to sollin s algorithm for finding the minimum spanning tree of a graph the second uses a novel data reduction technique that constructs an auxiliary graph with no more than 2n 2 edges whose bridges and articulation points are the bridges and articulation points of the original graph

on the scoring approach to admissibility of uncertainty measures in expert systems abstract this paper arose from our need to rigorize clarify and address fully the results of lindley s paper scoring rules and the inevitability of probability internat statist rev 50 1982 1 26 herein we develop a calculus of admissibility in a game theoretic setting in the case of an additive aggregation function it is shown that decomposable measures such as those used in fuzzy logics are admissible also the problem of the admissibility of the dempster shafer belief functions is investigated via the concept of random sets it is shown that the class of admissible measures in a scoring framework depends on the assumptions concerning the aggregation function in use in particular for nonadditive aggregation functions an admissible measure may not be transformable to a finitely additive probability measure

optimal hardy weight for second order elliptic operator an answer to a problem of agmon abstract for a general subcritical second order elliptic operator p in a domain r n or noncompact manifold we construct hardy weight w which is optimal in the following sense the operator p w is subcritical in for all 1 null critical in for 1 and supercritical near any neighborhood of infinity in for any 1 moreover if p is symmetric and w 0 then the spectrum and the essential spectrum of w 1 p are equal to 1 and the corresponding agmon metric is complete our method is based on the theory of positive solutions and applies to both symmetric and nonsymmetric operators the constructed hardy weight is given by an explicit simple formula involving two distinct positive solutions of the equation p u 0 the existence of which depends on the subcriticality of p in

self similar solutions of a semilinear parabolic equation with inverse square potential abstract we investigate existence nonexistence and asymptotical behaviour both at the origin and at infinity of radial self similar solutions to a semilinear parabolic equation with inverse square potential these solutions are relevant to prove nonuniqueness of the cauchy problem for the parabolic equation in certain lebesgue spaces generalizing the result proved by haraux and weissler non uniqueness for a semilinear initial value problem indiana univ math j 31 1982 167 189 for the case of vanishing potential

on the existence of inferences which are consistent with a given model if p is a additive statistical model and a finitely additive prior then any statistic t is sufficient with respect to a suitable inference consistent with p and provided only that p t t 0 for all and t here sufficiency is to be intended in the bayesian sense and consistency in the sense of lane and sudderth as a corollary if p is additive and diffuse then whatever the prior there is an inference which is consistent with p and two versions of the main result are also obtained for predictive problems

some remarks on the use of improper priors for the analysis of exponential regression models summary we consider bayesian inference on the exponential regression model it is known that standard improper priors on the parameters of this model lead to marginal posterior distributions on one of the parameters involved which are also improper on the interval 0 1 this has sometimes been interpreted as meaning that the observations are irrelevant we re analyse this problem using a finitely additive approach and show that the above conclusion is not generally correct this result emphasizes once again the dangers of a routine approach to bayesian inference using improper priors

regularity theorems for parabolic equations abstract we study regularity properties of solutions of a parabolic equation t a b b u 0 in r r d d 3 under fairly general conditions on the drift term coefficients the results are already new for the case a i b 0 b b x and div b 0

linear parabolic equations with strong singular potentials using an extension of a recent method of cabre and martel 1999 we extend the blow up and existence result in the paper of baras and goldstein 1984 to parabolic equations with variable leading coefficients under almost optimal conditions on the singular potentials this problem has been left open in baras and goldstein these potentials lie at a borderline case where standard theories such as the strong maximum principle and boundedness of weak solutions fail even in the special case when the leading operator is the laplacian we extend a recent result in cabre and martel from bounded smooth domains to unbounded nonsmooth domains