uniformization of analytic spaces in this article we give an explicit elementary proof of a local version of resolution of singularities in characteristic zero local means that the centres of blowing up are chosen locally so that a finite number of finite sequences of local blowings up may be required to cover a neighbourhood of a given point hence we use the term uniformization rather than local desingularization although uniformization in our sense is considerably stronger than the original idea of zariski 16 in the last two decades several mathematicians notably abhyankar 1 hironaka and spivakovsky 12 and youssin 14 15 have proposed simpler or more explicit versions of the inductive procedure in hironaka s proof of his great theorem 8 these approaches would seem to lead to some form of uniformization though full details of none of them have yet appeared the idea of seeking an explicit local procedure to determine the centres of blowing up is that a sufficiently good local choice should globalize automatically our method for example gives global resolution of singularities of surfaces in any codimension throughout this paper k denotes either the field of real numbers r or the field of complex numbers c we will work in the category of analytic spaces over k although our techniques apply as well to algebraic spaces over a field

when facilities coincide exact optimality conditions in multifacility location abstract in continuous minisum multifacility location problems it has been observed that optimal solutions often involve coincidences of facilities this paper gives a complete analysis by way of subdifferential calculus of the exact optimality conditions at such solutions these conditions are expressed as the existence of a multidimensional conservative flow in a network satisfying a nonlinear constraint on each edge by way of network flow theory a description with a minimal number of variables is obtained this procedure is illustrated by several examples showing how it enables a sensitivity analysis of the optimal solution with respect to the weights of the problem the optimality conditions are shown to be always directly verifiable if the network is a tree necessary conditions for coincidences at an optimal solution which previously appeared in the literature are generalized and it is shown in which cases these are also sufficient

fuzzy clustering with structural constraints abstract in this paper we propose a generalization of the standard clustering problem which we call structural constrained clustering scc problem in scc problem the cluster interconnections are given by a binary relation r if this relation is empty then scc problem reduces to the standard classification problem the cluster structure imposed by r may be described by the covering graph of r for example if this graph is a rooted tree then a hierarchical structure is imposed to the clusters we formulate scc as a fuzzy clustering problem with prototype inter relation a general algorithm to solve this problem is proposed for three particular distance measures squared euclidean and l1 metric we compute the prototypes by solving a particular multifacility location problem

capacitary estimates for dirichlet eigenvalues abstract lethbe the non negative definite selfadjoint operator associated to a regular irreducible dirichlet form onl2 x m assume thathhas discrete spectrum we study perturbations of this operator which arise through the imposition of dirichlet boundary conditions on a compact subset ofx the eigenvalues of the perturbed operator are of course shifted to the right under an ultracontractivity condition we show that the magnitude of this shift can be estimated by the capacity we also obtain a capacitary lower bound for the ground state shift under suitable conditions an application to the crushed ice problem is described

on the convergence of miehle s algorithm for the euclidean multifacility location problem for the euclidean single facility location problem e weiszfeld proposed a simple iterative algorithm in 1937 later it was proved by numerous authors that it is a convergent descent algorithm w miehle extended weiszfeld s algorithm to solve the euclidean multifacility location problem then l m ostresh proved that miehle s algorithm is a descent algorithm recently f rado modified miehle s algorithm and provided several sets of sufficient conditions for the modified algorithm to converge he also indicated that the convergence of miehle s algorithm was an open problem in this paper the relationship between miehle s multifacility location algorithm and weiszfeld s single facility location algorithm is analyzed counterexamples show that miehle s algorithm may converge to nonoptimal points for well structured problems

asymptotics of the principal eigenvalue and expected hitting time for positive recurrent elliptic operators in a domain with a small puncture abstract let x t be a positive recurrent diffusion process corresponding to an operator l on a domain d r d with oblique reflection at d if d r d for each x d we define a volume preserving norm that depends on the diffusion matrix a x we calculate the asymptotic behavior as e 0 of the expected hitting time of the e ball centered at x and of the principal eigenvalue for l in the exterior domain formed by deleting the ball with the oblique derivative boundary condition at d and the dirichlet boundary condition on the boundary of the ball this operator is non self adjoint in general the behavior is described in terms of the invariant probability density at x and det a x in the case of normally reflected brownian motion the results become isoperimetric type equalities

spectra of manifolds less a small domain soit m une variete de riemann c connexe compacte et l operateur de laplace beltrami associee on etudie le spectre pour une sous variete m compacte e 0 et b e le voisinage tubulaire de m de rayon e d operateur e

an optimal method for solving the generalized multi weber problem abstract the single weber problem and the multi weber problem have troubled generations of mathematicians economists and geographers by enumerating all feasible elements of a solution non overlapping convex hulls linear programming can be employed to obtain optimal solutions to the multi weber problem and the generalized multi weber problem in euclidean space first lists of all feasible convex hulls are generated these are the universe of potential elements of an optimal solution second these convex hulls are used to cover the fixed points of the problem a linear programme based on the set covering problem is then used to cover the fixed points minimizing the total weighted distance computational experience is presented this method guarantees the optimality of the solution

on the convergence of a hyperboloid approximation procedure for the perturbed euclidean multifacility location problem for the euclidean single facility location problem e weiszfeld proposed a simple closed form iterative algorithm in 1937 later numerous authors proved that it is a convergent descent algorithm in 1973 j eyster j white and w wierwille extended weiszfeld s idea and proposed a hyperboloid approximation procedure hap for solving the euclidean multifacility location problem they believed based on considerable computational experience that the hap always converges in 1977 ostresh proved that the hap is a descent algorithm under certain conditions in 1981 morris proved that a variant of the hap always converges however no convergence proof for the original hap has ever been given in this paper we prove that the hap is a descent algorithm and that it always converges to the minimizer of the objective function from any initial point

a fixed point algorithm for solving the euclidean multifacility location problem in a tree the optimality conditions for the euclidean multifacility location problem with m new facilities in a tree are stated as optimality conditions of a certain set of m weber problems an algorithm is presented which solves the emfl problem by iteratively solving such weber problems

convergence of the weiszfeld algorithm for weber problems using a generalized distance function this paper considers a generalization of the single and multisource weber problem for the case when the distance function is some power k of the usual ip distance properties of the generalized problem are established and an appropriate generalization of the weiszfeld iterative approach is given a convergence proof is supplied for an approximation to the original problem under certain restrictions on p and k

canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant this article contains an elementary constructive proof of resolution of singularities in characteristic zero our proof applies in particular to schemes of finite type and to analytic spaces so we recover the great theorems of hironaka we introduce a discrete local invariant rm inv x a whose maximum locus determines a smooth centre of blowing up leading to desingularization to define rm inv x we need only to work with a category of local ringed spaces x x cal o x satisfying certain natural conditions if a in x then rm inv x a depends only on widehat cal o x a more generally rm inv x is defined inductively after any sequence of blowings up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of rm inv x cdot the paper is self contained and includes detailed examples one of our goals is that the reader understand the desingularization theorem rather than simply know it is true

the euclidean multifacility location problem to solve the euclidean multifacility location problem w miehle extended the weiszfeld algorithm from one to several facilities l m ostresh established that the objective function for the iterates of miehle s algorithm decreases in value but his results do not give a convergence proof in this paper we give a new extension of the weiszfeld algorithm and by generalizing the kuhn ostresh convergence theorem prove separate results for convergence and for optimality both under mild hypotheses

accelerating the convergence in the single source and multi source weber problems abstract the modified weiszfeld method y vardi c h zhang a modified weiszfeld algorithm for the fermat weber location problem mathematical programming 90 2001 559 566 is perhaps the most widely used algorithm for the single source weber problem swp in this paper in order to accelerate the efficiency for solving swp a new numerical method called weiszfeld newton method is developed by combining the modified weiszfeld method with the well known newton method global convergence of the new weiszfeld newton method is proved under mild assumptions for the multi source weber problem mwp a new location allocation heuristic cooper weiszfeld newton method is presented in the spirit of cooper algorithm l cooper heuristic methods for location allocation problems siam review 6 1964 37 53 using the new weiszfeld newton method in the location phase to locate facilities and adopting the nearest center reclassification algorithm ncra in the allocation phase to allocate the customers preliminary numerical results are reported to verify the evident effectiveness of weiszfeld newton method for swp and cooper weiszfeld newton method for mwp

an o nm algorithm for a special case of the multimedian location problem on a tree abstract the multimedian location problem on a connected network g is concerned with locating m new facilities on the network the network g has one existing facility customer at each of the n nodes of g the objective is to locate the new facilities so as to minimize total cost which is the sum of a weighted distances between pairs of new and existing facilities and b weighted distances between certain pairs of new facilities we show that this problem can be solved in o nm when g is a tree and the set of pairs of new facilities which interact has special structure

virtual poincare polynomial of the link of a real algebraic variety the link of an affine real algebraic variety at a point is defined to be the intersection of the variety with a small sphere centred at the point the euler characteristic of the link leads to local topological characterisation of real algebraic varieties in law dimensions we prove in the paper that not only the euler characteristic but also the stronger virtual poincare polynomial is well defined for the link at a point of an affine algebraic variety

a note on optimality conditions for the euclidean multifacility location problem thekey problem of the euclidean multifacility location emfl problem is to decide whether a givendead point is optimal if it is not optimal we wish to compute a descent direction this paper extends the optimality conditions of calamai and conn and overton to the case when the rows of the active constraints matrix are linearly dependent we show that linear dependence occurs wheneverg the graph of the coinciding facilities has a cycle in this case the key problem is formulated as a linear least squares problem with bounds on the euclidean norms of certain subvectors

domain perturbations shift of eigenvalues and capacity abstract the notion of capacity of a subspace which was introduced in 16 is used to prove new estimates on the shift of the eigenvalues which arises if the form domain of a self adjoint and semibounded operator is restricted to a smaller subspace the upper bound on the shift of the spectral bound given in 16 is improved and another lower bound is proved which leads to a generalization of thirring s inequality if the underlying hilbert space is an l 2 space moreover we prove a similar capacitary upper bound for the second eigenvalue the results are applied to elliptic constant coefficient differential operators of arbitrary order finally it is given a capacitary characterization for the shift of the spectral bound being positive which works for operators with spectral bound of arbitrary type

finiteness of semialgebraic types of nash mappings defined on a nash surface in this paper we consider a problem on whether the number of semialgebraic types appearing in a family of nash mappings defined on a two dimensional nash surface is finite we show that if the nash surface has isolated singularities then this number is finite on the other hand we show that if it has non isolated singularities namely its singular locus is one dimensional then even the number of topological types can be infinite we give such a negative example in the algebraic case