linear programming system identification the general nonnegative parameters case abstract by linear programming system identification we mean the problem of estimating the objective function coefficient vector and the technological coefficient matrix a for a linear programming system that best explains a set of input output vectors input vectors are regarded as available resources output vectors are compared to imputed optimal ones by a decisional efficiency measure and a likelihood function is constructed in an earlier paper we obtained results for a simplified version of the problem in this paper we propose a genetic algorithm approach for the general case in which and a are of arbitrary finite dimensions and have nonnegative components a method based on householder transformations and monte carlo integration is used as an alternative to combinatorial algorithms for the extreme points and volumes of certain required convex polyhedral sets the method exhibits excellent face validity for a published test data set in data envelopment analysis

solvability of linear local and nonlocal robin problems over c ω abstract let r n be a bounded lipschitz domain we first consider an elliptic boundary value problem with general robin boundary conditions the boundary conditions can be either local or nonlocal depending on the conditions imposed on the elliptic operator we prove that this boundary value problem is uniquely solvable and moreover we show that such weak solution is holder continuous on we also prove that a realization of the associated differential operator with generalized local or nonlocal robin boundary conditions generates an analytic c 0 semigroup of angle 2 over c we conclude by applying the elliptic regularity theory to solve the corresponding cauchy problem over c

spectral convergence and nonlinear dynamics of reaction diffusion equations under perturbations of the domain abstract in this paper we obtain the continuity of attractors for semilinear parabolic problems with neumann boundary conditions relatively to perturbations of the domain we show that if the perturbations on the domain are such that the convergence of eigenvalues and eigenfunctions of the neumann laplacian is granted then we obtain the upper semicontinuity of the attractors if moreover every equilibrium of the unperturbed problem is hyperbolic we also obtain the continuity of attractors we also give necessary and sufficient conditions for the spectral convergence of neumann problems under perturbations of the domain

varying boundary conditions in a general class of elliptic problems of mixed type abstract in this paper we use the linear theory developed in cano casanova and lopez gomez j differential equations 178 2002 123 to show the continuous dependence of the positive solutions of a general class of sublinear elliptic boundary value problems of mixed type with respect to the boundary operator besides working with mixed non classical boundary conditions this paper considers problems where bifurcation from infinity occurs treating this kind of problems is far from easy since a complete knowledge of the set of values of the parameters where they exhibit a positive solution is imperative our results are far from immediate as a consequence of the vanishing weight functions involved in our general setting now a days the analysis of these general problems where the coefficients are allowed to vary and eventually vanishing or changing sign is focusing a great deal of attention

singular perturbation of domains and the semilinear elliptic equation ii on considere un domaine a perturbation singuliere d 1 d 2 q avec un petit parametre 0 et on etudie le comportement des solutions et leur structure du probleme aux valeurs limites elliptique semilineaire pour quand 0 est petit v f v 0 dans v v 0 sur ou f est une fonction lisse a valeur reelle non lineaire

properties of the principal eigenvalues of a general class of non classical mixed boundary value problems in this paper we characterize the existence of principal eigenvalues for a general class of linear weighted second order elliptic boundary value problems subject to a very general class of mixed boundary conditions our theory is a substantial extension of the classical theory by p hess and t kato 1980 comm partial differential equations5 999 1030 in obtaining our main results we must give a number of new results on the continuous dependence of the principal eigenvalue of a second order linear elliptic boundary value problem with respect to the underlying domain and the boundary condition itself these auxiliary results complement and in some sense complete the theory of d daners and e n dancer 1997 j differential equations138 86 132 the main technical tool used throughout this paper is a very recent characterization of the strong maximum principle in terms of the existence of a positive strict supersolution due to h amann and j lopez gomez 1998 j differential equations146 336 374

a limit equation associated to the solvability of the vacuum einstein constraint equations by using the conformal method let m g be a compact riemannian manifold on which a trace free and divergence free sigma is an element of w 1 w p and a positive function tau is an element of w 1 w p p n are fixed in thi

reduced thin sandwich equations on manifolds euclidean at infinity and on closed manifolds existence and multiplicity the reduced thin sandwich equations rtse appear within wheeler s thin sandwich approach toward the einstein constraint equations ece of general relativity it is known that these equations cannot be well posed in general but on closed manifolds sufficient conditions for well posedness have been established in particular it has been shown that the rtse are well posed in a neighborhood of umbilical solutions of the constraint equations without conformal killing fields in this paper we will analyze such a set of equations on the manifolds euclidean at infinity in a neighborhood of asymptotically euclidean ae solutions of the ece the main conclusion in this direction is that on ae manifolds admitting a yamabe positive metric the solutions of the rtse parameterize an open subset in the space of solutions of the ece in addition we show that in the case of closed manifolds these equations are well posed around umbilical solutions of the ece admitting killing fields and present some relevant examples finally it will be shown that in the set of umbilical solutions of the vacuum ece on closed manifolds the rtse are generically well posed

a faber krahn inequality for robin problems in any space dimension we prove a faber krahn inequality for the first eigenvalue of the laplacian with robin boundary conditions asserting that amongst all lipschitz domains of fixed volume the ball has the smallest first eigenvalue we prove the result in all space dimensions using ideas from m h bossel c r acad sci paris ser i math 302 1986 47 50 where a proof for smooth domains in the plane was given the method does not involve the use of symmetrisation arguments the results also imply variants of the cheeger inequality for the first eigenvalue

uniform resolvent convergence for strip with fast oscillating boundary abstract in a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small on the oscillating boundary we impose dirichlet neumann or robin boundary condition in all cases we describe the homogenized operator establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one and prove the estimates for the rate of convergence these results are obtained as the order of the amplitude of the oscillations is less equal or greater than that of the period it is shown that under the homogenization the type of the boundary condition can change

enhanced bisection strategies for the maximin efficiency ratio model abstract the maximin efficiency ratio mer model may be regarded as a new form of data envelopment analysis dea model which is based on the maximum decisional efficiency mde estimation principle the mer model involves a special class of generalized fractional programming problems this paper proposes some improved computational algorithms as alternatives to the original bolzano search and other general purpose algorithms for solving the mer model one of these which may be called a cutting wedges algorithm is similar to the algorithms of the cutting planes type but iteratively modifies coefficients of existing constraints rather than adding new constraints a numerical illustration is presented for the new algorithm a combination of the cutting wedges and the general purpose dinkelbach strategies leads to an enhanced bisection algorithm which improves either the upper or lower bound at all iterations

the nodal line of the second eigenfunction of the robin laplacian in r2 can be closed abstract we construct a multiply connected domain in r 2 for which the second eigenfunction of the laplacian with robin boundary conditions has an interior nodal line in the process we adapt a bound of donnelly fefferman type to obtain a uniform estimate on the size of the nodal sets of a sequence of solutions to a certain class of elliptic equations in the interior of a sequence of domains which does not depend directly on any boundary behaviour this also gives a new proof of the nodal line property of the example in the dirichlet case

theory of a curved planar waveguide with robin boundary conditions a model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative robin boundary condition is analyzed theoretically within the framework of the linear schrodinger equation and is applied to the study of the processes in the bent magnetic multilayers superconducting films and metallic ferrite filled waveguides in particular subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the robin parameter 1 lambda with lambda being an extrapolation length entering robin boundary condition for the arbitrary robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest mode energy of the continuously curved duct is always smaller than its straight counterpart accordingly the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend in terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart localized level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius conditions of the bound state existence for the different robin parameters on the opposite edges are analyzed too in particular it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one in the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode for example for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths lambda at the opposite interfaces various transport properties of the film such as interference blockade of the current flow at some special energies is also discussed with the special attention being paid to the transformation from the dirichlet to the neumann case as the extrapolation length lambda sweeps the positive axis

domain perturbation for elliptic equations subject to robin boundary conditions abstract we prove domain perturbation theorems for linear and nonlinear elliptic equations under robin boundary conditions the theory allows very singular perturbation of domains in particular it includes cutting holes parts degenerating to a set of measure zero such as the dumbbell problem or wildly oscillating boundaries in the last case we show that the limiting problem is the dirichlet problem

strong localized perturbations of eigenvalue problems this paper considers the effect of three types of perturbations of large magnitude but small extent on a class of linear eigenvalue problems for elliptic partial differential equations in bounded o

maximally productive input output units abstract technical or pareto koopmans efficiency models can be based on ratios of weighted sums of outputs to weighted sums of inputs differing meanings have been considered for such factor weights in this paper we use value or cost rate meanings depending on model orientation these meanings permit considering the simultaneous assignment of input and output factor weights along with optimal intensity values for a virtual composite unit constructed from the observed units an optimization principle we call the winners take all criterion is proposed for determining the maximally productive unit s no assumptions are required on the internal transformation processes of the units the model simultaneously determines the intensities and factor weights and results in indefinite quadratic programming problems that simplify to linear programming in certain cases for the general case genetic search is applied numerical illustrations are provided for faculty merit scoring and for the 15 hospital dataset of sherman

a maximum decisional efficiency estimation principle this paper proposes a systematic approach to certain parameter estimation problems relevant to applied optimization models a context specific measure of decision maker performance called decisional efficiency is defined as a function of the unknown parameter vector the values of this measure are considered to be distributed according to a performance density then a principle of maximum decisional efficiency mde is proposed and its relationship to the maximum likelihood principle of statistics is discussed the principle is first illustrated on a problem of group ideal point estimation next estimation of the ratio of ordering and holding costs in inventories managed by the eoq model is considered the results in both these examples are intuitively appealing suggesting face validity of the principle a more detailed illustration is developed for the problem of deriving a consensus scoring model for credit applicants which combines the data of more than one loan officer

summing logarithmic expansions for singularly perturbed eigenvalue problems strong localized perturbations of linear and nonlinear eigenvalue problems in a bounded two dimensional domain d are considered the effects on an eigenvalue lambda 0 of the lapla cian and on the fold point lambda c0 of a nonlinear eigenvalue problem of removing a small subdomain d epsilon of radius epsilon from d and imposing a condition on the boundary of the resulting hole are determined using the method of matched asymptotic expansions it is shown that the expansions of the eigenvalues and fold points for these perturbed problems start with infinite series in powers of 1 log epsilon d kappa here d kappa is a constant that depends on the shape of d epsilon and on the precise form of the boundary condition on the hole in each case it is shown that the entire infinite series is contained in the solution of a single related problem that does not involve the size or shape of the hole this related problem is not stiff and can be solved numerically

local existence of solutions of self gravitating relativistic perfect fluids this paper deals with the evolution of the einstein gravitational fields which are coupled to a perfect fluid we consider the einstein euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity and that the pressure is a fractional power of the energy density in this setting we prove local in time existence uniqueness and well posedness of classical solutions the zero order term of our system contains an expression which might not be a c function and therefore causes an additional technical difficulty in order to achieve our goals we use a certain type of weighted sobolev space of fractional order in brauer and karp j diff eqs 251 1428 1446 2011 we constructed an initial data set for these of systems in the same type of weighted sobolev spaces

singularity of eigenfunctions at the junction of shrinking tubes part ii abstract consider two domains connected by a thin tube it can be shown that generically the mass of a given eigenfunction of the dirichlet laplacian concentrates in only one of them the restriction to the other domain when suitably normalized develops a singularity at the junction of the tube as the channel section tends to zero our main result states that under a nondegeneracy condition the normalized limiting profile has a singularity of order n 1 where n is the space dimension we give a precise description of the asymptotic behavior of eigenfunctions at the singular junction which provides us with some important information about its sign near the tunnel entrance more precisely the solution is shown to be one sign in a neighborhood of the singular junction in other words we prove that the nodal set does not enter inside the channel

well posedness of the einstein euler system in asymptotically flat spacetimes the constraint equations this paper deals with the construction of initial data for the coupled einstein euler system we consider the condition where the energy density might vanish or tend to zero at infinity and where the pressure is a fractional power of the energy density in order to achieve our goals we use a type of weighted sobolev space of fractional order par the common lichnerowicz york scaling method choquet bruhat and york 1980 9 cantor 1979 7 for solving the constraint equations cannot be applied here directly the basic problem is that the matter sources are scaled conformally and the fluid variables have to be recovered from the conformally transformed matter sources this problem has been addressed although in a different context by dain and nagy 2002 11 we show that if the matter variables are restricted to a certain region then the einstein constraint equations have a unique solution in the weighted sobolev spaces of fractional order the regularity depends upon the fractional power of the equation of state

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

genetic search over probability spaces abstract this paper proposes two new crossover operators for searching over discrete probability spaces the design of the operators is considered in the light of recent theoretical insights into genetic search provided by forma analysis a non trivial test problem in enforcing coherency of probability estimates in cross impact analysis highlights the utility of the designed operators the presented operators will be useful for a variety of probability fitting and optimization applications

on the indices of fixed points of mappings in cones and applications abstract assume that k is a cone in a banach space and a k k is completely continuous we obtain a formula for the index in k of a fixed point of a under the assumption that a linearization exists and satisfies an invertibility condition we then use this formula to generalize some results of amann on the number of fixed points of a to the case where k has empty interior

the singularly perturbed domain and the characterization for the eigenfunctions with neumann boundary condition on considere un domaine mobile 0 parametre qui degenere partiellement quand 0 et on donne une caracterisation elaboree des comportements des fonctions propres du laplacien avec la condition limite de neumann

robin boundary value problems on arbitrary domains we develop a theory of generalised solutions for elliptic boundary value problems subject to robin boundary conditions on arbitrary domains which resembles in many ways that of the dirichlet problem in particular we establish lp lq estimates which turn out to be the best possible in that framework we also discuss consequences to the spectrum of robin boundary value problems finally we apply the theory to parabolic equations

causal geometry of einstein vacuum spacetimes with finite curvature flux one of the central difficulties of settling the l2 bounded curvature conjecture for the einstein vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity in this paper we show how to circumvent this difficulty by showing that the geometry of null hypersurfaces of enstein vacuum spacetimes can be controlled in terms of initial data and the total curvature flux through the hypersurface

boundary harmonic coordinates on manifolds with boundary in low regularity in this paper we prove the existence of h 2 regular coordinates on riemannian 3 manifolds with boundary assuming only l 2 bounds on the ricci curvature l 4 bounds on the second fundamental form of the boundary and a positive lower bound on the volume radius the proof follows by extending the theory of cheeger gromov convergence to include manifolds with boundary in the above low regularity setting the main tools are boundary harmonic coordinates together with elliptic estimates and a geometric trace estimate and a rigidity argument using manifold doubling assuming higher regularity of the ricci curvature we also prove corresponding higher regularity estimates for the coordinates

nonlocal robin laplacians and some remarks on a paper by filonov on eigenvalue inequalities abstract the aim of this paper is twofold first we characterize an essentially optimal class of boundary operators which give rise to self adjoint laplacians in l 2 d n x with nonlocal and local robin type boundary conditions on bounded lipschitz domains r n n n n 2 second we extend friedlander s inequalities between neumann and dirichlet laplacian eigenvalues to those between nonlocal robin and dirichlet laplacian eigenvalues associated with bounded lipschitz domains following an approach introduced by filonov for this type of problems

the boost problem in general relativity we show that any asymptotically flat initial data for the einstein field equations have a development which includes complete spacelike surfaces boosted relative to the initial surface furthermore the asymptotic fall off is preserved along these boosted surfaces and there exists a global system of harmonic coordinates on such a development we also extend former results on global solutions of the constraint equations by virtue of this extension the constraint and evolution parts of the problem fit together exactly several theorems are given which concern the behaviour in the large of general classes of linear and quasilinear differential systems this paper contains in addition a systematic exposition of the functional spaces employed

perturbation of semi linear evolution equations under weak assumptions at initial time abstract we prove perturbation results for abstract semi linear evolution equations in a banach space the main feature is that only very weak assumptions are needed at initial time this allows to prove weak continuity properties and to deal with rather general domain perturbation problems for semi linear parabolic and hyperbolic boundary value problems with various boundary conditions the theory also implies the well known theory on parameter dependent equations

abstract fractional cauchy problems with almost sectorial operators abstract of concern are the cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part a linear operator a whose resolvent satisfies the estimate of growth 1 0 in a sector of the complex plane which occurs when one considers for instance the partial differential operators in the limit domain of dumb bell with a thin handle or in the space of holder continuous functions by constructing a pair of families of operators in terms of the generalized mittag leffler type functions and the resolvent operators associated with a for the first time and a deep analysis on the properties for these families we obtain the existence and uniqueness of mild solutions and classical solutions to the cauchy problems moreover we present three examples to illustrate the feasibility of our results

a minimum variance of utility approach to ideal point estimation in certain biased groups abstract this paper discusses a problem of group decision making called ideal point estimation this problem is equivalent to all individuals of the group or a representative committee attempting to estimate the maximum point for an unknown group multiattribute value function the paper concentrates on a type of systematic error which is possible in such processes and proposes a method of estimation the minimum variance of utility method which is capable of debiasing such estimates in certain cases a model of group error called the dome error process is shown to provide a concrete instance of this type of systematic bias the method is illustrated numerically and some applications are discussed

improving the consistency of conditional probability assessments for forecasting and decision making public agencies are very keen on amassing statistics they collect them add them raise them to the nth power take the cube root and prepare wonderful diagrams but what you must never forget is that every one of those figures comes in the first instance from the village watchman who just puts down what he damn pleases sir josiah stamp the assessment of the conditional probabilities of events is useful and needed for forecasting planning and decision making in this paper the difficulties associated with the assessment of these conditional probabilities are examined the necessary and sufficient conditions that the elicited information on conditional probabilities must satisfy are evaluated against actual assessments in several different controlled settings a high frequency of implicit violations of the probability calculus was observed the consistency of the assessments is affected by the causal diagnostic and positive negative relationships of the events use of a judgmental aid in the form of a joint probability table reduces the number of inconsistent responses significantly using the probability axioms it is also shown that only the first order conditional probabilities need be assessed as higher order probabilities are robust to the unconditional and first order conditional assessments

behavioral estimation of mathematical programming objective function coefficients we propose a parameter estimation method based on what we call the minimum decisional regret principle we focus on mathematical programming models with objective functions that depend linearly on costs or other parameters the approach is illustrated for cost estimation in production planning using linear programming models the method uses past planning data to estimate costs that are otherwise difficult to estimate we define a monetary measure of distance between observed plans and optimal ones called decisional regret the proposed estimation algorithm finds parameter values for which the associated optimal plans are as near as possible to the observed ones on average such techniques may be called behavioral estimation because they are based on the observed planning or decision making behavior of managers or firms two numerical illustrations are given a supporting hyperplane algorithm is used to solve the estimation model a method is proposed for obtaining range estimates of the parameters when multiple alternative estimates exist we also propose a new validation approach for this estimation principle which we call the target mode agreement criterion

data driven inverse optimization with imperfect information in data driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal thus the observer seeks the agent s objective function that best explains a historical sequence of signals and corresponding optimal actions we formalize this inverse optimization problem as a distributionally robust program minimizing the worst case risk that the estimated decision i e the decision implied by a particular candidate objective differs from the agent s actual response to a random signal we show that our framework offers attractive out of sample performance guarantees for different prediction errors and that the emerging inverse optimization problems can be reformulated as or approximated by tractable convex programs when the prediction error is measured in the space of objective values a main strength of the proposed approach is that it naturally generalizes to situations where the observer has imperfect information e g when the agent s true objective function is not contained in the space of candidate objectives when the agent suffers from bounded rationality or implementation errors or when the observed signal response pairs are corrupted by measurement noise

generalized inverse multiobjective optimization with application to cancer therapy we generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible in multiobjective linear optimization given a solution that is not a weakly efficient solution to the forward problem our method generates objective function weights that make the given solution a near weakly efficient solution our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem we provide a novel interpretation of our inverse formulation as the dual of the well known benson s method and by doing so develop a new connection between inverse optimization and pareto surface approximation techniques we apply our method to prostate cancer data obtained from princess margaret cancer centre in toronto canada we demonstrate that clinically acceptable treatments can be generated using a small number of objective

domain perturbation for linear and nonlinear parabolic equations abstract we shall develop a general theory for domain perturbation for linear and nonlinear parabolic equations with measurable coefficients subject to dirichlet boundary conditions we show how solutions of linear and nonlinear parabolic equations behave as a sequence of domains approaches an open set convergence of domains is understood in a very general sense which allows that certain parts of the domains degenerate and are deleted in the limit or that small sets are removed we also consider the periodic problem and establish existence and uniqueness results for periodic solutions for the perturbed problem in a neighborhood of a periodic solution of the original equation the theory can be used for instance to construct domains where a given nonlinear periodic parabolic equation has many periodic solutions

rough solutions of the einstein constraints on closed manifolds without near cmc conditions we consider the conformal decomposition of einstein s constraint equations introduced by lichnerowicz and york on a closed manifold we establish existence of non cmc weak solutions using a combination of priori estimates for the individual hamiltonian and momentum constraints barrier constructions and fixed point techniques for the hamiltonian constraint riesz schauder theory for the momentum constraint together with a topological fixed point argument for the coupled system although we present general existence results for non cmc weak solutions when the rescaled background metric is in any of the three yamabe classes an important new feature of the results we present for the positive yamabe class is the absence of the near cmc assumption if the freely specifiable part of the data given by the traceless transverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small and if the energy density of matter is not identically zero in this case the mean extrinsic curvature can be taken to be an arbitrary smooth function without restrictions on the size of its spatial derivatives so that it can be arbitrarily far from constant giving what is apparently the first existence results for non cmc solutions without the near cmc assumption using a coupled topological fixed point argument that avoids near cmc conditions we establish existence of coupled non cmc weak solutions with positive conformal factor w s p where p 1 and s p 1 3 p in the cmc case the regularity can be reduced to p 1 and s p 3 p 1 in the case of s 2 we reproduce the cmc existence results of choquet bruhat 10 and in the case p 2 we reproduce the cmc existence results of maxwell 33 but with a proof that goes through the same analysis framework that we use to obtain the non cmc results the non cmc results on closed manifolds here extend the 1996 non cmc result of isenberg and moncrief in three ways 1 the near cmc assumption is removed in the case of the positive yamabe class 2 regularity is extended down to the maximum allowed by the background metric and the matter and 3 the result holds for all three yamabe classes this last extension was also accomplished recently by allen clausen and isenberg although their result is restricted to the near cmc case and to smoother background metrics and data

a note on dea efficiency assessment using ideal point an improvement of wang and luo s model abstract evaluating the efficiency of organizational units continues to be a difficult problem to solve especially when the multiplicity of inputs resources costs and outputs services products associated with these units is considered this paper considers a previous article published by wang and luo y wang y luo dea efficiency assessment using ideal and anti ideal decision making units applied mathematics and computation 173 2 2006 902 915 in the journal of applied mathematics and computation where data envelopment analysis dea and the technique for order preference by similarity to ideal solution topsis are integrated in ranking of decision making units dmus wang and luo 2006 contribute to a very interesting topic by showing that the topsis idea can be combined to dea for a comprehensive ranking of dmus however this paper finds that their approach is problematic in employing the negative ideal point nip for dea computation their ideal point based models rely on using conflicting efficiency concepts we slightly revised the models so that a dea analysis using topsis idea can be performed numerical demonstration reveals that our approach produces a ranking result that is consistent with that in previous studies

the maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems abstract in this work we deal with the problem of the existence and uniqueness of principal eigenvalues for some linear weighted boundary value problems associated to a general second order uniformly elliptic operator for a large class of sign definited weights we characterize whether the boundary value problem admits a principal eigenvalue or not

rough solutions of the einstein vacuum equations this is the first in a series of papers in which we initiate the study of very rough solutions to the initial value problem for the einstein vacuum equations expressed relative to wave coordinates by very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and sobolev inequalities following kl ro we develop new analytic methods based on strichartz type inequalities which result in a gain of half a derivative relative to the classical result our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates the latter allows us to take full advantage of the specific structure of the einstein equations

non cmc solutions of the einstein constraint equations on compact manifolds with apparent horizon boundaries in this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the einstein constraint equations on compact manifolds with boundary by building in a natural way on our recent work in holst and tsogtgerel class quantum gravity 30 205011 2013 and holst et al phys rev lett 100 16 161101 2008 commun math phys 288 2 547 613 2009 and also on the work of maxwell j hyperbolic differ eqs 2 2 521 546 2005a commun math phys 253 3 561 583 2005b math res lett 16 4 627 645 2009 and dain class quantum gravity 21 2 555 573 2004 under reasonable assumptions on the data we prove existence of both near and far from constant mean curvature cmc solutions for a class of robin boundary conditions commonly used in the literature for modeling black holes with a third existence result for cmc appearing as a special case dain and maxwell addressed initial data engineering for space times that evolve to contain black holes determining solutions to the conformal formulation on an asymptotically euclidean manifold in the cmc setting with interior boundary conditions representing excised interior black hole regions holst and tsogtgerel compiled the interior boundary results covered by dain and maxwell and then developed general interior conditions to model the apparent horizon boundary conditions of dainand maxwell for compact manifolds with boundary and subsequently proved existence of solutions to the lichnerowicz equation on compact manifolds with such boundary conditions this paper picks up where holst and tsogtgerel left off addressing the general non cmc case for compact manifolds with boundary as in our previous articles our focus here is again on low regularity data and on the interaction between different types of boundary conditions while our work here serves primarily to extend the solution theory for the compact with boundary case we also develop several technical tools that have potential for use for other cases

sharp local well posedness results for the nonlinear wave equation this article is concerned with local well posedness of the cauchy problem for second order quasilinear hyperbolic equations with rough initial data the new results obtained here are sharp in low dimension

linear programming system identification we define a version of the inverse linear programming problem that we call linear programming system identification this version of the problem seeks to identify both the objective function coefficient vector and the constraint matrix of a linear programming problem that best fits a set of observed vector pairs one vector is that of actual decisions that we call outputs these are regarded as approximations of optimal decision vectors the other vector consists of the inputs or resources actually used to produce the corresponding outputs we propose an algorithm for approximating the maximum likelihood solution the major limitation of the method is the computation of exact volumes of convex polytopes a numerical illustration is given for simulated data

positive radial symmetric solutions to an exterior elliptic robin boundary value problem and application abstract we study the existence uniqueness and behavior of positive radial symmetric solutions of the exterior boundary value problem u h x f u in r n b 0 r 0 u n a u on and u x 0 as x when a 0 the robin boundary condition has a wrong sign and this makes the analysis of the problem interesting and non trivial we determine a sharp condition on the coefficient a for the existence of positive spherically symmetric solutions of the boundary value problem the important model case f u u 1 7 a 1 2 r 0 and 1 2 r 0 is related to the initial data problem in general relativity for this model case as an example of application of our results we obtain the existence and uniqueness of the conformal factor corresponding to the hamiltonian constraint equation in the case of a single black hole in the radial symmetric regime