variable neighborhood tabu search and its application to the median cycle problem abstract the variable neighborhood tabu search consists of a constructive phase and a series of local searches that use tabu tools when the local search stops at a nontabu local minimum a shake procedure starts a new local search the local searches and the shake procedure are based on a series of standard moves the local search consists of applying the best possible move until no such move exists the shake procedure consists of applying a number of random moves since the shake could provide an infeasible solution the local search considers as possible moves those providing a feasible solution or reducing the infeasibility a location allocation problem consists of selecting the location for some facilities and the allocation of the users to them two functions to be minimized are considered the length of the solution as a measure of the set of locations and the total cost of the allocations the standard moves for these problems are the add drop and add drop moves the heuristic procedure is tested on the median cycle problem

volume averaging for determining the effective dispersion tensor closure using periodic unit cells and comparison with ensemble averaging in this work we use the method of volume averaging to determine the effective dispersion tensor for a heterogeneous porous medium closure for the averaged equation is obtained by solution of a concentration deviation equation over a periodic unit cell our purpose is to show how the method of volume averaging with closure can be rectified with the results obtained by other upscaling methods under particular conditions although this rectification is something that is generally believed to be true there has been very little research that explores this issue explicitly we show that under certain limiting but mild assumptions the closure problem provides a fourier series solution for the effective dispersion tensor when second order spatial stationarity is imposed on the velocity field the method yields a simple fourier series that converges to an integral form in the limit as the period of the unit cell approaches infinity this limiting result is identical to the quasi fickian forms that have been developed previously via ensemble averaging by deng et al 1993 and recently by fiori and dagan 2000 except in the definition of the averaging operation as a second objective we have conducted a numerical study to evaluate the influence of the size of the averaging volume on the effective dispersion tensor and its volume averaged statistics this second objective is complimentary in many ways to recent research reported by rubin et al 1999 via ensemble averaging and by wang and kitanidis 1999 via volume averaging on the block averaged effective dispersion tensor the variability of the effective dispersion tensor from realization to realization is assessed by computing the volume averaged effective dispersion tensor for an ensemble of finite fields with the same ensemble statistics ensembles were generated using three different sizes of unit cells all three unit cell sizes yield similar results for the value of the mean effective dispersion tensor however the coefficient of variation depends strongly upon the size of the unit cell and our results are consistent with those developed by fiori 1998 from the ensemble averaging perspective this implies that in applications the actual value of the effective dispersion tensor may be significantly different than expected on the basis of unconditioned hydraulic conductivity statistics and this variation should be considered when applying macrodispersion to real world systems

spherical characters on p adic symmetric spaces symmetric spaces over local fields and the harmonic analysis of their class one representations arise as the local calculation of jacquet s theory of the relative trace formula there is an extensive literature at the real place but few general results for p adic fields are known the objective here is to carry over to symmetric spaces as much as possible of queens and the prerequisite results of howe and to provide counterexamples for those things which do not generalize we derive the weyl integration formula local constancy of the spherical character on the regular set howe s conjecture for groups the germ expansion for spherical characters at the origin and a spherical version of howe s kirillov theory for compact p adic groups we find that the density property of regular orbital integrals fails some of the basic ideas are nascent in hakim s thesis written under herve jacquet

the median tour and maximal covering tour problems formulations and heuristics abstract in this paper the authors introduce two bicriterion routing problems the median tour problem mtp and the maximal covering tour problem mctp in both problems the tour must visit only p of the n nodes on the network in addition both problems have as one of their objectives the minimization of total tour length the second objective in both problems maximizes access to the tour for the nodes not directly on it in the mtp the access objective is the minimization of the total travel distance necessary for demand at the nodes to reach their nearest stop on the tour in the mctp the access objective is to maximize the total demand within some prespecified maximal travel distance from a tour stop it is shown that the mctp may be viewed as a special case of the mtp consequently solution procedures developed for the mtp may also be employed to solve the mctp unfortunately both problems are np hard in addition the number of efficient solutions may grow exponentially with the number of nodes in the particular problem instance consequently a heuristic procedure is developed to generate a good approximation of the efficient frontier not only does this approximation provide the decision marker with insight into the magnitudes of the inherent tradeoffs between the two objectives but it also provides him or her with a set of feasible options to consider computational experience on a realistically scaled problem is provided applications of the problems include the design of mobile service delivery systems e g healthcare delivery in rural areas of developing countries bi modal transportation systems e g overnight mail delivery and distributed computer networks among others

orbits and invariants associated with a pair of commuting involutions let be commuting involutions of the connected reductive algebraic group g where and g are defined over a usually algebraically closed field k char k 2 we have fixed point groups h g and k g and an action h k g g where h k g hgk 1 h h k k g g let g h k denote spec o g h k the categorical quotient let a be maximal among subtori s of g such that s s s 1 for all s s there is the associated weyl group w wh k a we show the inclusion a g induces an isomorphism a w g h k in particular the closed h k orbits are precisely those which intersect a the fibers of g g h k are the same as those occurring in certain associated symmetric varieties in particular the fibers consist of finitely many orbits we investigate the structure of w and its relation to other naturally occurring weyl groups and to the action of on the a weight spaces of the relation of the orbit type stratifications of a w and g h k along the way we simplify some of richardson s proofs for the symmetric case and at the end we quickly recover results of berger flensted jensen hoogenboom and matsuki ber57 fj78 hoo84 mat97 for the case k

on the classification of k involutions let g be a connected reductive algebraic group defined over a field k of characteristic not 2 an involution of g defined over k h a k open subgroup of the fixed point group of and gk resp hk the set of k rational points of g resp h the variety gk hk is called a symmetric k variety these varieties occur in many problems in representation theory geometry and singularity theory over the last few decades the representation theory of these varieties has been extensively studied for k r and c as most of the work in these two cases was completed the study of the representation theory over other fields like local fields and finite fields began the representations of a homogeneous space usually depend heavily on the fine structure of the homogeneous space like the restricted root systems with weyl groups etc thus it is essential to study first this structure and the related geometry in this paper we give a characterization of the isomorphy classes of these symmetric k varieties together with their fine structure of restricted root systems and also a classification of this fine structure for the real numbers p adic numbers finite fields and number fields

threshold accepting a general purpose optimization algorithm appearing superior to simulated annealing abstract a new general purpose algorithm for the solution of combinatorial optimization problems is presented the new threshold accepting method is even simpler structured than the wellknown simulated annealing approach the power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error correcting codes moreover deterministic versions of the new heuristic turn out to perform nearly equally well consuming only a fraction of the computing time of the stochastic versions as an example the deterministic threshold accepting method yields very near to optimum tours for the famous 442 cities traveling salesman problem of grotschel within 1 to 2 s of cpu time

aquifer operator scaling and the effect on solute mixing and dispersion 1 since aquifer parameters may have statistical dependence structures that are present across a huge range of scales the concepts of fractional brownian motion fbm have been used in both analytic and numerical stochastic settings most previous models have used isotropic scaling characterized by a single scalar hurst coefficient any real world anisotropy has been handled by an elliptical stretching random k field we define a d dimensional extension of fbm in which the fractional order integration may take on different orders in the d primary possibly nonorthogonal scaling directions and the degree of connectivity and long range dependence is freely assigned via a probability measure on the unit sphere this approach accounts for the different scaling found in the vertical versus horizontal directions in sedimentary aquifers and allows very general degrees of continuity of k in certain directions it also allows for the representation of fracture networks in a continuum setting the eigenvectors of the scaling matrix describe the primary fracture scaling directions and discrete weights of fractional integration represent fracture continuity that may be limited to a small number of directions in a numerical experiment the motion of solutes through 2 d operator fractional gaussian fields depends very much on transverse hurst coefficients transverse scaling in the range of fractional gaussian noise engenders greater plume mixing and a transition to a fickian regime higher orders of integration in the range of fractional brownian motion are associated with thicker layering of aquifer sediments and more preferential unmixed transport therefore direct representation of the unique directional scaling properties of an aquifer is important for realistic simulation of transport

geometric realization of discrete series for semisimple symmetric spaces let g be a connected semisimple lie group a an involution of g and h the connected component of the fixed point set of a containing the identity then g h is a semisimple symmetric space we assume g is a real form of a complex lie group and rank g h rank k k c h where k is a a stable maximal compact subgroup of g flensted jensen using his duality principle and poisson transform constructed countably many discrete series in u g h f j i then using deep results of hyperfunction theory and microlocal analysis oshima and matsuki gave a detailed characterization of these discrete series including a proof of flensted jensen s conjecture c 0 om based on these results we give the discrete series a geometric interpretation in locally symmetric spaces f c where g k and f cg is a cocompact discrete group such that f c h c h is cocompact our geometric interpretation is the following first of all to a flensted jensen function which is the generating function of a discrete series v we associate a harmonic form cb z on g with values in a finite dimensional g module v right g translates of coefficients of 5z realizes the contragredient t of r and tba is left invariant under h and under right k action it transforms according to the minimal k type with highest weight of 3 is the pull back of a v valued from coz on and v determines a locally constant bundle e on f so that if convergence holds

numerical simulations of preasymptotic transport in heterogeneous porous media departures from the gaussian limit 1 the objective of this work is to determine whether conventional solute macrodispersion theories adequately predict the behavior of individual subsurface plumes over time and length scales relevant to practical risk assessment and remediation activities this issue is studied with a set of high resolution numerical simulations of conservative tracers moving through saturated two dimensional heterogeneous conductivity fields the simulation experiments are designed to mimic long term field studies spatially correlated statistically stationary lognormal conductivity realizations are generated with a fourier transform procedure steady state velocity solutions are calculated for these fields using an accurate darcian solver velocity contour plots reveal the presence of disconnected networks of preferential pathways over a range of correlation lengths reverse flow cells are rare the velocity probability density functions have exponential tails and strong longitudinal asymmetries solute concentrations are derived from the simulated velocity fields with an accurate taut spline transport code that minimizes numerical dispersion the resulting plumes are tracked for travel distances of over one hundred spatial correlation lengths corresponding to scales of practical interest first moments and macrodispersivities which measure the location and extent of the plume are reasonably well approximated by conventional fickian theories but continue to vary after long travel distances this temporal variability highlights the slow convergence of the plume moments to gaussian limits calculations of the relative dilution index which is a measure of the plume mixing state indicate strongly non gaussian behavior other measures of plume structure suggested by anomalous dispersion theories also reveal the persistence of non gaussian behavior after long travel distances these measures appear to be more sensitive to non gaussian behavior than the spatial moments taken together the simulation results suggest that conservative solute plumes moving through statistically stationary random media may not converge to gaussian limits even after traveling hundreds of log conductivity correlation scales

vecteurs distributions h invariants pour les series principales generalisees d espaces symetriques reductifs et prolongement meromorphe d integrales d eisenstein

algorithms for central median paths with bounded length on trees abstract the location of path shaped facilities on trees has been receiving a growing attention in the specialized literature in the recent years examples of such facilities include railroad lines highways and public transit lines most of the papers deal with the problem of locating a path on a tree by minimizing either the maximum distance from the vertices of the tree to the facility or of minimizing the sum of the distances from all the vertices of the tree to the path however neither of the two above criteria alone capture all essential elements of a location problem the sum of the distances criterion alone may result in solutions which are unacceptable from the point of view of the service level for the clients who are located far away from the facilities on the other hand the criterion of the minimization of the maximum distance if used alone may lead to very costly service systems in the literature there is just one paper that considers the problem of finding an optimal location of a path on a tree using combinations of the two above criteria and efficient algorithms are provided in particular the cases where one criterion is optimized subject to a restriction on the value of the other are considered and linear time algorithms are presented however these problems do not consider any bound on the length or cost of the facility in this paper we consider the two following problems find a path which minimizes the sum of the distances such that the maximum distance from the vertices of the tree to the path is bounded by a fixed constant and such that the length of the path is not greater than a fixed value find a path which minimizes the maximum distance with the sum of the distances being not greater than a fixed value and with bounded length from an application point of view the constraint on the length of the path may refer to a budget constraint for establishing the facility the restriction on the length of the path complicates the two problems but for both of them we give o n log 2 n divide and conquer algorithms

on involutions of type o q k over a field of characteristic two abstract in this article we study the involutions of o v q an orthogonal group for a vector space v with quadratic form q over a field of characteristic two the classification proceeds by discussing conjugacy classes of involutions arising as a product of transvections involutions with respect to a hyperbolic space and involutions acting nontrivially in the radical of v we achieve a complete classification of the conjugacy classes of involutions when the quadratic space v q is non defective and conclude with a discussion of the defective case

comparing different metaheuristic approaches for the median path problem with bounded length abstract in this paper we consider the bounded length median path problem which can be defined as the problem of locating a path shaped facility that departures from a given origin and arrives at a given destination in a network the length of the path is assumed to be bounded by a given maximum length at each vertex of the network customer point the demand for the service is given and the cost to reach the closest service point is computed the objective is to minimize the sum of these costs over all the customer points in the network we consider two local search metaheuristics the well known tabu search and the old bachelor acceptance and we propose a comparative analysis of the performances of the two procedures we implement streamlined versions of tabu search and old bachelor acceptance our main concern is to provide knowledge about the intrinsic strategy adopted by each metaheuristic and to know whether one is more appropriate than the other for our problem

a multi modal approach to the location of a rapid transit line abstract the location of a rapid transit line rtl represents a very complex decision problem because of the large number of decision makers unquantifiable criteria and uncertain data in this context operational research can help in the design process by providing tools to generate and assess alternative solutions for this purpose two bicriterion mathematical programming models the maximum coverage shortest path model and the median shortest path model have been developed in the past in this paper a new bicriterion model which can evaluate in a more realistic way the attractivity of an rtl is introduced to calculate an estimation of the non inferior solution set of the problem a procedure based on a k shortest path algorithm was developed this approach was applied to a well known sample problem and the results are discussed and compared with those obtained using a median shortest path model

algebraic groups with a commuting pair of involutions and semisimple symmetric spaces let g be a connected reductive algebraic group defined over an algebraically closed field f of characteristic not 2 denote the lie algebra of g by 9 in this paper we shall classify the isomorphism classes of ordered pairs of commuting involutorial automorphisms of g this is shown to be independent of the characteristic of f and can be applied to describe all semisimple locally symmetric spaces together with their line structure involutorial automorphisms of g occur in several places in the literature cartan has already shown that for f c the isomorphism classes of involutorial automorphisms of g correspond bijectively to the isomorphism classes of real semisimple lie algebras which correspond in their turn to the isomorphism classes of riemannian symmetric spaces see helgason 111 if one lifts this involution to the group g then the present work gives a characteristic free description of these isomorphism classes in a similar manner we can show that semisimple locally symmetric spaces correspond to pairs of commuting involutorial automorphisms of g namely let go a be a semisimple locally symmetric pair i e go is a real semisimple lie algebra and rr e aut g an involution then by a result of berger 2 there exists a cartan involution 8 of go such that 00 ea if we denote the complexilication of go by g then o and 8 induce a pair of commuting involutions of g conversely if c 8 e aut g are commuting involutions then c and 8 determine two locally semisimple symmetric pairs for if u is a o and o stable compact real form with conjugation r then ger 1 ge and g f3 i ger are semisimple locally symmetric pairs where

meromorphic basis of h invariant distribution vectors for the generalized principal series of reductive symmetrical spaces functional equation abstract let g be the group of real points of a reductive algebraic group defined over r an involution of g and a cartan involution of g commuting with let h be an open subgroup of the group of fixed points for one builds a meromorphic basis for the space of h fixed distributions vectors of induced representations from a stable parabolic subgroup p of g for this we use a method which extends the domain of application of bruhat s thesis in particular to the irreducibility problem for generalized principal series the meromorphy is obtained by means of a functional equation that we establish and which generalizes the equation obtained by e van den ban in the case when p is minimal stable

tori invariant under an involutorial automorphism i abstract the geometry of the orbits of a minimal parabolick subgroup acting on a symmetrick variety is essential in several areas but its main importance is in the study of the representations associated with these symmetrick varieties see for example 5 6 20 and 31 up to an action of the restricted weyl group ofg these orbits can be characterized by thehk conjugacy classes of maximalk split tori which are stable underk involution associated with the symmetrick variety herehis a openk subgroup of the fixed point group of this is the second in a series of papers in which we characterize and classify thehk conjugacy classes of maximalk split tori the first paper in this series dealt with the case of algebraically closed fields in this paper we lay the foundation for a characterization and classification for the case of nonalgebraically closed fields this includes a partial classification in the cases where the base field is the real numbers p adic numbers finite fields and number fields

flow through porous media with multifractal hydraulic conductivity 1 we make a nonlinear analysis of flow through saturated porous media when the hydraulic conductivity k is an isotropic lognormal field with multifractal scale invariance in this case logk is isotropic gaussian with spectral density where d is the space dimension our main result is that the hydraulic gradient h and specific flow q are also multifractal fields whose renormalization under space contraction involves random rotation of the field and random scaling of its amplitude the scaling properties and marginal distributions of h and q are obtained analytically as functions of the space dimension d and a multifractal parameter of k the codimension ck the fields h and q are anisotropic at large scales but approach isotropy at very small scales using scaling arguments we obtain the effective conductivity of the medium keff as an explicit function of d ck and the scaling range of k

two paths location of a tree with positive or negative weights this paper studies two problems of locating two paths in a tree with positive and negative weights the first problem has objective to minimize the sum of minimum weighted distances from every vertex of the tree to the two paths while the second is to minimize the sum of the weighted minimum distances from every vertex of the tree to the two paths we develop an o n 2 algorithm based on the optimal properties for the first problem and also an o n 3 algorithm for the second problem this paper studies two problems of locating two paths in weighted trees we provide an algorithm in time o n 2 by the optimal properties for the one problem we provide an algorithm in time o n 3 for the other problem

orbits invariants and representations associated to involutions of reductive groups by an involution of an algebraic group or lie algebra we mean an automorphism 0 such that 0 2 is the identity automorphism let 0 be an involution of a complex reductive lie algebra q and let p denote the 1 eigenspace of 0 on q get g be the adjoint group of q and let k g glog go kostant and rallis 10 have made a detailed study of the action of k on p in particular they obtain very precise information concerning the orbits of k on p and the representation of k on c p the algebra of polynomial functions on p in this paper we consider a global analogue of the problem studied by kostant and rallis let g be a reductive affine algebraic group over an algebraically closed field k of characteristic 2 let 0 be an involution of g and let k gegi0 g g if g is semisimple and the base field is c then g k is the complexification of a riemannian symmetric space we study the action of k and of groups closely related to k by left translation on the coset space g k for technical reasons it is convenient to study a slightly different but equivalent problem let r g g be defined by r g g0 g i then z g p is a closed subvariety of g furthermore z is constant on left cosets of g modulo k and induces an isomorphism o g k p we have o k g k k o g k for k e k and geg thus p is stable under conjugation by k and a is a k isomorphism of affine k varieties we consider the action of k on p by conjugation let x e g have jordan decomposition x x x then we show that x e p if and only if both x and x are in p thus we have a jordan decomposition for elements of p this will play a key role in our results a torus s of g is o anisotropic if o s s 1 for every ses it is known that any two maximal 0 anisotropic tori of g are k let a be a maximal 0 anisotropic torus of g the following result characterizes semisimple elements of p