injectivity of compressing maps on primitive sequences over bbz p e let zopf pe be the integer residue ring with odd prime p and integer eges2 for a sequence a over zopf pe one has a unique p adic expansion a a 0 a 1 p a e 1 pe 1 where a i can be regarded as a sequence over zopf p for 0lesilese 1 let f x be a strongly primitive polynomial over zopf pe and g f x pe be the set of all primitive sequences generated f x by over zopf pe recently the authors xuan yong zhu and wen feng qi have proved that for a function phi x0 xe 1 g xe 1 eta x0 xe 2 over zopf p and a b ising f x pe where 2lesdeg glesp 1 phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b to further complete their work we show that such injectivity also holds for deg g 1 that is for a function phi x0 xe 1 xe 1 eta x0 xe 2 over zopf p and a b ising f x pe phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b

the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

distribution properties of compressing sequences derived from primitive sequences over bbz p e let z pe be the integer residue ring with odd prime p and integer e 2 any sequence a over z pe has a unique p adic expansion a a0 a1 p ae 1 pe 1 where ai can be regarded as a sequence over z p for 0 i e 1 let f x be a strongly primitive polynomial over z pe and a b be two primitive sequences generated by f x over z pe assume x0 xe 1 xe 1 x0 xe 2 is an e variable function over z p with the monomial p 1 2 xe 2 p 1 x1 p 1 not pearing in the expression of x0 x1 xe 2 it is shown that if there exists an s z p such that a0 t ae 1 t s if and only if b0 t be 1 t s for all nonnegative t with i 0 where is an m sequence determined by f x and a0 then a b this implies that for compressing sequences derived from primitive sequences generated by f x over z pe single element distribution is unique on all positions t with t 0 in particular when x0 x1 xe 2 0 it is a completion of the former result on the uniqueness of distribution of element 0 in highest level sequences

algorithms for a multi level network optimization problem in this paper we work on a multi level network optimization problem that integrates into the same model important aspects of i discrete facility location ii topological network design and iii network dimensioning potential applications for the model are discussed stressing its growing importance the multi level network optimization problem treated is defined and a mathematical programming formulation is presented we make use of a branch and bound algorithm based on lagrangean relaxation lower bounds to introduce some new powerful auxiliary algorithms to exactly solve the problem we conduct a set of computational experiments that indicate the quality of the proposed approach

k stability and parabolic stability parabolic structures with rational weights encode certain iterated blowups of geometrically ruled surfaces in this paper we show that the three notions of parabolic polystability k polystability and existence of constant scalar curvature kahler metrics on the iterated blowup are equivalent for certain polarizations close to the boundary of the kahler cone

generating alternative mixed integer programming models using variable redefinition dropping the complicating constraints in a mixed integer linear program often yields a special structure subproblem that can be reformulated using a different set of decision variables once the new variables have been identified the entire problem can be reformulated in terms of the new variables we develop a theory of variable redefinition based on relating the two sets of decision variables by a linear transformation and describe methods for reformulating the special structure problem the reformulated models have a more accurate linear relaxation than the problems from which they were derived an important property within the context of linear programming based branch and bound modeling approaches

probabilistic properties of the dual structure of the multidimensional knapsack problem and fast statistically efficient algorithms properties of several dual characteristics of the multidimensional knapsack problem such as the probability of existence of optimal and optimal feasible lagrange function generalized saddle points magnitude of relative duality gap etc are investigated for different probabilistic models sufficient conditions of good asymptotic behavior of the dual characteristics are given a fast statistically efficient approximate algorithm with linear running time complexity for problems with random coefficients is presented

a constrained nonlinear 0 1 program for data allocation abstract this paper analyzes the problem of allocating copies of relations from a global database to the sites of a geographically distributed communication network the objective of the allocation is to minimize the total cost due to transmissions generated by queries from the various sites including queries that access multiple relations this allocation problem is modeled as a constrained nonlinear 0 1 subproblems generated during subgradient optimization are solved as optimization some of the unconstrained quadratic 0 1 subproblems generated during subgradient optimization are solved as maximum flow problems while the others require implicit enumeration depending on the nature of the objective function coefficients of the subproblems our solution approach is tested extensively on data allocation problems with as many as 100 sites and 20 relations on a set of randomly generated test problems our approach was close to two orders of magnitude faster than the general purpose integer programming code osl

toric self dual einstein metrics on compact orbifolds we prove that any compact self dual einstein 4 orbifold of positive scalar curvature whose isometry group contains a 2 torus is up to an orbifold covering a quaternion kahler quotient of k 1 dimensional quaternionic projective space by a k 2 torus for some k geq 2 we also obtain a topological classification in terms of the intersection form of the 4 orbifold

a lagrangean relaxation approach for very large scale capacitated lot sizing in this paper we develop a lagrangean relaxation based heuristic procedure to generate near optimal solutions to very large scale capacitated lot sizing problems clsp with setup times and limited overtime our computational results show that large problems involving several thousand products and several thousand 0 1 integer variables can be solved in a reasonable amount of computer time to within one percent of their optimal solution the proposed procedure is general enough to be applied directly or with slight modification to real life production problems

capacitated multi item lot sizing problems with time windows this research concerns a new family of capacitated multi item lot sizing problems namely lot sizing problems with time windows two classes of the problem are analyzed and solved using different lagrangian heuristics capacity constraints and a subset of time window constraints are relaxed resulting in particular single item time window problems that are solved in polynomial time other relaxations leading to the classical wagner whitin problem are also tested several smoothing heuristics are implemented and tested and their results are compared the gaps between lower and upper bounds for most problems are very small less than 1 moreover the proposed algorithms are robust and do not seem to be too affected when different parameters of the problem are varied

toric self dual einstein metrics as quotients we use the quaternion kahler reduction technique to study old and new self dual einstein metrics of negative scalar curvature with at least a two dimensional isometry group and relate the quotient construction to the hyperbolic eigenfunction ansatz we focus in particular on the semi quaternion kahler quotients of semi quaternion kahler hyperboloids analysing the completeness and topology and relating them to the self dual einstein hermitian metrics of apostolov gauduchon and bryant

heuristics for multilevel lot sizing with a bottleneck in this paper we present a heuristic method based on lagrangian relaxation for multilevel lot sizing when there is a single bottleneck facility a series of lagrangian relaxations one for each item in the product structure is imbedded in a branch and bound procedure the objective is to find a production schedule that fits within available capacity at minimum cost the method has two solution phases dual and primal in the dual phase of the procedure implied costs of setups and production are determined based on a tentative schedule the primal phase is repeated with these new prices and we iterate to reach a good solution the solution procedure is first tested on two special cases uncapacitated multilevel lot sizing and the capacitated single level multi item lot sizing problem the results show that the solution procedure can provide better solutions than some heuristics designed especially for those problems test results on the bottleneck problem indicate that good feasible solutions are found for problems too difficult to solve with exact methods

hyper kahler metrics and a generalization of the bogomolny equations we generalize the bogomolny equations to field equations on 3 n and describe a twistor correspondence we consider a general hyper kahler metric in dimension 4n with an action of the torustn compatible with the hyper kahler structure we prove that such a metric can be described in terms of thetn solution of the field equations coming from the twistor space of the metric

bach flat asymptotically locally euclidean metrics we obtain a volume growth and curvature decay result for various classes of complete noncompact riemannian metrics in dimension 4 in particular our method applies to anti self dual or kahler metrics with zero scalar curvature and metrics with harmonic curvature similar results were obtained for einstein metrics in and89 bkn89 tia90 but our analysis differs from the einstein case in that 1 we consider more generally a fourth order system in the metric and 2 we do not assume any pointwise ricci curvature bound

a branch and bound algorithm for the total weighted tardiness problem this paper presents a new branch and bound algorithm for the single machine total weighted tardiness problem it obtains lower bounds using a lagrangian relaxation approach with subproblems that are total weighted completion time problems the well known subgradient optimization technique is replaced by a multiplier adjustment method that leads to an extremely fast bound calculation the method incorporates various devices for checking dynamic programming dominance in the search tree extensive computational results for problems with up to 50 jobs show the superiority of the algorithm over existing methods

compression mappings on primitive sequences over z p sup e let z p sup e be the integer residue ring with odd prime p spl ges 5 and integer e spl ges 2 for a sequence a over z p sup e there is a unique p adic expansion a a sub 0 a spl middot p a sub e 1 spl middot p sup e 1 where each a sub i is a sequence over 0 1 p 1 and can be regarded as a sequence over the finite field gf p naturally let f x be a primitive polynomial over z p sup e and g f x p sup e the set of all primitive sequences generated by f x over z p sup e set spl phi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 1 x sub 0 x sub 1 x sub e 2 spl psi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 2 x sub 0 x sub 1 x sub e 2 where spl eta sub e 2 1 and spl eta sub e 2 2 are arbitrary functions of e 1 variables over gf p and 2 spl les k spl les p 1 then the compression mapping spl phi sub e 1 g f x p sup e spl rarr gf p sup spl infin a spl rarr spl phi sub e 1 a sub 0 a sub e 1 is injective that is a b if and only if spl phi sub e 1 a sub 0 a sub e 1 spl phi sub e 1 b sub 0 b sub e 1 for a b spl isin g f x p sup e furthermore if f x is a strongly primitive polynomial over z p sup e then spl phi sub e 1 a sub 0 a sub e 1 spl psi sub e 1 b sub 0 b sub e 1 if and only if a b and spl phi sub e 1 x sub 0 x sub e 1 spl psi sub e 1 x sub 0 x sub e 1 for a b spl isin g f x p sup e

a polynomial time approximation scheme for general multiprocessor job scheduling recently there have been considerable interests in the multiprocessor job scheduling problem in which a job can be processed in parallel on one of several alternative subsets of processors in this paper a polynomial time approximation scheme is presented for the problem in which the number of processors in the system is a fixed constant this result is the best possible because of the strong np hardness of the problem and is a significant improvement over the past results the best previous result was an approximation algorithm of ratio 7 6 epsilon for 3 processor systems based on goemans s algorithm for a restricted version of the problem

blowing up and desingularizing constant scalar curvature kahler manifolds this paper is concerned with the existence of constant scalar curvature kahler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature kahler metrics we also consider the desingularization of isolated quotient singularities of compact orbifolds which carry constant scalar curvature kahler metrics

the most significant bit of maximum length sequences over spl zopf 2 sup l autocorrelation and imbalance the imbalance and the autocorrelation of the binary sequences in the title are explored by combining the local weil bound with spectral analysis recent estimates on these quantities are improved by a factor of order 2 sup l 2 for large l

exact and approximation algorithms for the operational fixed interval scheduling problem the operational fixed interval scheduling problem ofisp is characterized as the problem of scheduling a number of jobs each with a fixed starting time a fixed finishing time a priority index and a job class the objective is to find an assignment of jobs to machines with maximal total priority the problem is complicated by the restrictions that i each machine can handle only one job at a time ii each machine can handle only jobs from a prespecified subset of all possible job classes and iii preemption is not allowed it follows from the above that ofisp has both the character of a job scheduling problem and the character of an assignment problem in this paper we discuss the occurrence of the problem in practice and we present newly developed exact and approximation algorithms for solving ofisp finally some computational results are shown

counter examples to the generalized positive action conjecture we give examples of complete locally asymptotically flat riemannian 4 manifolds with zero scalar curvature and negative mass the generalized positive action conjecture of hawking and pope 5 is therefore false

ale scalar flat kahler metrics on non compact weighted projective spaces we construct new explicit toric scalar flat kahler ale metrics with orbifold singularities which we use to obtain smooth extremal kahler metrics on appropriate resolutions of orbifolds

an efficient algorithm for the lagrangean dual of nonlinear knapsack problems with additional nested constraints abstract this paper presents an efficient algorithm for solving the lagrangean dual of nonlinear knapsack problems with additional nested constraints the dual solution provides a feasible primal solution if it exists and associated lower and upper bounds on the optimal objective function value of the primal problem computational experience is cited indicating computation time number of dual iterations and tightness of the bounds

on conformally kahler einstein manifolds we prove that any compact complex surface with c1 0 admits an einstein metric which is conformally related to a kahler metric the key new ingredient is the existence of such a metric on the blow up cp2 2cp2 of the complex projective plane at two distinct points

a method for the cutting stock problem with different qualities abstract an operations research project at a swedish company is reported the project deals with the problem of allocating wood products with different quality requirements to be cut from wooden boards which in turn consists of a number of quality zones a major difficulty is the existence of distinct time limits since the cross cutting of the boards is done in a real time process in this paper we derive a mathematical model which includes a set packing problem that accurately describes the real world problem this problem is then solved using a combination of lagrangean relaxation and subgradient optimization numerical results for practical problems are reported the results indicate a valid model and satisfactory efficiency of the proposed solution procedure

on the distinctness of modular reductions of maximal length sequences modulo odd prime powers we discuss the distinctness problem of the reductions modulo m of maximal length sequences modulo powers of an odd prime p where the integer m has a prime factor different from p for any two different maximal length sequences generated by the same polynomial we prove that their reductions modulo m are distinct in other words the reduction modulo m of a maximal length sequence is proved to contain all the information of the original sequence

facilities location in a competitive environment a promethee based multiple criteria analysis abstract in this paper a methodology for locating facilities in a competitive environment is introduced in this methodology the multi criteria approach and the notion of efficiency are appropriately integrated the classic distance criterion is combined with a second one a quality criterion to produce a more realistic representation of a customer s decision process

mathscr h space with a cosmological constant it is demonstrated that a real analytic 3 manifold with riemannian conformal metric is naturally the conformal infinity of a germ unique real analytic 4 manifold with real analytic riemannian metric satisfying the self dual einstein equations with cosmological constant 1 moreover this result holds if riemannian is replaced in the first case by lorentzian i e signature and in the second case by pseudo riemannian with signature or if real analytic is replaced by complex analytic and 9riemannian is replaced by holomorphic this provides a cosmological constant analogue of newman s space construction newman 1976 1977

using confidence limits for the global optimum in combinatorial optimization let z be the unknown optimal value of a combinatorial optimization problem in minimization form and let z be a constant satisfying probz z 1 for a fixed 0 1 then z is called a statistical or probabilistic lower bound at significance level 1 we discuss how statistical lower bounds can be used to measure the effectiveness of an approximate solution and to fathom subproblems in a branch and bound approach after reviewing some methods for obtaining statistical lower bounds we report on extensive computational experience for two notoriously difficult combinatorial optimization problems the traveling salesman problem and the quadratic assignment problem from our experience we conclude that statistical bounds are highly useful for quadratic assignment problems in this problem context the quality of simple analytic formulas is comparable to the quality of the maximum likelihood formula in general using statistics to aid in the solution of combinatorial optimization problems should be most useful when such problems are large

simultaneous resource scheduling to minimize weighted flow times many scheduling problems in manufacturing and service firms involve tasks that require more than one resource to be used simultaneously to execute the task two formulations of this scheduling problem are given we develop a lagrangian relaxation for the problem that has an intuitive interpretation the relaxation suggests heuristics and provides a lower bound on the optimal solution next a surrogate relaxation is developed that provides a second bound and a heuristic solution an enumeration procedure to determine the optimal solution is described and computational results on the effectiveness of the bounds and the heuristics are presented the lagrangian relaxation performs better on problems with a low degree of simultaneity and the surrogate relaxation does better with a high degree of simultaneity

capacitated lot sizing and scheduling by lagrangean relaxation abstract development of new models and solution procedures for production planning has been of research interest for several decades implementation of these models has resulted in lower production costs by reducing inventories number of setups and labor costs in this paper we develop several optimal near optimal procedures for the capacitated lot sizing and scheduling problem clsp with setup times limited regular time and limited overtime we formulate a mixed integer linear programming model of the problem and solve it by lagrangean relaxation we experiment with alternative lagrangean relaxations and develop new procedures to solve these relaxations overall the capacity constraints relaxation seems to be superior to the demand constraints relaxation our results show that large problems can be solved in reasonable computer times and within one percent accuracy of the optimal solutions we solved 99 8 i e 99 items and 8 periods 50 12 and 50 8 problems in 30 61 36 25 and 12 65 seconds of cdc cyber 730 computer time respectively our procedures are general enough to be applied directly or with slight modifications in real life production settings

dynamic aggregation of set partitioning constraints in column generation column generation is often used to solve problems involving set partitioning constraints such as vehicle routing and crew scheduling problems when these constraints are in large numbers and the columns have on average more than 8 12 nonzero elements column generation often becomes inefficient because solving the master problem requires very long solution times at each iteration due to high degeneracy to overcome this difficulty we introduce a dynamic constraint aggregation method that reduces the number of set partitioning constraints in the master problem by aggregating some of them according to an equivalence relation to guarantee optimality this equivalence relation is updated dynamically throughout the solution process tests on the linear relaxation of the simultaneous vehicle and crew scheduling problem in urban mass transit show that this method significantly reduces the size of the master problem degeneracy and solution times especially for larger problems in fact for an instance involving 1 600 set partitioning constraints the master problem solution time is reduced by a factor of 8

normal cr structures on compact 3 manifolds we study normal cr compact manifolds in dimension 3 for a choice of a cr reeb vector field we associate a sasakian metric on them and we classify those metrics as a consequence the underlying manifolds are topologically finite quotients of s 3 or of a non flat circle bundle over a riemann surface of positive genus in the latter case we prove that their cr automorphisms group is a finite extension of s 1 and we classify the normal cr structures on these manifolds

metriques autoduales sur la boule a conformal metric on a 4 ball induces on the boundary 3 sphere a conformal metric and a trace free second fundamental form conversely such a data on the 3 sphere is the boundary of a unique selfdual conformal metric defined in a neighborhood of the sphere in this paper we characterize the conformal metrics and trace free second fundamental forms on the 3 sphere close to the standard round metric which are boundaries of selfdual conformal metrics on the whole 4 ball when the data on the boundary is reduced to a conformal metric the trace free part of the second fundamental form vanishes one may hope to find in the conformal class of the filling metric an einstein metric with a pole of order 2 on the boundary we determine which conformal metrics on the 3 sphere are boundaries of such selfdual einstein metrics on the 4 ball in particular this implies the positive frequency conjecture of lebrun the proof uses twistor theory which enables to translate the problem in terms of complex analysis this leads us to prove a criterion for certain integrable cr structures of signature 1 1 to be fillable by a complex domain finally we solve an analogous higher dimensional problem selfdual einstein metrics are replaced by quaternionic kahler metrics and conformal structures on the boundary by quaternionic contact structures previously introduced by the author in contrast with the 4 dimensional case we prove that any small deformation of the standard quaternionic contact structure on the 4m 1 sphere is the boundary of a quaternionic kahler metric on the 4m ball

further result of compressing maps on primitive sequences modulo odd prime powers let be the integer residue ring with odd prime and integer for a sequence over there is an unique adic expansion where each is a sequence over and can be regarded as a sequence over the prime field gf naturally let be a strongly primitive polynomial over and the set of all primitive sequences generated by over suppose that gf gf it is shown that any function in is an injective map from to gf and the derived sequences of different functions are also different that is if and only if and for and these injective functions in can be considered as good candidates for the keys of a stream cipher

a multiperiod two echelon multicommodity capacitated plant location problem abstract in this paper we deal with a facility location problem where one desires to establish facilities at two different distribution levels by selecting the time periods our model intends to minimize the total cost for meeting demands for all the products specified over the planning horizon at various customer locations while satisfying the capacity requirements of the production plants and intermediate warehouses we address this problem by means of a formulation as a mixed integer programming problem a lagrangean relaxation is proposed to solve the problem together with a heuristic procedure that constructs feasible solutions of the original problem from the solutions at the lower bounds obtained by the relaxed problems computational tests are provided showing the good performance of this approach for a wide range of problems

further result on distribution properties of compressing sequences derived from primitive sequences over bf z p e let p be an odd prime number e an integer greater than 1 and z pe the integer residue ring modulo pe in this paper we obtain an improved result of the previous paper ieee trans inf theory 56 1 2010 555 563 on distribution properties of compressing sequences derived from primitive sequences over z pe it is shown that two primitive sequences and b generated by a strongly primitive polynomial f x over z pe are the same if there exist s z p and k z p such that the distribution of in their compressing sequences ae 1 a0 ae 2 and be 1 b0 be 2 is coincident at the positions t with t k where x0 xe 2 is an e variable polynomial over z p with the coefficient of xe 2p 1 x1p 1x0p 1 not equal to 1 e p 1 2 and is an m sequence over z p determined by f x and a compared with the previous result this gives a more precise characterization on the positions of a compressing sequence i e of the form ae 1 a0 ae 2 derived from a primitive sequence a over z pe that completely determines a in particular the result is also true for the highest level sequence ae 1 by taking x0 xe 2 0

the construction of ale spaces as hyper kahler quotients on decrit la construction d une famille particuliere de 4 varietes hyper kahler les espaces asymptotiquement localement euclidiens ale on decrit une 4 variete de riemann avec juste une extremite qui a l infini ressemble au quotient r 4 de l espace euclidien r 4 par un groupe fini d identifications

maskit combinations of poincare einstein metrics we establish a boundary connected sum theorem for asymptotically hyperbolic einstein metrics and also show that if the two metrics have scalar positive conformal infinities then the same is true for this boundary join this construction is also extended to spaces with a finite number of interior conic singularities and as a result we show that any 3 manifold which is a finite connected sum of quotients of s3 and s2 s1 bounds such a space with conic singularities putatively any 3 manifold admitting a metric of positive scalar curvature is of this form

reliable facility location design under the risk of disruptions reliable facility location models consider unexpected failures with site dependent probabilities as well as possible customer reassignment this paper proposes a compact mixed integer program mip formulation and a continuum approximation ca model to study the reliable uncapacitated fixed charge location problem rufl which seeks to minimize initial setup costs and expected transportation costs in normal and failure scenarios the mip determines the optimal facility locations as well as the optimal customer assignments and is solved using a custom designed lagrangian relaxation lr algorithm the ca model predicts the total system cost without details about facility locations and customer assignments and it provides a fast heuristic to find near optimum solutions our computational results show that the lr algorithm is efficient for mid sized rufl problems and that the ca solutions are close to optimal in most of the test instances for large scale problems the ca method is a good alternative to the lr algorithm that avoids prohibitively long running times

modeling and solving the two facility capacitated network loading problem this paper studies a topical and economically significant capacitated network design problem that arises in the telecommunications industry in this problem given point to point communication demand in a network must be met by installing loading capacitated facilities on the arcs loading a facility incurs an arc specific and facility dependent cost this paper develops modeling and solution approaches for loading facilities to satisfy the given demand at minimum cost we consider two approaches for solving the underlying mixed integer program a lagrangian relaxation strategy and a cutting plane approach that uses three classes of valid inequalities that we identify for the problem we show that a linear programming formulation that includes these inequalities always approximates the value of the mixed integer program at least as well as the lagrangian relaxation bound our computational results on a set of prototypical telecommunication data show that including these inequalities considerably improves the gap between the integer programming formulation and its linear programming relaxation from an average of 25 to an average of 8 these results show that strong cutting planes can be an effective modeling and algorithmic tool for solving problems of the size that arise in the telecommunications industry

the scheduling problem where multiple machines compete for a common local buffer abstract the problem of scheduling jobshops with restricted buffer space between machines to hold the work in process has received scant attention in the scheduling literature one interesting aspect of this problem is to understand how jobs arriving simultaneously from different machines would compete for common limited buffer space this paper considers this issue by studying a two stage flowshop environment with multiple machines at the first stage a single machine at the second stage and a finite size buffer area between the two stages jobs are processed at a pre assigned machine at the first stage and then at the machine at the second stage we model the problem of minimizing the sum of weighted completion times of a given set of jobs as a mixed integer linear program two lower bounds to the problem are then developed using a lagrangian and a combined lagrangian surrogate relaxation respectively heuristics for the problem based on priority rules are proposed and analysed computationally we see that the multipliers from the relaxations carry sufficient information to be used to build successful priority rules for this problem

mass in kahler geometry we prove a simple explicit formula for the mass of any asymptotically locally euclidean ale kahler manifold assuming only the sort of weak fall off conditions required for the mass to actually be well defined for ale scalar flat kahler manifolds the mass turns out to be a topological invariant depending only on the underlying smooth manifold the first chern class of the complex structure and the kahler class of the metric when the metric is actually ae asymptotically euclidean our formula not only implies a positive mass theorem for kahler metrics but also yields a penrose type inequality for the mass

einstein metrics spinning top motions and monopoles on considere la construction de solutions pour l equation d einstein autoduale on applique la construction de lebrun a la sphere de berger la 3 sphere de metrique 1 2 2 2 i 3 3 2 ou 1 2 3 est une base de 1 formes invariante a gauche satisfaisant d i j k e ijk j k et i 3 est une constante

random properties of the highest level sequences of primitive sequences over z 2 sup e using the estimates of the exponential sums over galois rings we discuss the random properties of the highest level sequences spl alpha sub e 1 of primitive sequences generated by a primitive polynomial of degree n over z 2 sup e first we obtain an estimate of 0 1 distribution in one period of spl alpha sub e 1 on the other hand we give an estimate of the absolute value of the autocorrelation function c sub n h of spl alpha sub e 1 which is less than 2 sup e 1 2 sup e 1 1 spl radic 3 2 sup 2e 1 2 sup n 2 2 sup e 1 for h spl ne 0 both results show that the larger n is the more random spl alpha sub e 1 will be

distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers let a and b be primitive sequences over z pe with odd prime p and e 2 for certain compressing maps we consider the distribution properties of compressing sequences of a and b and prove that a b if the compressing sequences are equal at the times t such that t k where is a sequence related to a we also discuss the s uniform distribution property of compressing sequences for some compressing maps we have that there exist different primitive sequences such that the compressing sequences are s uniform we also discuss that compressing sequences can be s uniform for how many elements s

a new lagrangian relaxation approach to the generalized assignment problem abstract in this paper we present a new lagrangian relaxation approach to the generalized assignment problem gap the new approach is based on a reformulation of gap into an equivalent problem which is then relaxed by traditional lagrangian relaxation techniques the reformulation is created by introducing a set of auxiliary variables and a number of coupling constraints by relaxing the coupling constraints we get subproblems where both types of constraint structures present in the gap are active the lower bound from the lagrangian dual of this approach is shown to be at least as strong as that from the best of the traditional lagrangian relaxation approaches an important feature is also the possibility of generating upper bounds quite easily the new approach has been tested on 10 problems of size m 4 n 25 i e 100 0 1 variables and the results have been compared with the traditional approaches

einstein metrics and complex singularities this paper is concerned with the construction of special metrics on non compact 4 manifolds which arise as resolutions of complex orbifold singularities our study is close in spirit to the construction of the hyperkahler gravitational instantons but we focus on a different class of singularities we show that any resolution x of an isolated cyclic quotient singularity admits a complete scalar flat kahler metric which is hyperkahler if and only if k x is trivial and that if k x is strictly nef then x also admits a complete non kahler self dual einstein metric of negative scalar curvature in particular complete self dual einstein metrics are constructed on simply connected non compact 4 manifolds with arbitrary second betti number

generating fenchel cutting planes for knapsack polyhedra the author recently proposed a class of cutting planes for integer programs called fenchel cuts which distinguish themselves from more conventional cuts in that they are generated by directly seeking to solve the separation problem rather than by using explicit knowledge of the polyhedral structure of the integer program an algorithm for generating fenchel cuts is presented and described in detail for the separation problem associated with knapsack polyhedra computational results are presented for a collection of real world integer programs to demonstrate the effectiveness of the cutting planes

wormholes in ach einstein manifolds we give a new construction of einstein manifolds which are asymptotically complex hyperbolic inspired by the work of mazzeo pacard in the real hyperbolic case the idea is to develop a gluing theorem for 1 handle surgery at infinity which generalizes the klein construction for the complex hyperbolic metric

the tv break packing problem abstract instead of selling advertisement spots one by one some french satellite channels decided in 2002 to modify their commercial offer in order to sell packages of spots these new general conditions of sale lead to an interesting optimization problem that we named the tv b reak p acking p roblem tvbp we establish its np hardness and study various resolutions approaches including linear programming lp lagrangian relaxation lr constraint programming cp and local search ls finally we propose a generic cp ls hybridization scheme branch and move whose application to the tvbp obtained the best results in our experiments dual upper bounds of the maximal revenue are also computed

selfdual einstein metrics with torus symmetry it is well known that any 4 dimensional hyperkahler metric with two commuting killing fields may be obtained explicitly via the gibbons hawking ansatz from a harmonic function invariant under a killing field on 3 in this paper we find all selfdual einstein metrics of nonzero scalar curvature with two commuting killing fields they are given explicitly in terms of a local eigenfunction of the laplacian on the hyperbolic plane we discuss the relation of this construction to a class of selfdual spaces found by joyce and some einstein weyl spaces found by ward and then show that certain multipole hyperbolic eigenfunctions yield explicit formulae for the quaternion kahler quotients of pm 1 by an m 2 torus studied by galicki and lawson as a consequence we are able to place the well known cohomogeneity one metrics the quaternion kahler quotients of p2 and noncompact analogues and the more recently studied selfdual einstein hermitian metrics in a unified framework and give new complete examples

non minimal scalar flat kahler surfaces and parabolic stability a new construction is presented of scalar flat kahler metrics on non minimal ruled surfaces the method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank 2 parabolically stable holomorphic bundles this rather general construction is shown also to give new examples of low genus in particular it is shown that mathbb cp 2 blown up at 10 suitably chosen points admits a scalar flat kahler metric this answers a question raised by claude lebrun in 1986 in connection with the classification of compact self dual 4 manifolds

a multiplier adjustment method for the generalized assignment problem we describe a branch and bound algorithm for the generalized assignment problem in which bounds are obtained from a lagrangian relaxation with the multipliers set by a heuristic adjustment method the algorithm was tested on a large sample of small random problems and a number of large problems derived from a vehicle routing application computation times were reasonable in all cases and the branch and bound trees generated had nearly two orders of magnitude fewer nodes than for competing algorithms although comparison of running times on different machines is difficult the multiplier adjustment method appears to be about one order of magnitude faster than the best previously existing algorithms for this problem

single machine scheduling with symmetric earliness and tardiness penalties abstract this research focuses on scheduling jobs with varying processing times and distinct due dates on a single machine subject to earliness and tardiness penalties hence this work will find application in a just in time jit production environment the scheduling problem is formulated as a 0 1 linear integer program with three sets of constraints where the objective is to minimize the sum of the absolute deviations between job completion times and their respective due dates the first two sets of constraints are equivalent to the supply and demand constraints of an assignment problem the third set which represents the process time non overlap constraints is relaxed to form the lagrangian dual problem the dual problem is then solved using the subgradient algorithm efficient heuristics have also been developed in this work to yield initial primal feasible solutions and to convert primal infeasible solutions to feasibility the computational results show that the relative deviation from optimality obtained by the subgradient algorithm is less than 3 for problem sizes varying from 10 to 100 jobs