a rigorous computational comparison of alternative solution methods for the generalized assignment problem statistical experimental design and analysis is a cornerstone for scientific inquiry that is rarely applied in reporting computational testing this approach is employed to study the relative performance characteristics of the four leading algorithmic and heuristic alternatives to solve the linear cost generalized assignment problem lcgap against a newly developed heuristic variable depth search heuristic vdsh in assessing the relative effectiveness of the prominent solution methodologies and vdsh under the effects of various problem characteristics we devise a carefully designed experimentation of state of the art implementations through a rigorous statistical analysis we identify the most efficient method s for commonly studied lcgaps and determine the effect on solution time and quality of problem class and size

lie structure in semiprime superalgebras with superinvolution abstract in this paper we investigate the lie structure of the lie superalgebra k of skew elements of a semiprime associative superalgebra a with superinvolution we show that if u is a lie ideal of k then either there exists an ideal j of a such that the lie ideal j k k is nonzero and contained in u or a is a subdirect sum of a a where the image of u in a is central and a is a subdirect product of orders in simple superalgebras each at most 16 dimensional over its center

functional identities in superalgebras abstract the aim of this paper is to establish the theory of functional identities in superalgebras as an application of this theory k supercommuting maps in superalgebras are investigated

the inviscid limit of navier stokes equations for analytic data on the half space in their classical work sammartino and caflisch commun math phys 192 2 433 461 1998a commun math phys 192 2 463 491 1998b proved the inviscid limit of the incompressible navier stokes equations for well prepared data with analytic regularity in the half space their proof is based on the detailed construction of prandtl s boundary layer asymptotic expansions in this paper we give a direct proof of the inviscid limit for general analytic data without having to construct prandtl s boundary layer correctors our analysis makes use of the boundary vorticity formulation and the abstract cauchy kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity

incompressible flow around a small obstacle and the vanishing viscosity limit in this article we consider viscous flow in the exterior of an obstacle satisfying the standard no slip boundary condition at the surface of the obstacle we seek conditions under which solutions of the navier stokes system in the exterior domain converge to solutions of the euler system in the full space when both viscosity and the size of the obstacle vanish we prove that this convergence is true assuming two hypotheses first that the initial exterior domain velocity converges strongly in l 2 to the full space initial velocity and second that the diameter of the obstacle is smaller than a suitable constant times viscosity or in other words that the obstacle is sufficiently small the convergence holds as long as the solution to the limit problem is known to exist and stays sufficiently smooth this work complements the study of incompressible flow around small obstacles which has been carried out in 4 6

on the stability of boundary layers of incompressible euler equations abstract in this paper we investigate the stability and instability of boundary layers of incompressible euler equations copyright 2000 academic press dans cet article on etudie la stabilite et l instabilite de couches limites des equations d euler

sensitivity analysis for branch and bound integer programming after an integer program is solved we may be interested in the effect of small changes in the right hand side or objective function coefficients without modifying the underlying branch and bound or cutting plane algorithm we show what additional data to collect during the solution of the original integer program to give useful bounds on the solution of the modified problem

on the lie structure of the skew elements of a simple superalgebra with superinvolution abstract we investigate the lie structure of the lie superalgebra k of skew elements of a unital simple associative superalgebra a with superinvolution over a field of characteristic not 2 it is proved that if a is more than 16 dimensional over its center z then any lie ideal u of k satisfies either u z or u k k moreover any lie ideal u of k k satisfies either u z or u k k in particular k k z k k is a simple lie superalgebra

existence and uniqueness for a class of nonlinear higher order partial differential equations in the complex plane we prove existence and uniqueness results for nonlinear third order partial differential equations of the form

the exponent for superalgebras with superinvolution abstract let a be a superalgebra with superinvolution over a field of characteristic zero and let c n a n 1 2 be its sequence of codimensions in 6 it was proved that such a sequence is exponentially bounded in this paper we capture this exponential growth for finitely generated superalgebras with superinvolution a over an algebraically closed field of characteristic zero we shall prove that lim n c n a n exists and it is an integer denoted exp a and called exponent of a moreover we shall characterize finitely generated superalgebras with superinvolution according to their exponent

zero viscosity limit for analytic solutions of the navier stokes equation on a half space i existence for euler and prandtl equations this is the first of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in this paper we prove short time existence theorems for the euler and prandtl equations with analytic initial data in either two or three spatial dimensions the main technical tool in this analysis is the abstract cauchy kowalewski theorem for the euler equations the projection method is used in the primitive variables to which the cauchy kowalewski theorem is directly applicable for the prandtl equations cauchy kowalewski is applicable once the diffusion operator in the vertical direction is inverted

semiprime prime and simple jordan superpairs covered by grids in this paper we continue the investigation of jordan superpairs covered by a grid which have recently been described by the second author e neher j algebra 269 2003 28 73 for such a jordan superpair we characterize semiprimeness primeness and simplicity in terms of its associated supercoordinate system

algebras with involution and multiplicities bounded by a constant abstract let a be an algebra with involution over a field of characteristic zero in this paper we characterize in two different ways when the multiplicities of the cocharacter of a are bounded by a constant as a consequence we characterize the algebras with involution of bounded colength

initial boundary layer associated with the nonlinear darcy brinkman system abstract we study the interaction of initial layer and boundary layer in the nonlinear darcy brinkman system in the vanishing darcy number limit in particular we show the existence of a function of corner layer type so called initial boundary layer in the solution of the nonlinear darcy brinkman system an approximate solution is constructed by the method of multiple scale expansion in space and in time we establish the optimal convergence rates in various sobolev norms via energy method

heuristic sensitivity analysis in a combinatoric environment an exposition and case study abstract sensitivity orpost optimality analysis investigates the effect of parametric changes on heuristic robustness and solution quality this approach is relatively unexplored for combinatorial optimization problems and yet is of considerable interest in analyzing performance characteristics of heuristic approaches the purpose of this paper is to 1 develop the semantics and rationale of parametric analysis within the combinatoric environment 2 present as an example the design and implementation of sensitivity analysis procedures for a newly developed heuristic thevariable depth search heuristic vdsh to solve the generalized assignment problem gap the concepts and methodology discussed in this paper may as well be applied to other heuristics or in developing a heuristic sensitivity analysis procedure for a large scale optimization method

lie superhomomorphisms in superalgebras with superinvolution abstract the main purpose of the present paper is to give a description of lie superhomomorphisms from the set of skew elements of a superalgebra with superinvolution into a unital superalgebra

tabu search for the multilevel generalized assignment problem abstract the multilevel generalized assignment problem mgap differs from the classical gap in that agents can perform tasks at more than one efficiency level important manufacturing problems such as lot sizing can be formulated as mgaps however the large number of variables in the related 0 1 integer program makes the use of commercial optimization packages impractical in this paper we present a heuristic approach to the solution of the mgap which consists of a novel application of tabu search ts our ts method employs neighborhoods defined by ejection chains that produce moves of greater power without significantly increasing the computational effort

vanishing vertical viscosity limit of anisotropic navier stokes equation with no slip boundary condition abstract in this paper we consider the zero viscosity limit of the anisotropic incompressible navier stokes equations with no slip boundary condition see 1 1 in r 2 we prove that there exist t independently on e such that the strong solutions of 1 1 convergence to the solution of 1 2 away from the boundary and to solution of 1 3 near the boundary in l 0 t l 2 l r 2 when the vertical viscosity vanish provided that the initial velocity is regular enough and we obtain the optimal convergence rate

a hybrid heuristic for the generalized assignment problem abstract the objective of this study is to develop a hybrid heuristic hh for solving the generalized assignment problem gap and conduct a computational comparison with the leading alternative heuristic approaches hh is designed around the two best known heuristics heuristic gap hgap and variable depth search heuristic vdsh previous performance characteristic studies have shown that hgap dominates vdsh in terms of solution cpu time while vdsh obtains solutions of 13 to 300 better quality within a reasonable time the main idea in this paper is to hybridize the two approaches such that the inherent values of both heuristics are realized

lie identities for skew and symmetric elements of semiprime superalgebras with superinvolution let a be a non trivial semiprime associative superalgebra with superinvolution in the present note we investigate when the subspaces of symmetric elements or skew elements of a are lie nilpotent or lie solvable we show that these conditions determine the algebraic structure of a

group gradings on superinvolution simple superalgebras in this paper we describe all group gradings by an arbitrary finite group g on non simple finite dimensional superinvolution simple associative superalgebras over an algebraically closed field f of characteristic 0 or coprime to the order of g

zero viscosity limit for analytic solutions of the navier stokes equation on a half space ii construction of the navier stokes solution this is the second of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in either 2d or 3d under the assumption of analytic initial data we construct solutions of navier stokes for a short time which is independent of the viscosity the navier stokes solution is constructed through a composite asymptotic expansion involving the solutions of the euler and prandtl equations which were constructed in the first paper plus an error term this shows that the navier stokes solution goes to an euler solution outside a boundary layer and to a solution of the prandtl equations within the boundary layer the error term is written as a sum of first order euler and prandtl corrections plus a further error term the equation for the error term is weakly nonlinear its linear part is the time dependent stokes equation this error equation is solved by inversion of the stokes equation through expressing the solution as a regular euler like part plus a boundary layer prandtl like part the main technical tool in this analysis is the abstract cauchy kowalewski theorem

a survey of algorithms for the generalized assignment problem abstract this paper surveys algorithms for the well known problem of finding the minimum cost assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded all approaches seem to be based on branch and bound with bound supplied through heuristics and through relaxations of the primal problem formulation from the survey one can select building blocks for the design of one s own tailor made algorithm the survey also reveals that although just about every mathematical programming technique was tried on this problem there is still a lack of a representative set of test problems on which competing enumeration algorithms can be compared as well as a shortage of effective heuristics

vanishing viscosity limit for incompressible navier stokes equations with navier boundary conditions for small slip length in this paper we will analyze the vanishing viscosity limit of the incompressible navier stokes equations with the navier slip boundary conditions in a bounded domain of r2 when the slip length is smaller than or equal to the order of viscosity by using an energy method and developing kato s approach given in the work of kato math sci res inst publ 2 85 98 1984 we obtain several conditions to guarantee that the solution of the navier stokes equations with the navier slip boundary conditions goes to the solution of the associated problem of the euler equations in the energy space l2 uniformly in time as the viscosity goes to zero

the derived superalgebra of skew elements of a semiprime superalgebra with superinvolution abstract in this paper we investigate the lie structure of the derived lie superalgebra k k with k the set of skew elements of a semiprime associative superalgebra a with superinvolution we show that if u is a lie ideal of k k then either there exists an ideal j of a such that the lie ideal j k k is nonzero and contained in u or a is a subdirect sum of a a where the image of u in a is central and a is a subdirect product of orders in simple superalgebras each at most 16 dimensional over its center

regularity conditions on skew and symmetric elements in superalgebras with superinvolution abstract we study semiprime superalgebras with superinvolution under certain additional regularity conditions more precisely we assume regularity conditions either on every nonzero homogeneous symmetric element or on every nonzero homogeneous skewsymmetric element

technical note an improved dual based algorithm for the generalized assignment problem the generalized assignment problem gap determines the minimum cost assignment of n jobs to m agents such that each job is assigned to exactly one agent subject to an agent s capacity existing solution algorithms have not solved problems with more than 100 decision variables this paper designs an optimization algorithm for the gap that effectively solves problems with up to 500 variables compared with existing procedures this algorithm requires fewer enumeration nodes and shorter running times improved performance stems from an enhanced lagrangian dual ascent procedure that solves a lagrangian dual at each enumeration node adding a surrogate constraint to the lagrangian relaxed model and an elaborate branch and bound scheme an empirical investigation of various problem structures not considered in existing literature is also presented

classical lie superalgebras over simple associative algebras over arbitrary fields of characteristic not equal to 2 we construct three families of simple lie algebras and six families of simple lie superalgebras of matrices with entries chosen from different one sided ideals of a simple associative algebra these families correspond to the classical lie algebras and superalgebras our constructions intermix the structure of the associative algebra and the structure of the matrix algebra in an essential compatible way many examples of simple associative algebras without an identity element arise as a by product the study of conformal algebras and superalgebras often involves matrix algebras over associative algebras such as weyl algebras and for that reason we illustrate our constructions by taking various one sided ideals from a weyl algebra or a quantum torus

the van dommelen and shen singularity in the prandtl equations abstract in 1980 van dommelen and shen provided a numerical simulation that predicted the spontaneous generation of a singularity in the prandtl boundary layer equations from a smooth initial datum for a nontrivial euler background in this paper we prove this numerical conjecture by rigorously establishing the finite time blowup of the boundary layer thickness

uniform regularity and relaxation limit for the outer pressure problem of gas dynamics with several thermal nonequilibrium modes abstract we study in this paper the uniform regularity and relaxation limit for the outer pressure problem of one dimensional gas dynamics with several thermal nonequilibrium modes the uniform regularity is established for the initial data satisfying the compatible conditions on the boundary the relaxation limit to equilibrium flow or frozen flow is also investigated by a compactness argument

local existence and uniqueness of euler equation in weighted sobolev space abstract in this paper we study the existence and uniqueness of euler equation in the weighted sobolev space this is motivated by the study of inviscid limit of navier stokes equation in half plane the use of the weighted calderon zygmund inequality in the estimate of the pressure term is the improvement of our work

needed an empirical science of algorithms deductive algorithmic science has reached a high level of sophistication but its worst case and average case results seldom tell us how well an algorithm is actually going to work in practice i argue that an empirical science of algorithms is a viable alternative i respond to misgivings about an empirical approach including the prevalent notion that only a deductive treatment can be theoretical or sophisticated np completeness theory for instance is interesting partly because it has significant if unacknowledged empirical content an empirical approach requires not only rigorous experimental design and analysis but also the invention of empirically based explanatory theories i give some examples of recent work that partially achieves this aim

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

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

on the lie structure of a prime associative superalgebra abstract in this paper some results on the lie structure of prime superalgebras are discussed we prove that with the exception of some special cases for a prime superalgebra a over a ring of scalars with 1 2 if l is a lie ideal of a and w is a subalgebra of a such that w l w then either l z or w z likewise if v is a submodule of a and v l v then either v z or l z or there exists an ideal of a m such that 0 m a v this work extends to prime superalgebras some results of i n herstein c lanski and s montgomery on prime algebras