lagrangian relaxation and column generation based lower bounds for the p m h j 1 σ w i c i scheduling problem we consider an identical parallel machine scheduling problem to minimize the sum of weighted completion times of jobs however instead of allowing machines to be continuously available as it is generally assumed we consider that each machine is subject to a deterministic and finite maintenance period this condition increases the problem complexity we provide for the problem an adapted heuristic lower bounds based on lagrangian relaxation and column generation methods computational study shows satisfactory results

determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

on continuous dependence for an inverse initial boundary value problem for the wave equation abstract we show that the bounded coefficient q x of the wave equation u tt u qu x t 0 t u x 0 u t x 0 0 x u v x x x t 0 t can be continuously determined by its neumann to dirichlet map in certain function spaces

a novel method for solving the inverse scattering problem for time harmonic acoustic waves in the resonance region ii in a previous paper siam j appl math 1985 pp 1039 1053 we presented a new method for determining the shape of an acoustically soft obstacle from a knowledge of the time harmonic incident wave and the far field pattern of the scattered wave the method given there was based on knowing the far field pattern for an interval of values of the square of the wave number k such that this interval contained the first eigenvalue lambda 1 of the interior dirichlet problem the purpose of this paper is to extend the methods of our earlier paper to treat the case when the far field pattern is only known for a single value of the wave number such that k 2 is not equal to lambda 1 in addition we show how to combine the results of this paper with the first to obtain a method that is valid for any fixed value of k independent of whether or not k 2 is an eigenvalue we also extend our analysis to include the case of the impedance boundary value problem numerical examples are given showing the pra

three dimensional earth conductivity inversion abstract we have constructed two inverse algorithms using tikhonov regularization one follows the well known method of solving the linearized data model relation subject to some regularizing operator which forces the solution to satisfy some desirable features we refer to the other more novel approach as the inverse scattering currents method this procedure uses the linear relation between data and scattering currents induced in an inhomogeneous structure and the relation between the scattering currents and the unknown conductivity the inverse problem is solved iteratively using these two relations

weighted flow time bounds for scheduling identical processors abstract we present two lower bounds for the identical parallel processor weighted flow time problem and identify theoretical properties regarding relationships among these and other bounds for the problem the new bounds along with other bounds from the literature are evaluated in a computational study and are found to be among the top three in performance conditions favorable to each of the top three performing bounds are identified

an improved heuristic for parallel machine weighted flowtime scheduling with family set up times this paper studies the identical parallel machine scheduling problem with family set up times and an objective of minimizing total weighted completion time weighted flowtime the family set up time is incurred whenever there is a switch of processing from a job in one family to a job in another family a heuristic is proposed in this paper for the problem computational results show that the proposed heuristic outperforms an existing heuristic especially for large sized problems in terms of both solution quality and computation times the improvement of solution quality is as high as 4 753 for six machine problem and 7 822 for nine machine problem while the proposed heuristic runs three times faster than the existing one

robust h sub spl infin control for a class of cascaded nonlinear systems this paper is concerned with the problem of robust h sub spl infin control for a class of nonlinear systems with parameter uncertainty the system under consideration is composed of two cascaded subsystems a zero input asymptotically stable nonlinear one and a linearizable one which is controllable the uncertain parameters are from a known compact set and are allowed to enter the system nonlinearly based on a lyapunov approach a nonlinear static state feedback controller is designed such that the l sub 2 gain of the closed loop system is below a prespecified value for all admissible uncertainties furthermore the closed loop system is shown to be robust input to state stable under some conditions

a comparison of branch and bound algorithms for a family scheduling problem with identical parallel machines this paper investigates branch and bound algorithms for the problem of scheduling jobs with family setups on identical parallel machines to minimize the weighted sum of completion times in particular we propose a new branching scheme that appears to substantially outperform current procedures in terms of computation time and search tree size

the inverse scattering problem for time harmonic acoustic waves in an inhomogeneous medium with complex refraction index abstract the inverse scattering problem of determining the complex refraction index of a compact inhomogeneous medium from a knowledge of the far field patterns of the scattered fields corresponding to many incident time harmonic plane acoustic waves is solved by using the colton monk method again by using the same method the analogue of karp s theorem for the scattering of acoustic waves through an inhomogeneous medium with compact support is proven

multidimensional inverse problems and completeness of the products of solutions to pde a method is given for proving uniqueness theorems for some inverse problems the method is based on a result on completeness of the products of solutions to pde as an example the following uniqueness theorems are proved 1 the scattering amplitude a k known for all s2 and a fixed k 0 determines the compactly supported q x l2 d uniquely 2 the surface data u x y k known for all x y p x x3 0 and a fixed k 0 determine the compactly supported x l2 d d r 3 x x3 0 is arbitrarily small determine aj x j 1 2 uniquely here 2u k2u k2a1x a2 x u x y in r3 a1 l2 d a2 h2 d the same conclusion holds if the surface data are known at two distinct frequencies 4 the surface data u x y k known for all x y p and all k 0 determine v x and h k uniquely here 2 k2 k2 x u x y h k x l2 d h k is fourier transform of a wavelet of compact support 5 the conductivity x w2 2 d x c 0 is uniquely determined by the measurements of u and un on d here n is the outward normal to d d r3 is a bounded domain with a smooth boundary d x u 0 in d 6 necessary and sufficient conditions are given for a function a k s2 k 0 is fixed to be the scattering amplitude corresponding to a local potential from a certain class

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

robust control of nonlinear feedback passive systems in this paper we consider a class of nonlinear systems with uncertain parameters which enter the system nonlinearly we assume that the uncertain nonlinear system is minimum phase and the uncertain parameters are from a bounded compact set the problem under consideration is the design of a nonlinear static state feedback controller such that the closed loop system is passive for all admissible uncertainties

stability of the solution to 3d fixed energy inverse scattering problem let sup s2 a a 0 is a given number b a r3 ba 0 is a small number a numerical method is given to calculate a stable approximation q to the fourier transform q of q x an estimate of the error of the approximation is given for q qq and q qa l ba

numerical recovery of the layered medium from the surface data abstract in this paper an inverse problem is formulated and its numerical solution is given the problem is of interest for example in geophysics numerical results show that the algorithm is efficient for noisy data practical recommendations are given the problem consists of finding n z the refraction coefficient of the medium given the surface data u x k x p x x3 0 and all k 0 k0 where k0 0 is an arbitrary small wave number the governing equation is 2 k2n z u x x x1 x2 z analytical solution to this inverse problem is given a numerical implementation is suggested and the results of the numerical experiments are reported

formal solutions of inverse scattering problems iv error estimates the formal solutions of certain three dimensional inverse scattering problems presented in papers i iii in this series j math phys 10 1819 1969 17 1175 1976 21 2648 1980 are employed here to obtain quantitative estimates on the error resulting from the use of the born approximations in both direct and inverse potential scattering problems these estimates are uniformly valid at all energies and for all sufficiently weak potentials

an inverse problem of the wave equation this paper is organized as follows in sect 1 the statement of the inverse problem is formulated the basic results are formulated and proved in sect 2 some auxiliary material on the x ray transform is given in a self contained way for convenience of the reader this material is used in section one

passivity and absolute stabilization of a class of discrete time nonlinear systems abstract by using the theory of discrete time passive systems and the concept of feedback equivalence we present an approach toward deriving sufficient conditions for the global stabilization of discrete time nonlinear systems in the form x k 1 tf x k g x k u k the central feature of the approach is that a unifying set of stability criteria can be obtained and the stability results recover the previous stabilization schemes proposed in the literature

behavior of the solutions to exterior boundary value problems at low frequencies abstract a simple method is given to study the low frequency behavior of the solutions to exterior boundary value problems for elliptic equations of second order

uniqueness theorems for multidimensional inverse problems with unbounded coefficients abstract in a g ramm inverse problems 3 1987 l77 l82 a method to prove uniqueness theorems is given the method uses an estimate of the solution to a partial differential equation with l d coefficients here the estimate is established for l2 d coefficients and the resulting uniqueness theorems are formulated

symmetry properties of scattering amplitudes and applications to inverse problems abstract for the transformations of the potential q q l where l is one of the following transformations rotation scaling or translation the corresponding transformation of the scattering amplitude is given a necessary and sufficient condition on the scattering amplitude for the scatterer to be spherically symmetric is derived as an application of the above results

parallel machine scheduling by column generation parallel machine scheduling problems concern the scheduling of n jobs on m machines to minimize some function of the job completion times if preemption is not allowed then most problems are not only np hard but also very hard from a practical point of view in this paper we show that strong and fast linear programming lower bounds can be computed for an important class of machine scheduling problems with additive objective functions characteristic of these problems is that on each machine the order of the jobs in the relevant part of the schedule is obtained through some priority rule to that end we formulate these parallel machine scheduling problems as a set covering problem with an exponential number of binary variables n covering constraints and a single side constraint we show that the linear programming relaxation can be solved efficiently by column generation because the pricing problem is solvable in pseudo polynomial time we display this approach on the problem of minimizing total weighted completion time on m identical machines our computational results show that the lower bound is singularly strong and that the outcome of the linear program is often integral moreover they show that our branch and bound algorithm that uses the linear programming lower bound outperforms the previously best algorithm

property c and an inverse problem for a hyperbolic equation let utt u q x t u 0 in d 0 t where d r3 is a bounded domain with a smooth boundary d t d d diam d q x t c 0 t l d suppose that for every u d f x t c1 d 0 t the value un d h s t is known where n is the outer normal to d u solves and and satisfies the initial conditions u ut 0 at t 0 then q x t is uniquely determined by the data f h f c1 d 0 t in the subset s of d 0 t consisting of the lines which make 45 with the t axis and which meet the planes t 0 and t t outside d 0 t provided that q x t is known outside s here d is the closure of d

finding conductivity from surface measurements abstract a method is given to determine conductivity of a body from the measurements of the potential and either normal component of the current on the surface of the body or the normal derivative of the potential on and the value of conductivity at a single point on

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors

direct passivity of a class of mimo non linear systems using adaptive feedback in this paper an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi input multi output mimo non linear system with explicit linear parametric uncertainty equivalent to a passive system these results are an extension of those obtained by the authors for the siso case some stability issues associated to the resultant closed loop passive system are also discussed the results obtained are applied to models of dynamical mimo systems to illustrate the controller design methodology

new bounds for the identical parallel processor weighted flow time problem in 1964 eastman even and isaacs eei presented a polynomial time lower bound for the np hard problem of scheduling n jobs on m available and identical processors to minimize weighted flow time a general bound of which the eei bound is a special case is proposed four new bounds for the identical processor problem are given all of the new bounds can be applied to problems with variable processor ready times the eei bound is limited to problems where all processors are initially available at the same time two of the four new bounds are shown to dominate the eei bound the two other bounds are found to be effective for a particular problem class two polynomial time lower bounds for problems with nonidentical processors are introduced one bound is applicable to the uniform processor problem the other bound can be applied to the general processor problem no bounds have previously been proposed for these problems