Speedup estimates for some variants of the parallel implementations of the branch-and-bound method

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered.     

Theory of Non-Equilibrium Stationary States as a Theory of Resonances

We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized by two numbers, T ₁ and T ₂ (‘reservoir temperatures’). If T ₁ ≠ T ₂, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T ₁ and T ₂, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T ₁,T ₂) > g ^{2 + α}, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions. Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007. Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments of Mathematics of McGill University and the University of Toronto, Canada. Matthias Mück: Supported by DAAD under grant HSP III. Israel Michael Sigal: Supported by NSERC under grant NA7901.     

Approximate neutrality of large-Z ions

LetN(Z) denote the number of electrons which a nucleus of chargeZ can bind in non-relativistic quantum mechanics (assuming that electrons are fermions). We prove thatN(Z)/Z1 asZ.Research partially supported by the NSERC under Grant NA7901 and by the USNSF under Grants DMS-8416049 and PHY 85-15288-A01     

Optimal Control for Switched Systems with Pre-defined Order and Switch-Dependent Dynamics

The optimal control problem for switched systems, with a predefined order of switches, is considered. The differential equations may depend explicitly on previous switching instants, and the latter may be state dependent. The solution is based on the Calculus-of-Variations, which leads to a single two-point boundary-value problem. A new condition for the Hamiltonian jump at the switching instants is obtained. Simple numerical examples demonstrate the results.     

Ground State and Resonances in the Standard Model of the Non-Relativistic QED

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.     

Consistent values and the core in continuum market games with two types of players

The consistent value is an extension of the Shapley value to the class of games with non-transferable utility.? In this paper, the consistent value will be characterized for market games with a continuum of players of two types. We will show that for such games the consistent value need not belong to the core, and provide conditions under which there is equivalence between the two concepts. Received: October 1998 RID="*" ID="*"  This thesis was completed under the supervision of Professor Sergiu Hart, The Center for Rationality and Interactive Decision Theory, Department of Mathematics, Department of Economics, The Hebrew University of Jerusalem. I would like to thank Professor Hart for introducing me to this area of research, for his help and guidance, and, especially, for all his patience.? I would also like to thank Michael Borns for improving the style, and an anonymous referee for helpful comments.     

Analytic properties of the scattering matrix of many particle systems

We generalize the previous results on a meromorphic continuation of the scattering matrix for N particle systems. Our proofs seem to be much simpler than those given before.Dedicated to the dear memory of david Milman     

Spectral methods for compressible reactive flows

High order simulations are necessary in order to capture fine details in resolving supersonic reactive flows. However, high Mach number compressible flows feature sharp gradients and discontinuities, which present a challenge to successful simulations using high order methods. Spectral methods have proven a powerful tool in simulation of incompressible turbulent flows, and recent advances allow the application of spectral methods to compressible reactive flows. We review the recent advances in the theory and application of spectral methods which allow stable computations of discontinuous phenomena, and the recovery of high order information via postprocessing, and present applications of high Mach number reactive flows. To cite this article: D. Gottlieb, S. Gottlieb, C. R. Mecanique 333 (2005).