Thermodynamic and dynamical properties of the hard sphere system revisited by molecular dynamics simulation

Acknowledgements Some of the MD calculations were performed at the Poznan Supercomputing and Networking Center (PCSS). DMH would like to thank Dr. T. Crane (Department of Physics, Royal Holloway, University of London, UK) for helpful software support.Peer reviewedPostprin

Scheduling Algorithms for Procrastinators

This paper presents scheduling algorithms for procrastinators, where the speed that a procrastinator executes a job increases as the due date approaches. We give optimal off-line scheduling policies for linearly increasing speed functions. We then explain the computational/numerical issues involved in implementing this policy. We next explore the online setting, showing that there exist adversaries that force any online scheduling policy to miss due dates. This impossibility result motivates the problem of minimizing the maximum interval stretch of any job; the interval stretch of a job is the job's flow time divided by the job's due date minus release time. We show that several common scheduling strategies, including the "hit-the-highest-nail" strategy beloved by procrastinators, have arbitrarily large maximum interval stretch. Then we give the "thrashing" scheduling policy and show that it is a \Theta(1) approximation algorithm for the maximum interval stretch.Comment: 12 pages, 3 figure

Laplace method for the diagrams of elastic scattering in the model of multiparticle fields

In this paper we show how the differential cross-section of elastic proton scattering can be calculated from the square of the transmitted four-momentum using the model of multiparticle fields. We consider a single-loop diagram and the corresponding analytical expression for this loop. This expression contains a multidimensional integral over virtual four-momentum, which we calculate using the Laplace method. These multidimensional integrals were reduced to two-dimensional or one-dimensional and then were calculated numerically. A qualitative correspondence of the differential cross section to the experimental data is obtained. Achieving a quantitative match with the experiment requires taking into account more loop diagrams.Comment: 50 pages, 12 figures, in Ukrainia

A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs

We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual solutions whose costs are within a factor of 1+eps of the optimal cost in time O((r+c)log(n)/eps^2 + n).Comment: corrected version of FOCS 2007 paper: 10.1109/FOCS.2007.62. Accepted to Algorithmica, 201