Location of terror response facilities: A game between state and terrorist

We study a leader follower game with two players: a terrorist and a state where the later one installs facilities that provide support in case of a terrorist attack. While the Terrorist attacks one of the metropolitan areas to maximize his utility, the State, which acts as a leader, installs the facilities such that the metropolitan area attacked is the one that minimizes her disutility (i.e., minimizes ‘loss’). We solve the problem efficiently for one facility and we formulate it as a mathematical programming problem for a general number of facilities. We demonstrate the problem via a case study of the 20 largest metropolitan areas in the United States.     

CONVERSION OF LIGHT ENERGY TO ELECTROSTATIC ENERGY IN THE PROTON PUMP OF HALOBACTERIUM HALOBIUM

Abstract— The energetics of the proton pump in Halobacterium halobium is considered on a molecular level. It is proposed that absorption of light by bacteriorhodopsin leads to charge separation and sequential changes in the proton affinities some of the protein groups resulting in proton pumping against the pH gradient. Two alternative models of 'through-space' and 'through-bond' charge separation are proposed. Novel diagrams that describe the energetics of the pumping process are presented. These diagrams can be used both to examine different models of bacteriorhodopsin and for considering other photobiological processes that involve conversion of light energy to electrostatic energy.     

Stability and Asymptotic Stability of Functional-Differential Equations

We investigate asymptotic behaviour of solutions of the functional-differentialequation where f and g arelocally Lipschitz functions, C is a continuous matrix and thesmooth lag function obeys 0 (t) t for t 0. We transformthe equation into a delay equation with an infinity of delaysand use a theorem of Söderlind to derive sufficient conditionsfor stability and for asymptotic stability in the case lim_t (t) = . The situation is qualitatively different when lim_t (t) = * < and we outline stability conditions for thatcase by employing direct techniques.     

Solubilization of methane,ethane, propane andn-butane in aqueous solutions of sodium dodecylsulfate

The solubilities of methane, ethane, propane, and n-butane were measured in aqueous solutions of sodium dodecylsulfate (NaDS) (0–0.1M) from 15 to 27°C. From these measurements the standard Gibbs energies, entropies, and enthalpies for the process of transferring the solute molecules from the gaseous phase into the solutions were calculated. An approximate relationship was found relating the volume fraction of the micelles to NaDS concentration.     

Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.     

Time course of loudness recalibration: implications for loudness enhancement

Loudness recalibration, the effect of a relatively loud 2500-Hz recalibrating tone on the loudness of a relatively soft 2500-Hz target tone, was measured as a function of the interstimulus interval (ISI) between them. The loudness of the target tone, assessed by a 500-Hz comparison tone, declined when the ISI equaled or exceeded about 200 ms and leveled off at an ISI of about 700 ms. Notably, the target tone's loudness did not change significantly at very short ISIs (< 150 ms). The latter result is incompatible with the literature reporting loudness enhancement in this time window, but is compatible with the suggestion made by Scharf, Buus, and Nieder [J. Acoust. Soc. Am. 112, 807-810 (2002)] that early measurements of enhancement were contaminated by the influence of the recalibrating tone on the comparison tone when the two shared the same frequency. In a second experiment the frequency of the comparison tone was changed to 2500 Hz and the results of a loudness enhancement paradigm was successfully predicted from the time course of recalibration obtained in experiment 1.     

Rank of inclusion matrices and modular representation theory

We use results from the modular representation theory of the groupsS _n and GL _n (F _q ) to determine the rank of inclusion matrices.     

Revenue in contests with many participants

We show that in a contest with a single prize, the expected effort made by the k$k$th highest valuation participant bounds the sum of the expected efforts made by all of the participants with valuations less than the k$k$th highest valuations. We also show that in the limit case of a contest with m$m$ prizes, the expected effort made by the k$k$th highest valuation participant when the bidders are risk-neutral is greater than the expected effort in the risk-averse case.     

Effective Approximation for the Semiclassical Schrödinger Equation

The computation of the semiclassical Schrödinger equation presents major challenges because of the presence of a small parameter. Assuming periodic boundary conditions, the standard approach consists of semi-discretisation with a spectral method, followed by an exponential splitting. In this paper we sketch an alternative strategy. Our analysis commences with the investigation of the free Lie algebra generated by differentiation and by multiplication with the interaction potential: it turns out that this algebra possesses a structure which renders it amenable to a very effective form of asymptotic splitting: exponential splitting where consecutive terms are scaled by increasing powers of the small parameter. This leads to methods which attain high spatial and temporal accuracy and whose cost scales as \({\mathcal {O}}\!\left( M\log M\right) \) , where \(M\) is the number of degrees of freedom in the discretisation.