Ultraslow phonon-assisted collapse of tubular image states

We predict ultraslow collapse of “tubular image states” (TIS) on material surfaces. TIS are bound Rydberg-like electronic states formed at large distances (∼30 nm) from the surfaces of suspended circularly-symmetric nanowires, such as metallic C nanotubes. The states are formed in potential wells, resulting from a combination of the TIS-electron attraction to image charges in the nanotube and its centrifugal repulsion, caused by spinning around the tube. We demonstrate that TIS can collapse on the tube surface by passing their angular momentum l to circularly polarized flexural phonons excited in the tube. Our analysis shows that for highly detached TIS with l ? 6 the relaxation lifetimes are of the order of 10 ns-1 μs, while for l < 6 these lifetimes are reduced by several orders of magnitude.     

The boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption

In the first part of the paper we establish the existence of a boundary trace for positive solutions of the equation ?Δu + g(x, u) = 0 in a smooth domain Ω ? ?^N, for a general class of positive nonlinearities. This class includes every space independent, monotone increasing g which satisfies the Keller‐Osserman condition as well as degenerate nonlinearities g_α,q of the form g_α,q (x, u) = d(x, ?Ω)^α |u|^q?1 u, with α > ?2 and q > 1. The boundary trace is given by a positive regular Borel measure which may blow up on compact sets. In the second part we concentrate on the family of nonlinearities {g_α,q}, determine the critical value of the exponent q (for fixed α > ?2) and discuss (a) positive solutions with an isolated singularity, for subcritical nonlinearities and (b) the boundary value problem for ?Δu + g_α,q (x, u) = 0 with boundary data given by a positive regular Borel measure (possibly unbounded). We show that, in the subcritical case, the problem possesses a unique solution for every such measure. © 2003 Wiley Periodicals, Inc.     

Information recovery from black holes

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss. First Award in the 2006 Essay Competition of the Gravity Research Foundation.     

Solving a class of multiplicative programming problems via c-programming

In this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kunoet al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]–[8] and its techniques.     

Calculation of the infrared spectrum and density of the vibrational states of an SiO2 melt by molecular dynamics

The density of the vibrational states of an SiO₂ melt under various PT conditions, the distributions of the Si-O-Si and O-Si-O angles in it, and its IR absorption spectra have been calculated by molecular dynamics with the use of a pairwise additive Born-Mayer potential. A comparison with the experimental data reveals that the ionic approximation selected is capable of basically reproducing the structural and spectroscopic properties of the melt, but the distributions of the bond angles are considerably broader than the experimentally determined distributions, and the absorption band caused by the stretching vibrations is not displayed in the calculated spectrum. The disparities indicated are apparently due to the isotropic nature of the potential of the interparticle interactions.V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 467–470, July–August, 1991. Original article submitted October 12, 1990.     

Stable Subnorms II

In this paper we continue our study of stability properties of subnorms on subsets of finite-dimensional, power-associative algebras over the real or the complex numbers.     

Inverse Pattern Matching

Let a textstringTofnsymbols from some alphabet Σ and an integerm < nbe given. A patternPof lengthmover Σ is sought such thatPminimizes (alternatively, maximizes) the total number of pairwise character mismatches generated whenPis compared with allm-character substrings ofT. Two additional variants of the problem are obtained by adding the constraint thatPbe (respectively, not be) a substring ofT. Efficient sequential algorithms are proposed in this paper for the problem and its variants.     

Policies for biodefense revisited: The prioritized vaccination process for smallpox

Handling bioterror events that involve contagious agents is a major concern for authorities and a cause for debate among policymakers about the best response policy. At the core of this debate stands the question which of the two post-event policies to adopt: mass vaccination or trace (also called ring or targeted) vaccination. We present a new dynamic epidemic-intervention model that captures key features of the situation and generalizes some previous assumptions regarding the probability distributions of inter-temporal parameters. It is shown that a mixture of mass and trace vaccination policies—the prioritized vaccination policy—is more effective than either of the two aforementioned policies.     

Analysis of a class of fractional programming problems

We propose a solution strategy for fractional programming problems of the form max _xx g(x)/ (u(x)), where the function satisfies certain convexity conditions. It is shown that subject to these conditions optimal solutions to this problem can be obtained from the solution of the problem max _xx g(x) + u(x), where is an exogenous parameter. The proposed strategy combines fractional programming andc-programming techniques. A maximal mean-standard deviation ratio problem is solved to illustrate the strategy in action.