New Variational Principles in Classical and Semiclassical Mechanics

We demonstrate that reciprocal Maupertuis' Principle is the classical limit of Schr\"{o}dinger's Variational Principle in Quantum Mechanics.Comment: To appear in the Michael Marinov Memorial Volume, "Multiple facets of quantization and supersymmetry", edited by M. Olshanetsky and A. Vainshtein (World Scientific). We corrected TEX style of the paper so that the names of both authors can be seen in PS file no

On the resonances and eigenvalues for a 1D half-crystal with localised impurity

We consider the Schr\"odinger operator $H$ on the half-line with a periodic potential $p$ plus a compactly supported potential $q$. For generic $p$, its essential spectrum has an infinite sequence of open gaps. We determine the asymptotics of the resonance counting function and show that, for sufficiently high energy, each non-degenerate gap contains exactly one eigenvalue or antibound state, giving asymptotics for their positions. Conversely, for any potential $q$ and for any sequences (\s_n)_{1}^\iy, \s_n\in \{0,1\}, and (\vk_n)_1^\iy\in \ell^2, \vk_n\ge 0, there exists a potential $p$ such that \vk_n is the length of the $n$-th gap, $n\in\N$, and $H$ has exactly \s_n eigenvalues and 1-\s_n antibound state in each high-energy gap. Moreover, we show that between any two eigenvalues in a gap, there is an odd number of antibound states, and hence deduce an asymptotic lower bound on the number of antibound states in an adiabatic limit.Comment: 25 page

Distributed representations accelerate evolution of adaptive behaviours

Animals with rudimentary innate abilities require substantial learning to transform those abilities into useful skills, where a skill can be considered as a set of sensory - motor associations. Using linear neural network models, it is proved that if skills are stored as distributed representations, then within- lifetime learning of part of a skill can induce automatic learning of the remaining parts of that skill. More importantly, it is shown that this " free- lunch'' learning ( FLL) is responsible for accelerated evolution of skills, when compared with networks which either 1) cannot benefit from FLL or 2) cannot learn. Specifically, it is shown that FLL accelerates the appearance of adaptive behaviour, both in its innate form and as FLL- induced behaviour, and that FLL can accelerate the rate at which learned behaviours become innate

Unary enhancements of inherently nonfinitely based semigroups

We exhibit a simple condition under which a finite involutary semigroup whose semigroup reduct is inherently nonfinitely based is also inherently nonfinitely based as a unary semigroup. As applications, we get already known as well as new examples of inherently nonfinitely based involutory semigroups. We also show that for finite regular semigroups, our condition is not only sufficient but also necessary for the property of being inherently nonfinitely based to persist. This leads to an algorithmic description of regular inherently nonfinitely based involutory semigroups.Comment: 11 pages, 1 figure. Section 4 has been improved and expanded according to suggestions of an anonymous referee of the journal version. A few minor improvements have been done in Section

The Earned Income Tax Credit

Since its inception in 1975, the Earned Income Tax Credit (EITC) has grown into the largest, Federally-funded means-tested cash assistance program in the United States. In this chapter, we review the political history of the EITC, its rules and goals and provide a broad set of program statistics on its growth and coverage. We summarize conceptual underpinnings of much of the recent economic research on the EITC, discussing participation in the credit and compliance with its provisions, and its effects on labor force participation and hours of work, marriage and fertility, skill formation and consumption. We note that participation rates of the credit are high, rates of credit noncompliance are also high, and that there are theoretical reasons to prefer the EITC to other anti-poverty programs if one's objective is to encourage work among the poor. We also note that the predicted effects of the EITC are not all pro-work, especially with respect to hours and its labor market incentives for two-earner couples. We then summarize the existing empirical research on the behavioral effects of the EITC, paying particularly emphasis to the effects of the 1986, 1990 and 1993 expansions of the credit on labor force participation and hours of work. The literature provides consistent evidence, generated from a variety of empirical approaches, that the EITC positively affects labor force participation. The literature also finds smaller, negative effects on hours of work for people already in the labor market and for secondary workers. We conclude the chapter with a discussion of the ongoing EITC-related policy debates and highlight what, if any, critical economic issues underlie these debates.

Thermal-structural test facilities at NASA Dryden

The National Aero-Space Plane (NASP) has renewed interest in hypersonic flight and hot-structures technology development for both the airframe and engine. The NASA Dryden Thermostructures Research Facility is a unique national facility that was designed to conduct thermal-mechanical tests on aircraft and aircraft components by simulating the flight thermal environment in the laboratory. The layout of the facility is presented, which includes descriptions of the high-bay test area, the instrumentation laboratories, the mechanical loading systems, and the state-of-the-art closed-loop thermal control system. The hot-structures test capability of the facility is emphasized by the Mach-3 thermal simulation conducted on the YF-12 airplane. The Liquid-Hydrogen Structural Test Facility, which is presently in the design phase, will provide the capability of thermally testing structures containing hydrogen