We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair M ⊂ N of models of set theory implying that every perfect set in N has an element in N which is not in M .

The development of cognitively plausible models of human spatial reasoning may ultimately result in computational systems that are better equipped to meet human needs. This paper explores how human subjects perceive the qualitative spatial relation nearness within an environmental space. Based on experimental data, a three-valued nearness relation is analysed in two stages. First, the results a...

In the early fties L. Schwartz posed the problem to characterize those linear partial differential operators P(D) that admit a (continuous linear) right inverse on the Fr echet space E(() of all innnitely diierentiable functions on an open set in IR n respectively on the space D 0 (() of all distributions on. This problem was solved in 6], 7]. Its solution was extended to diierential complexes ...

The notion of a first order topological structure was introduced by Pillay [1] as a generalization of the notion of an o-minimal structure. The idea is to provide a general framework in which model theory can be used to analyze a topological structure whose topology isn’t necessarily induced by a definable order. In the o-minimal case, the topology is generated from a basis where each basis set...

Spectroscopy is the study of the interaction between radiation and matter as a function of wavelength. Theoretical vibrational spectroscopy has been discussed in this paper. In this paper, various approximations for solving Schrödinger Equation have been discussed. Ab-initio methods and DFT methods, various basis set have been discussed in details.

We present a finite-size scaling approach for the calculations of the critical parameters for binding an electron to an electric dipole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. The approach is general and could be used to obtain the critical conditions for stable dipole-bound dianions. 2003 Published by E...

King and Korf [9] introduced, in the framework of a discrete-time dynamic market model on a general probability space, a new concept of arbitrage called free lunch in the limit which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbi...

This work analyses a case where.Murrell's proposal, stating that a second-order point must lie above a first-order one, is apparently violated. Study at the SCF-UMP2 level within the D95 + + basis set, of one critical point of the O2HFanion, previously proposed to be of order two by Lopez, shows the importance of the electronic correlation. The critical point associated with the 21-1 state shou...

For given quasi-continuous functions g, h with g ≤ h and diffusion process M determined by stochastic differential equations or symmetric Dirichlet forms, characterizations of the value functions eg(s, x) = sup σ J (s,x) (σ) and ¯ w(s, x) = infτ sup σ J (s,x) (σ, τ) are well studied so far. In this paper, by using the time dependent Dirichlet forms, we generalize these results to time inhomogen...

For two high-quality piecewise polynomial geometrically smooth (G) surface constructions, explicit G functions are derived that form the basis of a functions space on the G surfaces. The spaces are refinable and nested, i.e. the functions can be rerepresented at a finer level. By choosing all basis functions to be first order smooth a maximal set of degrees of freedom is obtained that have smal...