Randers space forms

This note chronicles various roles played by the Yasuda-Shimada theorem in some recent developments of Riemann--Finsler geometry. We shall demonstrate that the said theorem is, at various stages of its life, an enigma, an inspiration, a flawed icon, and a powerful catalyst.     

Halogenation effects on the conformational properties of alkanes

The rotational barriers of the CC bonds of halocarbons are believed to be rather different than those of hydrocarbons. We wish to systematically study the effect of halogen substituents on the conformational flexibility of hydrocarbons. As our initial approach to this problem, we have synthesized the following molecules: Pyrene-(CF₂)_n-Pyrene (n=3, 4, and 6) and Pyrene-(CF₂)_n-F (n=4 and 6). We describe here the concentration and temperature dependence of the emissive behavior of these materials.     

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning.     

Oscillations of linear integro-differential equations

Sufficient conditions which guarantee that certain linear integro-differential equation cannot have a positive solution are established.     

Emergence of classicality for primordial fluctuations: Concepts and analogies

We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as the robust pointer basis. We discuss in detail the interplay between these features and use simple analogies such as the free quantum particle to illustrate the main conceptual issues.