We consider the effects of bath size on the nature of the dynamics and transport properties for two simple models in which the bath is composed of a collinear chain of harmonic oscillators. The first model consists of an untwisted rotating chain (elastic rotor) for which we obtain a non-Markovian equation analogous to the generalized Langevin equation for the rotational degrees of freedom. We d...

Motivated by Wiener's work on generalized harmonic analysis, we consider the Marcinkiewicz space 6XP(R) of functions of bounded upper averagep power and the space St(R) of functions of bounded upper p variation. By identifying functions whose difference has norm zero, we show that St(R), 1 <p < oo, is a Banach space. The proof depends on the result that each equivalence class in cVP(R) contains...

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

We investigate 3-adic valuations of generalized harmonic numbers H n . These valuations are completely determined by the 3-adic expansion of n. Moreover, we also give 3-adic valuations of generalized alternating harmonic numbers.

&lt;abstract&gt;&lt;p&gt;This paper introduces a generalization of the alternating harmonic series, expresses sum in two closed forms, and examines relationship between these sums numbers.&lt;/p&gt;&lt;/abstract&gt;

It is shown that a large class of systems non-linear wave equations, based on the good-bad-ugly model, admit formal solutions with polyhomogeneous expansions near null infinity. A particular set variables introduced which allows us to write Einstein field equations in generalized harmonic gauge as system and functional form first few orders such an expansion found by applying aforementioned res...