We obtain some well-known expansions for the Lerch transcendent and the Hurwitz zeta function using elementary Fourier analytic methods. These Fourier series can be used to analytically continue the functions and prove the classical functional equations, which arise from the relations satisfied by the Fourier conjugate and flat Fourier series. In particular, the functional equation for the Riem...

A simple chemical vapor deposition technique at atmospheric pressure (APCVD) is adopted to synthesize the aligned arrays of functionalized multi-walled carbon nanotubes (AMWCNTs) without using any carrier gas, at 230◦C, 750◦C and 850 ◦C. Camphor (C10H16O) is used as carbon source because this botanical hydrocarbon is chip and abundant which convert the CVD technique to a green method for produc...

The MD simulations have been performed using the OPLS force-field [1]. The toluene and phosphine molecules have been treated as fully rigid bodies, whereas the borane molecule has been also parametrized for pyramidalization and aryl torsions. The functional form of the force-field consists of harmonic terms for bond stretching and angle bending, Fourier series for torsional energetics, and Coul...

We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of "stochastic feedback". We illustrate this approach by considering at a coarse-grained level the neuroautonomic regulation of the heart rate. The model generates complex dynamics and successfully acounts for key characteristics of cardiac variability, including the l/f pow...

We consider the question of how the cardiac rhythm spontaneously self-regulates and propose a new mechanism as a possible answer. We model the neuroautonomic regulation of the heart rate as a stochastic feedback system and find that the model successfully accounts for key characteristics of cardiac variability, including the 1/f power spectrum, the functional form and scaling of the distributio...

For a number field K with ring of integers O K , we prove an analogue over finite rings of the form O K /P m of the Fundamental Theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where P is a big enough prime ideal of O K and m > 1. In the appendix, F. to the functional equation of L-functions of Dirichlet type associated with prehomogeneous vector spaces.

Tests of hypotheses associated with the functional linear model are investigated under smoothness assumptions. The tests considered are those which use a quadratic-form test statistic calculated on a high-dimensional discrete model that is obtained by Fourier transformation. Asymptotic performance bounds for this class of tests are deduced under rates-of-testing theory, and explicit formulas ar...

A method and system for pattern recognition and processing is reported that has a data structure and theoretical basis that are unique. This novel approach anticipates the signal processing action of an ensemble of neurons as a unit and intends to simulate aspects of brain that give rise to capabilities such as intelligence, pattern recognition, and reasoning that have not been reproduced with ...