We calculate the linear response thermopower S of a quantum point contact using the Landauer formula and therefore assume non-interacting electrons. The purpose of the paper is to compare analytically and numerically the linear thermopower S of non-interacting electrons to the low-temperature approximation, [Formula: see text], and the so-called Mott expression, [Formula: see text], where G(μ,T...

Hurwitz formula for the generalized zeta function zeta (s,a) has been established under condition Re(s) = sigma < 0. Using the same contour integral, the proof proposed ill this paper allows the extension of this formula into the critical strip, 0 = a < 1. A similar result is obtained for the related function (1/Gamma (s)) integral (infinity)(0) x(s-1)(e(ax)/(1 + e(-x)))dx, 0 < a < 1.

We present a short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem based on Ore’s Defect Formula and Anderson’s proof of Tutte’s 1-Factor Theorem from Hall’s Theorem. The fundamental theorems on matchings in graphs have been proved in many ways, and generally they all imply each other. The most well-known is Hall’s Theorem [7] characterizing when a bipartite graph has ...

[This document is http://www.math.umn.edu/ ̃garrett/m/complex/notes 2014-15/09c Riemann and zeta.pdf] 1. Riemann’s explicit formula 2. Analytic continuation and functional equation of ζ(s) 3. Appendix: Perron identity [Riemann 1859] exhibited a precise relationship between primes and zeros of ζ(s). A similar idea applies to any zeta or L-function with analytic continuation, functional equation, ...

In this note, we show that Radford's formula for the fourth power of the antipode can be proven for any regular multiplier Hopf algebra with integrals (algebraic quantum groups). This of course not only includes the case of a finite-dimensional Hopf algebra but also the case of any Hopf algebra with integrals (co-Frobenius Hopf algebras). The proof follows in a few lines from well-known formula...

The Black-Scholes ( 1973) option pricing model is a universal standard among option valuation models. Despite its widespread popularity, however, the model has some known deficiencies in actual applications. For example, when calibrated to accurately price at-the-money options, the Black-Scholes model frequently misprices deep in-the-money and deep out-of-the-money options. Pricing biases assoc...

Theoretical analysis of Raman scattering spectra (RS) for single-crystal MoS2 sample and atomically thin MoS2 sample consisting from one to few layers was performed in order to explain the change of MoS2 vibrations at transition from a monoatomic layer to a bulk crystal. Experiments have shown that changes of frequencies of the most intensive bands arising from the in-plane, [Formula: see text]...

In various triangulated motivic categories, a vast family of aisles (these are certain classes objects) is introduced. These defined in terms the corresponding “motives” (or spectra) smooth varieties; it proved that they expressed homotopyt<mml:annotati...

In this paper, we express De Moivre’s formula for split quaternions and …nd roots of a split quaternion using this formula. MSC 2000 : 53B30, 15A66.

A formula for the generating function of prime repunits is given in terms of a Lambert series using S. Golomb’s formula.