The distribution of the maximum of character sums

We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character sums normalized by the square root of the modulus, finding almost double exponential decay in the tail of this distribution.Comment: 16 pages, 1 figure, new version with correction

Melodia : A Comprehensive Course in Sight-Singing (Solfeggio)

Melodia is a 1904 book designed to teach sight-singing. The educational plan is by Samuel W. Cole; the exercises were written and selected by Leo R. Lewis. Melodia is presented here as a complete edition and has also been divided into its four separate books.https://scholarworks.sjsu.edu/oer/1000/thumbnail.jp

The Case for Liberal Spectrum Licenses: A Technical and Economic Perspective

The traditional system of radio spectrum allocation has inefficiently restricted wireless services. Alternatively, liberal licenses ceding de facto spectrum ownership rights yield incentives for operators to maximize airwave value. These authorizations have been widely used for mobile services in the U.S. and internationally, leading to the development of highly productive services and waves of innovation in technology, applications and business models. Serious challenges to the efficacy of such a spectrum regime have arisen, however. Seeing the widespread adoption of such devices as cordless phones and wi-fi radios using bands set aside for unlicensed use, some scholars and policy makers posit that spectrum sharing technologies have become cheap and easy to deploy, mitigating airwave scarcity and, therefore, the utility of exclusive rights. This paper evaluates such claims technically and economically. We demonstrate that spectrum scarcity is alive and well. Costly conflicts over airwave use not only continue, but have intensified with scientific advances that dramatically improve the functionality of wireless devices and so increase demand for spectrum access. Exclusive ownership rights help direct spectrum inputs to where they deliver the highest social gains, making exclusive property rules relatively more socially valuable. Liberal licenses efficiently accommodate rival business models (including those commonly associated with unlicensed spectrum allocations) while mitigating the constraints levied on spectrum use by regulators imposing restrictions in traditional licenses or via use rules and technology standards in unlicensed spectrum allocations.

Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

TRADE NEGOTIATIONS AND THE FUTURE OF AMERICAN AGRICULTURE

International Relations/Trade,

IMPACT OF INDUSTRY IN RURAL ECONOMIES: AN INPUT-OUTPUT APPROACH

Community/Rural/Urban Development,

Quaternionic potentials in non-relativistic quantum mechanics

We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to investigate an underlying quaternionic quantum dynamics in particle physics. Experimental tests and proposals to observe quaternionic quantum effects by neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te