On Diamond's L1L^1 criterion for asymptotic density of Beurling generalized integers

We give a short proof of the $L^{1}$ criterion for Beurling generalized integers to have a positive asymptotic density. We actually prove the existence of density under a weaker hypothesis. We also discuss related sufficient conditions for the estimate $m(x)=\sum_{n_{k}\leq x} \mu(n_k)/n_k=o(1)$, with $\mu$ the Beurling analog of the Moebius function.Comment: 13 page

Optimal Tauberian constant in Ingham's theorem for Laplace transforms

It is well known that there is an absolute constant $\mathfrak{C}>0$ such that if the Laplace transform $G(s)=\int_{0}^{\infty}\rho(x)e^{-s x}\:\mathrm{d}x$ of a bounded function $\rho$ has analytic continuation through every point of the segment $(-i\lambda ,i\lambda )$ of the imaginary axis, then $$\limsup_{x\to\infty} \left|\int_{0}^{x}\rho(u)\:\mathrm{d}u - G(0)\right|\leq \frac{ \mathfrak{C}}{\lambda} \: \limsup_{x\to\infty} |\rho(x)|.$$ The best known value of the constant $\mathfrak{C}$ was so far $\mathfrak{C}=2$. In this article we show that the inequality holds with $\mathfrak{C}=\pi/2$ and that this value is best possible. We also sharpen Tauberian constants in finite forms of other related complex Tauberian theorems for Laplace transforms.Comment: 22 page

A(e,e'p) reactions at GeV energies

An unfactorized and relativistic framework for calculating A(e,e'p) observables at typical JLAB energies is presented. Results of (e,e'p) model calculations for the target nuclei ^{12}C and ^{16}O are presented and compared to data from SLAC and JLAB.Comment: 8 pages, 3 figures, Proceedings of the Third International Conference on Perspectives in Hadronic Physics (Trieste, 2001

On General Prime Number Theorems with Remainder

We show that for Beurling generalized numbers the prime number theorem in remainder form \pi(x) = \operatorname*{Li}(x) + O\left(\frac{x}{\log^{n}x}\right) \quad \mbox{for all } n\in\mathbb{N} is equivalent to (for some $a>0$) N(x) = ax + O\left(\frac{x}{\log^{n}x}\right) \quad \mbox{for all } n \in \mathbb{N}, where $N$ and $\pi$ are the counting functions of the generalized integers and primes, respectively. This was already considered by Nyman (Acta Math. 81 (1949), 299-307), but his article on the subject contains some mistakes. We also obtain an average version of this prime number theorem with remainders in the Ces\`aro sense.Comment: 15 page

Complex Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior

We provide several Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior. Our results generalize and improve various known versions of the Ingham-Fatou-Riesz theorem and the Wiener-Ikehara theorem. Using local pseudofunction boundary behavior enables us to relax boundary requirements to a minimum. Furthermore, we allow possible null sets of boundary singularities and remove unnecessary uniformity conditions occurring in earlier works; to this end, we obtain a useful characterization of local pseudofunctions. Most of our results are proved under one-sided Tauberian hypotheses; in this context, we also establish new boundedness theorems for Laplace transforms with pseudomeasure boundary behavior. As an application, we refine various results related to the Katznelson-Tzafriri theorem for power series

On PNT equivalences for Beurling numbers

In classical prime number theory several asymptotic relations are considered to be "equivalent" to the prime number theorem. In the setting of Beurling generalized numbers, this may no longer be the case. Under additional hypotheses on the generalized integer counting function, one can however still deduce various equivalences between the Beurling analogues of the classical PNT relations. We establish some of the equivalences under weaker conditions than were known so far

Harmonic effects on induction and line start permanent magnet machines

Power Electronics (PE) are implemented in a wide variety of appliances, either to increase its controllability or energy efficiency, or simply because a DC supply is needed. The massive integration of rectifiers has resulted in a decrease of the supply voltage quality. Although PE have enabled the end user to control electrical machines, the resulting distortion inversely affects Direct On-Line (DOL) machines. In this paper a review is presented of the influence of these supply anomalies on Induction Motors (IM). The suggested problems have already been subject of much study. However, as new DOL technologies are emerging, for example Line Start Permanent Magnet Machines or Induction Generator systems, the influence of supply distortion on these systems should also be considered. This paper will present a comprehensive overview of the loss mechanisms, the magnitude of the losses and the impact of these losses on operation of IM, LSPMM and IG