Existence of stationary,collisionless plasmas in bounded domains

We consider a collisionless plasma, which consists of electrons and positively charged ions and is confined to a bounded domain in ?³. The distribution functions of the particles are assumed to satisfy specular reflections on the boundary of the domain and the boundary is assumed to be perfectly conducting. We establish the existence of stationary plasmas in the non-relativistic, electrostatic case described by the Vlasov–Poisson system as well as in the relativistic, electrodynamic case described by the relativistic Vlasov–Maxwell system.     

Finding minimum areak-gons

Given a setP ofn points in the plane and a numberk, we want to find a polygon with vertices inP of minimum area that satisfies one of the following properties: (1) is a convexk-gon, (2) is an empty convexk-gon, or (3) is the convex hull of exactlyk points ofP. We give algorithms for solving each of these three problems in timeO(kn ³). The space complexity isO(n) fork=4 andO(kn ²) fork5. The algorithms are based on a dynamic programming approach. We generalize this approach to polygons with minimum perimeter, polygons with maximum perimeter or area, polygons containing the maximum or minimum number of points, polygons with minimum weight (for some weights added to vertices), etc., in similar time bounds.This paper includes work done while David Eppstein was at Columbia University, Department of Computer Science, and while Günter Rote and Gerhard Woeginger were at the Freie Universität Berlin, Fachbereich Mathematik, Institut für Informatik. Research was partially supported by the ESPRIT II Basic Research Actions Program of the EC under Contract No. 3075 (project ALCOM).     

Correspondence between spin-dynamic phases and pulse program phases of NMR spectrometers

Spin state selective experiments have become very useful tools in solution NMR spectroscopy, particularly in the context of TROSY line narrowing. However, the practical implementation of such pulse sequences is frequently complicated by unexpected instrument behavior. Furthermore, a literal theoretical analysis of sequences published with specific phase settings can fail to rationalize such experiments and can seemingly contradict experimental findings. In this communication, we develop a practical approach to this ostensible paradox. Spin-dynamic design, rationalization, and simulation of NMR pulse sequences, as well as their confident and reliable implementation across current spectrometer hardware platforms, require precise understanding of the underlying nutation axis conventions. While currently often approached empirically, we demonstrate with a simple but general pulse program how to uncover these correspondences a priori in the general case. From this, we deduce a correspondence table between the spin-dynamic phases used in NMR theory and simulation on the one hand and pulse program phases of current commercial spectrometers on the other. As a practical application of these results, we analyze implementations of the original (1)H-(15)N TROSY experiment and illustrate how steady-state magnetization can be predictably, rather than empirically, added to a desired component. We show why and under which circumstances a literal adoption of phases from published sequences can lead to incorrect results. We suggest that pulse sequences should be consistently given with spin-dynamically correct (physical) phases, rather than in spectrometer-specific (software) syntax.     

Tuning high-power laser diodes with as much as 0.38 W of power and M(2) = 1.2 over a range of 32 nm with 3-GHz bandwidth

Gain-guided diode lasers usually have emission wavelengths determined by the manufacturing process, with typically 0.5-1-nm bandwidth. Furthermore, their beam quality is rather poor. We show that external cavities allow for tunable narrow-bandwidth operation of gain-guided diode lasers. At the same time the beam quality is drastically improved; almost diffraction-limited light of more than 200 mW has been achieved over the whole tuning range from 910 to 942 nm with narrow bandwidth.     

Internal electron-positron pair production from electric monopole transitions

The yield curve of the reaction⁵⁶Fe(p,γ)⁵⁷Co has been measured over the energy rangeE _p =1,300–1,900 keV and the decay of nine resonances has been investigated. For twelve of the resonances the strengths have been determined. The angular distributions of the gamma rays have been recorded for resonances atE _p =1,599, 1,623, 1,643 and 1,649 keV, giving spin-parity assignmentsJ ^π=3/2^? for all four resonances. The resonances atE _p =1,623, 1,643 and 1,649 keV have been identified as the split analogue resonances of the 367 (J ^π=3/2^?) states in⁵⁷Fe. TheM1 transition strengths to the corresponding antianalogue states have been measured and compared with theoretical predictions.     

On the verification of Clark's example of a euclidean but not norm-euclidean number field

In the preceding paper [2], D. Clark proved—modulo a finite amount of computation—that the ring of integersR of admits explicit euclidean algorithms, although it is not euclidean for the norm: In fact, every completely multiplicative function ϕ:R→R _>-0 which sends the prime elements above 23 to a value larger than 25 and which agrees with the absolute norm at all other primes defines a euclidean algorithm forR. The referee had felt that an independent verification of the computer-assisted proofs of Lemmas 1 and 2 of [2] was desirable, and that it should be carried out separately from the refereeing process in the light of the public, conforming to C. Lam's eloquent suggestions [3]. F. Lemmermeyer and the present author succeeded in confirming Clark's result (independently of each other). This note gives some details of the methods employed in the verifications.     

Exponential weak Bernoulli mixing for collet-eckmann maps

We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK] and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim , wherec is the unique critical point ofT.     

A characterization ofL n(K) as a permutation group

In 1972 M. O'Nan proved thatL _n (q),h 3; can be characterized as a doubly-transitive groupG on a finite set , whereG _a has an Abelian normal subgroup acting not semi-regularly on -a. In the Main Theorem we show that a similar statement holds if is infinite. Our result implies O'Nan's theorem.This paper is part of the author's Ph.D. thesis written under supervision of Prof. F. G. Timmesfeld.     

The influence of rotational coupling on K-vacancy formation in U-Pb collisions

The beta endpoint energies of the alkaline fission products^88–94Rb and^139–144Cs have been measured with an intrinsic Ge-detector at the OSTIS fission product separator. The linearity and high resolution of the detector yields an accuracy of up to a few keV. Additional beta gamma coincidence spectra allow the deduction of Q_β-values.