Infinite products of finite simple groups

We classify the sequences of finite simple nonabelian groups such that has uncountable cofinality.

     

Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators

We provide a short proof of that case of the Gilbert-Pearson theorem that is most often used: That all eigenfunctions bounded implies purely a.c. spectrum. Two appendices illuminate Weidmann's result that potentials of bounded variation have strictly a.c. spectrum on a half-axis.

     

Generalized logic and the representation of rings

Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation.     

On functions having Cauchy differences in some prescribed sets

Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK (6C) = {0}. If a functionh:E F is continuous at at least one point andh(x + y) – h(x) – h(y) K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E.     

有限元技术用于研究熔体生长中的小面化现象

开发了一种基于边界保角变换技术的有限元方法来处理自由边界问题,并成功地将其用于晶体定向生长过程中的界面动力学影响的研究。所建立的基于石榴石熔体生长过程的各向异性的界面动力学模型可导致相界面上小面的出现。讨论了界面动力学模型中的最大偏移角θｍａｘ对小面的形状和计算误差的影响,给出了一种十分有效地降低计算误差的措施：在模型方程中适当计人表面张力的影响。     

Accurate masses of unstable rare-earth isotopes by ISOLTRAP

Direct mass measurements of neutron-deficient rare-earth isotopes in the vicinity of ¹⁴⁶Gd were performed with the Penning trap mass spectrometer ISOLTRAP at ISOLDE/CERN. This paper reports on the measurement of more than 40 isotopes of the elements praseodymium, neodymium, promethium, samarium, europium, dysprosium and holmium, that have been measured with a typical accuracy of m 14 keV. An atomic mass evaluation has been performed taking into account other experimental mass values via a least-squares adjustment. The results of the adjustment are discussed. Received: 18 April 2000 / Accepted: 12 July 2000     

The REX-ISOLDE project

The Radioactive Beam Experiment REX-ISOLDE [1–3] is a pilot experiment at ISOLDE (CERN) testing the new concept of post acceleration of radioactive ion beams by using charge breeding of the ions in a high charge state ion source and the efficient acceleration of the highly charged ions in a short LINAC using modern ion accelerator structures. In order to prepare the ions for the experiments singly charged radioactive ions from the on-line mass separator ISOLDE will be cooled and bunched in a Penning trap, charge bred in an electron beam ion source (EBIS) and finally accelerated in the LINAC. The LINAC consists of a radiofrequency quadrupole (RFQ) accelerator, which accelerates the ions up to 0.3 MeV/u, an interdigital H-type (IH) structure with a final energy between 1.1 and 1.2 MeV/u and three seven gap resonators, which allow the variation of the final energy. With an energy of the radioactive beams between 0.8 MeV/u and 2.2 MeV/u a wide range of experiments in the field of nuclear spectroscopy, astrophysics and solid state physics will be addressed by REX-ISOLDE. This revised version was published online in July 2006 with corrections to the Cover Date.     

Observation of insulating–insulating monoclinic structural transition in macro‐sized VO2 single crystals [Phys. Status Solidi RRL 5, No. 3, R107–R109 (2011)]

In our article, we reported the observation of monoclinic M2 to M1 structural phase transition in VO₂ single crystal near the temperature of ～49 °C. However, the re‐examination of Laue patterns reveals that previously defined monoclinic M1 and M2 phases can be interpreted as monoclinic M2 and triclinic T phases instead. Careful experimental geometry calibration and further refinement of the lattice parameter ratios and angles show that monoclinic M2 and triclinic T phases fit better with the experimental data. On the other hand, our previous misidentification of the insulating phases does NOT affect the conclusions of our article. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Preparation and Eh--pH diagrams of Fe(II)--Fe(III) green rust compounds; hyperfine interaction characteristics and stoichiometry of hydroxy-chloride, -sulphate and -carbonate

Fe(II)--Fe(III) hydroxy-chloride, -sulphate and -carbonate were prepared by oxidation of a ferrous hydroxide precipitate in anion-containing aqueous solutions. The compounds are characterized by monitoring the redox potential E_h and the pH of stochiometric suspension vs time with the appropriate concentration ratios. X-ray diffraction allows us to characterize the crystal structure by distinguishing “green rust one” (GR1) from “green rust two” (GR2). Since green rusts (GRs) are of a pyroaurite-sjögrenite-like structure, i.e., consisting of intercalated foreign anions and water molecules in the interlayers between the brucite-like layers of Fe(OH)₂, their chemical formulae can be determined from the Mössbauer spectra. Three quadrupole doublets are observed: D₁ and D₂ correspond to a ferrous state with isomershift IS of about 1.27 mm s^-1 and quadrupole splittings QS of about 2.85 and 2.60 mm s^-1, respectively, whereas D₃ corresponds to a ferric state with IS and QS of about 0.4 mm s^-1. The hyperfine parameters of these doublets are similar from one green rust to another but their intensity ratios vary considerably. Finally, E_h and pH equilibrium diagrams of the Fe species in the presence of chloride, sulphate and carbonate anions contained within the water solution are drawn and the thermodynamic conditions of existence and degrees of oxidation of green rusts are discussed.     

Characterization and optimization of a laser-scanning microscope in the femtosecond regime

Received: 26 August 1997/Revised version: 2 February 1998