A Glivenko-Cantelli Theorem and Strong Laws for L-Statistics

We prove a weighted Glivenko-Cantelli theorem and apply it to study the rate of convergence in the strong law for L-statistics.     

On a problem of Zygmund

It is proved that there exists an integrable function on [0, 1]² whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 749–762, November, 1998.     

Magnetic order in LaEuSrCuO studied [2pt] by Fe Mössbauer spectroscopy

⁵⁷Fe M?ssbauer effect studies of La_1.65Eu_0.20Sr_0.15CuO₄ doped with 0.5 at% ⁵⁷Fe performed in the temperature region 300 K > T > 4.2 K give an onset temperature for magnetic ordering of K. This temperature practically is the same as that found in Nd doped La_2-xSr_xCuO₄. It indicates that the magnetic ordering temperature in the LTT phase of rare earth (RE) doped La_2-xSr_xCuO₄ is independent of the RE moment. The direction of the ⁵⁷Fe magnetic moment in the magnetically ordered state is within the CuO₂ plane, while it has been found to be parallel to the c-axis in Nd doped La_2-xSr_xCuO₄. Received: 23 June 1998 / Accepted: 14 July 1998     

Evolution of shapes in 59Cu

High-spin states in ⁵⁹Cu were populated using the fusion-evaporation reaction ²⁸Si + ⁴⁰Ca at a beam energy of 122 MeV. The Gammasphere Ge-detector array in conjunction with the 4π charged-particle detector array Microball allowed for the detection of γ-rays in coincidence with evaporated light particles. The resulting extensive high-spin decay scheme of ⁵⁹Cu is presented, which comprises more than 320 γ-ray transitions connecting about 150 excited states. Their spins and parities have been assigned via directional correlations of γ-rays emitted from oriented states. Average quadrupole moments of rotational bands have been determined from the analysis of residual Doppler shifts. Shell model calculations in the fp shell are invoked to study some of the low-spin states, while the experimental characteristics of the rotational bands are analyzed in the configuration-dependent cranked Nilsson-Strutinsky (CNS) approach. Received: 15 February 2002 / Accepted: 23 April 2002     

Optimale Quantisierung

Zusammenfassung. Optimale Quantisierungen oder – damit ?quivalent – minimale Summen von Momenten spielen in mehreren Zweigen der Mathematik und ihrer Anwendungen eine Rolle. Ausgehend von der Fejes Tóth'schen Ungleichung für Summen von Momenten in der euklidischen Ebene und einem zugeh?rigen Stabilit?tssatz, werden gewisse Erweiterungen auf normierte R?ume und riemannsche Mannigfaltigkeiten h?herer Dimension besprochen. Die Ergebnisse werden dann auf Probleme aus folgenden Bereichen angewendet: (i) Datenübertragung, (ii) Wahrscheinlichkeitstheorie, (iii) numerische Integration, (iv) Approximation konvexer K?rper und (v) isoperimetrische Probleme. Eingegangen am 29. Mai 2002 / Angenommen am 8. Juli 2002     

超模的同构定理

本文利用模论导出超模的三个同构定理,同时,给出超模的Jordan-Holder定理,最后,探讨了超模的基本关系∈~*,并研究其性质．     

Nuclear forward scattering vs. conventional Mössbauer studies of atomically tailored Eu-based materials

With the decrease in size of devices, rapid characterization of nano-devices is an inevitable necessity. It is shown that Mössbauer spectroscopy using synchrotron radiation from the advanced photon source provides such a tool of investigation. Results are presented and compared for conventional Mössbauer and Nuclear Forward Scattering for ¹⁵¹Eu-doped magnesium sulfide as an example, especially at low concentrations.     

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

Mössbauer, X-ray diffraction and magnetization studies of Fe–Mn–Al–Nb alloys prepared by high energy ball milling

Fe₆₀Mn₁₀Al₂₀Nb₁₀, (Fe₆₀Mn₁₀Al₃₀)₉₅Nb₅ and (Fe₆₀Mn₁₀Al₃₀)₉₀Nb₁₀ ball milled powdered alloys were investigated using X-ray diffraction, Mössbauer spectrometry, thermomagnetic (TGM) and magnetization measurements. We studied the influence of Nb content and of different milling times on the structural and magnetic properties. Two main features can be concluded: (1) the FeAlMn induces a BCC phase whatever the Nb content is, and (2) as both increasing Nb content and milling time give rise to an highly disordered state in conjunction with a decrease of the ferromagnetic behavior.     

How much sweetness is there in the universe?

We continue investigations of forcing notions with strong ccc properties introducing new methods of building sweet forcing notions. We also show that quotients of topologically sweet forcing notions over Cohen reals are topologically sweet while the quotients over random reals do not have to be such. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)