Fourier series and the conjugate function in the classes ϕ(L)

Обозначим через ? (L) кл асс всех ?-интегрируе мых 2π-периодических функ ций. При ограничении?(L)?L ¹ устанавливаются необходимые и достат очные условия, которым долж на удовлетворять?(t), что бы для каждой функцииf(x)ε ?(L) а) тригонометрически й ряд Фурье сходился в метрике ?, в) (С, а) средние ряда Фур ье сходились в метрик е ? для некоторого α > 0, с) сопряженная функци я \(\tilde f(x)\) также принадлежал а классу?(L).     

Mössbauer studies of thiospinels. V. The systems Cu1−xFexMe2S4 (Me = Cr, Rh) and Cu1−xFexCr2(S0.7Se0.3)4

With the exception of FeRh₂S₄, powder samples of all systems studied have been obtained as spinel phase without essential impurities. The lattice constants follow Vegard's law. From the Seebeck coefficients and the Mössbauer spectra the valence distribution Cu¹⁺_1−xFe²⁺_2x−1Fe³⁺_1−x[Me³⁺₂]X²⁻₄ is derived for 0.5 x 1, while there is only Fe³⁺ present for 0 < x 0.5. Samples with the overall composition FeRh₂S₄ contain mostly Rh₂S₃ and iron sulfide phases, but less than 20% of a spinel phase.     

1H-NMR-spektroskopische Analyse von 2-Chlor-1.3.2-dioxarsolan

The¹H-NMR-spectral data of 2-chloro-1.3.2-dioxarsolane are presented and discussed. The protons of the methylene groups form in concentrated solutions by rapide chlorine exchange anAAAA spin system. In dilute solutions the protons form anAABB spin system, which is changed to anAAAA system by addition of chlorine ions.The vicinal H–C–C–H-coupling constants indicate a twist-envelope conformation.

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Mit 1 Abbildung     

Windschiefe Kongruenzflächen konstanten Dralls

In this paper we study the curves of a surface ( _T -lines) which are base curves of ruled surfaces for which the parameter of distribution O has a constant value. Moreover we assume that the ruled surfaces belong to a given congruenceT of surface tangents of . Relations are established between the _T -lines and other curves of (asymptotic lines, lines of curvature, k _T -lines). The _T -lines are used to characterize the pseudospheres and the helicoids. The _T -lines of the surfaces of revolution are determined if the congruenceT consists of the tangents of the circles of latitude.

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Herrn WERNER BURAU zum 70.Geburtstag     

Sweet like chocolate

A new crystalline form of αβ‐d ‐lactose prepared by oven drying a concentrated aqueous solution of d ‐lactose is a lesson in the power of observation and the rigorous analysis of powder samples.     

Matrix Infrared Spectroscopy and Quantum‐Chemical Calculations for the Coinage‐Metal Fluorides: Comparisons of Ar?AuF,Ne?AuF,and Molecules MF2 and MF3

The reactions of laser‐ablated Au, Ag, and Cu atoms with F₂ in excess argon and neon gave new absorptions in the M? F stretching region of their IR spectra, which were assigned to metal‐fluoride species. For gold, a Ng? AuF bond was identified in mixed neon/argon samples. However, this bonding was much weaker with AgF and CuF. Molecules MF₂ and MF₃ (M=Au, Ag, Cu) were identified from the isotopic distribution of the Cu and Ag atoms, comparison of the frequencies for three metal fluorides, and theoretical frequency calculations. The AuF₅ molecule was characterized by its strongest stretching mode and theoretical frequency calculations. Additional evidence was observed for the formation of the Au₂F₆ molecule.