Reactions of 5-cyano-1,4,6,9-trioxathia-5-phosphaspiro[4,4]nonanes with compounds containing a labile hydrogen atom

All the investigated reactions of 5-cyano-1,4,6,9-trioxathia-5-phosphaspiro[4,4]nonanes with compounds containing a labile hydrogen atom proceed with the loss of HCN, predominant opening of the oxathiophospholane ring, and formation of 2-oxo-1,3,2-dioxaphospholane derivatives.A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Science Center, Russian Academy of Sciences, 420083 Kazan. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 11, p. 2670–2673, November, 1992.     

Where are the Sn atoms in LaSb2Snx, 0.1?x?∼0.75?

The composition range and (composite modulated) structure of compounds within the wide range non-stoichiometric LaSb₂Sn_x, 0.1?x?0.75, solid solution is carefully investigated via a combined electron diffraction, XRD and electron probe microanalysis study. Evidence for metastability of the LaSb₂Sn_x phase at the low x composition end of the solid solution is presented. Direct evidence is found for a reasonably (although by no means perfectly) well ordered Sn sub-structure which is, in general, mutually incommensurable with respect to a very well ordered underlying LaSb₂ sub-structure along both a and c directions. The overall (3+2)-d superspace group symmetry is given along with a discussion of the consequences as regards the arrangement of the Sn atoms. The Sn sub-structure c-axis cell dimension shows very little variation with composition x providing direct experimental evidence of the importance of Sn-Sn metallic bonding (along one-dimensional [001] Sn strings) for the stability of the phase.     

A new Far-Infrared Fourier Spectrometer

Summary This article describes a new commercial Far-Infrared Fourier Spectrometer system which has been developed for routine spectroscopy in the 10–1000 cm^–1 spectral region. The instrument incorporates real-time data processing and has been automated wherever possible for foolproof operation. A versatile sample chamber allows a wide range of spectroscopic studies to be performed, on solids, liquids and gases over a wide range of temperatures. A number of spectra are presented to illustrate the performance and typical applications of this Fourier spectrometer.

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Ein neues fourier-spektrometer für das ferne infrarot

Zusammenfassung Nach einer kurzen Einführung in die Methode der Fourier-Spektroskopie wird ein neues kommerzielles Fern-Infrarot-Fourier-Spektrometer mit real-time Datenverarbeitungsanlage beschrieben. Das Gerät ist für die Spektroskopie im Bereich 10–1000 cm^–1 konstruiert und weitgehend automatisiert. Eine vielseitig verwendbare Probenkammer ermöglicht umfangreiche spektroskopische Untersuchungen von Festkörpern, Flüssigkeiten und Gasen in einem sehr großen Temperaturbereich. Anhand einer Reihe von Spektren werden Leistung und typische Anwendungen dieses Fourier-Spektrometers erläutert.

Lecture presented at Euroanalysis I Conference, 28. 8.–1. 9. 1972 in Heidelberg, Germany.     

A Laplace-like method for solving linear difference equations

This paper is concerned with the problem of solving linear difference equations of ordern with constant coefficients and with given initial conditions in which the variable runs not only through the integers but over . The main idea is the introduction of a suitable commutative ring of functions with discrete convolution as multiplication rule which works, although it is not a field. The existence of inverses is studied and, after the introduction of suitable functions, the problem is reduced by means of a Laplace-like relation to an algebraic equation. Examples of application are given. Finally some remarks make the connection with the Operational Calculus of Mikusinski and with the Operational Calculus of Fenyö. The advantages of this method lie in the fact that it is applicable to functions others than the step functions, in its simplicity from the theoretical point of view, in its usefulness even when computation is required and in its formal similarity to the classical treatment of linear differential equations with constant coefficients.     

Approximation under an arc length constraint

Let f C[a, b]. LetP be a subset ofC[a, b], L b – a be a given real number. We say thatp P is a best approximation tof fromP, with arc length constraintL, ifA[p] _b ^a [1 + (p(x)) ²]dx L andp – f q – f for allq P withA[q] L. represents an arbitrary norm onC[a, b]. The constraintA[p] L might be interpreted physically as a materials constraint.In this paper we consider the questions of existence, uniqueness and characterization of constrained best approximations. In addition a bound, independent of degree, is found for the arc length of a best unconstrained Chebyshev polynomial approximation.The work of L. L. Keener is supported by the National Research Council of Canada Grant A8755.     

Symmetrische Permutationsmengen

A permutation set (M, I) consisting of a setM and a set of permutations ofM, is calledsymmetric, if for any two permutations, the existence of anx M with (x) (x) and ^–1 (x) = ^–1 (x) implies ^–1 = ^–1 , andsharply 3-transitive, if for any two triples (x ₁,x ₂,x ₃), (y ₁,y ₂,y ₃) M ³ with|{x ₁,x ₂,x ₃ }| = |{y ₁,y ₂,y ₃ }| = 3 there is exactly one permutation with(x ₁) =y ₁,(x ₂) =y ₂,(x ₃) =y ₃. The following theorem will be proved.THEOREM.Let (M, ) be a sharply 3-transitive symmetric permutation set with |M|3, such that contains the identity. Then is a group and there is a commutative field K such that and the projective linear group PGL(2, K) are isomorphic.     

Characterization of the normal distribution by constant regression of quadratic statistics on linear statistics

This paper contains applications of theorems of [1] for quadratic statistics which have constant regression on linear statistics. Two theorems are proved. The first is a sufficient condition which assumes that the characteristic function of a sample is an entire function. The second gives a new characterization of the normal distribution.     

On the divergence of certain Hermite-Fejér interpolation

Summary In his paper [1]P. Turán discovers the interesting behaviour of Hermite-Fejér interpolation (based on the ebyev roots) not describing the derivative values at exceptional nodes {_n} _n=1 . Answering to his question we construct such exceptional node-sequence for which the mentioned process is bounded for bounded functions whenever –1<x<1 but does not converge for a suitable continuous function at any point of the whole interval [–1, 1].     

~(14)N ENDOR Study on Bis(2-Hydroxylphenyl Ketoxime)-~(63)Cu(Ⅱ) Complex

The ENDOR spectrum of ~(14)N-~(63)Cu-HAP complex in DMSO/EtOH (5:1) freezing solution at 20 K has been studied using orientational selective method in this paper. The anisotropic superhyperfine coupling tensor and qusdrupole coupling tensor of ligand ~(14)N nucleus, and the superhyperfine coupling tensor of various ~1H nuclei have been measured precisely. Comparing the superhyperfine coupling tensor of ~(14)N-nucleus with previous work shows that the analytical method of spectrum is reasonable and the data are reliable in our previous work.     

Synthesis and reactivity of thieno[2,3-<Emphasis Type="Italic">b</Emphasis>]pyridine-2,3-diamines

It has been established that the interaction of N¹-(2-hydroxyphenylmethylthieno[2,3-b]pyrid-3-yl)arylamides with hydrazine hydrate leads to thieno[2,3-b]pyridine-2,3-diamines. It was shown that the reaction of the latter with acetylacetone and acetoacetic ester occurs regioselectively at the amino group in position 3 of the thiophene ring. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1400–1408, September, 2007.