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].     

Isocyanide addition to MN2(CO)5(Ph2PCH2PPh2)2 and the formation of a four-electron doubly-bridging isocyanide

The reactions of Fe(CO)₅, Fe(CO)₄P(C₆H₅)₃, M(CO)₆ (M  W, Mo, Cr), and (CH₃C₅H₄Mn(CO)₃ with KH and several boron and aluminium hydrides were investigated. Iron pentacarbonyl was converted quantitatively to K⁺Fe(CO)₄-(CHO) by hydride transfer from KBH(OCH₃)₃ allowing isolation of [P(C₆H₅)₃]₂-Nⁿ⁺Fe(CO)₄(CHO)^? in 50% yield. Lower yields were obtained with LiBH(C₂H₅)₃, and other hydride sources gave little or no formyl product. The stability of Fe(CO)₄(CHO)^? in THP was found to depend on the cation, decreasing in the order [P(C₆H₅)₃]₂N⁺ > K⁺ > Na⁺ > Li⁺. No formyl complexes were isolated and no spectroscopic evidence for formyl formation was observed in the reactions of the other transition metal carbonyls with several hydride sources. Fe(CO)₄-P(C₆H₅)₃ gave K₂Fe(CO)₄ when treated with KHB(OCH₃)₃. When treated with LiBH(C₂H₅)₃, W(CO)₆ gave a mixture of HW₂(CO)₁₀^?and (OC)₅W(COC₂H₅)^?; the latter was methylated to give the carbene complex (OC)₅WC(OCH₃)C₂H₅.     

On the electronic states of macrocycles of the extended porphyrin family and their coordination compounds

The electronic absorption spectra of Ni, Zn and Mg hemiporphyrazine derivatives are presented and discussed together with theoretical results obtained by INDO/S computations. The absorption spectra of all the metal derivatives show marked red shifts of the lowest energy absorption bands with respect to those of the metal free hemiporphyrazine. The possible explanation that in metal derivatives low lying excited states with a fully conjugated π electron system are present is supported by theoretical computations.     

R?ntgenspektrometrische Bestimmung von Eisen-55 in Luftstaub- und Niederschlagsproben

Zusammenfassung Eisen-55 wurde in Neuherberg bei München seit März 1970 in monatlich gesammelten Luftstaubproben und seit Januar 1971 in Monatsniederschlagsproben bestimmt. Nach dem Veraschen der Proben wurde Eisen durch Extraktion' mit Di-iso-propyläther abgetrennt. Zur weiteren Entfernung störender Radionuklide des Fallouts wurde eine Ionenaustauschertrennung angeschlossen. Nach der elektrolytischen Abscheidung des Eisens auf Kupferplättchen wurden die Röntgenspektren mit einem Proportionalzähler sowie einem Si(Li)-Detektor aufgenommen.Die mittlere spezifische Luftaktivität betrug in Neuherberg 1,0 fCi/m³ im Jahr 1970 (ab März), 1,2 fCi/m³ im Jahr 1971 und 0,36 fCi/m³ im Jahr 1972. Die dem Boden durch den Niederschlag zugeführte Aktivität wurde zu 697 pCi/m² · Jahr für 1971 und 178 pCi/m² · Jahr für 1972 bestimmt.Vortrag anläßlich der Tagung Spurenanalyse, 2. bis 5. April 1973 in Erlangen.     

Some positive cotes numbers for the chebyshev weight function

We show that, for the Chebyshev weight function (1–x ²)^–1/2, the Cotes numbers for the quadrature rule with nodes at the zeros of the ultraspherical polynomialP _n ^/() are nonnegative if and only if –1/2<1.     

Linear combination of concomitants of order statistics with application to testing and estimation

Summary Let (X ₁,Y ₁), (X ₂,Y ₂),…, (X _n,Y _n) be i.i.d. as (X, Y). TheY-variate paired with therth orderedX-variateX _rn is denoted byY _rn and terms the concomitant of therth order statistic. Statistics of the form are considered. The asymptotic normality ofT _n is established. The asymptotic results are used to test univariate and bivariate normality, to test independence and linearity ofX andY, and to estimate regression coefficient based on complete and censored samples.     

On coverings of plane convex sets by translates of strips

In the euclidean planeE ² letS ₁,S ₂, ... be a sequence of strips of widthsw ₁,w ₂, .... It is shown thatE ² can be covered by translates of the stripsS _i if w ₁ ^3/2 = . Further results concern conditions in order that a compact convex domain inE ² can be covered by translates ofS ₁,S ₂, ....This research was supported by National Science Foundation Research Grant MCS 76-06111.     

Sur la forme canonique des formes extérieures

Sans résumé

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The article is the text of a talk given at the Symposium on Differential Geometry in Debrecen, Hungary, on August 28–September 3, 1975.     

Infrared investigation of aluminum- and chromium-substituted magnetites and of the lacunar spinels resulting from their oxidation

When Fe³⁺ ions are substituted by aluminum or chromium on magnetite octahedral sites, the ir spectrum shows the conversion of an inverse spinel to a normal spinel. Both broad bands of magnetite are gradually replaced by the four characteristic bands of normal spinels II–III. They are also observed for solid solutions, FeCr₂O₄FeAl₂O₄, with, however, a further band at 780 cm^?1 which may be assigned to Al³⁺ ions on tetrahedral sites. Low-temperature (<400°C) oxidation of these compounds whose sizes are less than 2000 Å results in lacunar spinels III–III. The ir spectrum of these solids is characterized by two absorption bands (as for inverse spinels II–III) except for compounds close to pure γFe₂O₃ in which an order of vacancies could be put in evidence.