Comparison theorems forL-monosplines of minimal norm

Summary LetLM _N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x _i } ₁ ⁿ ,a <x ₁ < ... <x _n <b and an incidence matrixE = (e _ij ) _i=1 ⁿ , _r-1 ^j=0 with Denote byLM _N ^O the subset ofLM _N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL _p-norms inLM _N belong toLM _N ^O .The results are reformulated as comparison theorems for quadrature formulae.     

Silica hybrid nanocomposites

In this work we present experimental results about the formation, properties and structure of sol — gel silica based biocomposite containing Calcium alginate as an organic compound. Two different types of silicon precursors have been used in the synthesis: tetramethylortosilicate (TMOS) and ethyltrimethoxysilane (ETMS). The samples have been prepared at room temperature. The hybrids have been synthesized by replacing different quantitis of the inorganic precursor with alginate. The structure of the obtained hybrid materials has been studied by XRD, IR Spectroscopy, EDS, BET and AFM. The results proved that all samples are amorphous possessing a surface area from 70 to 290 m²/g. It has also been established by FT IR spectra that the hybrids containing TMOS display Van der Walls and Hydrogen bonding or electrostatic interactions between the organic and inorganic components. Strong chemical bonds between the inorganic and organic components in the samples with ETMS are present. A self-organized nanostructure has been observed by AFM. In the obtained hybrids the nanobuilding blocks average in size at about 8–14 nm for the particles.     

Multipole induced splitting of metal-cage vibrations in crystalline endohedral D2d-M2@C84 dimetallofullerenes

Metal-carbon cage vibrations of crystalline endohedral D2d-M2@C84 (M=Sc,Y,Dy) dimetallofullerenes were analyzed by temperature dependent Raman scattering and a dynamical force field model. Three groups of metal-carbon cage modes were found at energies of 35-200 cm(-1) and assigned to metal-cage stretching and deformation vibrations. They exhibit a textbook example for the splitting of molecular vibrations in a crystal field. Induced dipole-dipole and quadrupole-quadrupole interactions account quantitatively for the observed mode splitting. Based on the metal-cage vibrational structure it is demonstrated that D2d-Y2@C84 dimetallofullerene retains a monoclinic crystal structure up to 550 K and undergoes a transition from a disordered to an ordered orientational state at a temperature of approximately 150 K.     

Ab initio Study of the Keto-Enol Equilibriumof Malonaldehyde

 The mechanism of the keto-enol tautomerism of malonaldehyde was studied by ab initio methods using 6-21G^** and 6-311G^** basis functions at the HF level. Two separate mechanisms were examined: through-space proton transfer in the ω-shaped form and through-space proton transfer in a sickle-shaped form obtained from the ω form by rotation. The transition state structure of the ω form is non-planar, whereas that of the sickle form is planar. The sickle form is connected with a 2^nd order saddle, indicating that there should exist a lower energy barrier, i.e. that the through-bond mechanism may be preferred. The calculated energy barriers of keto-enol tautomerism for the sickle form is twice as high as those for the omega form.     

Darstellung,Struktur und Reaktionsfähigkeit einiger Metall(I)- und-(II)-Derivate des Diäthylphosphono-Acetons

Metalation of diethylphosphono-acetone (DÄPA) with potassium or lithium in benzene and with KNH₂, LiNH₂, or calcium in liquid ammonia afforded the metal derivatives ofDEPA, which were isolated in a pure state. Their structure has been investigated by i.r.- and¹H n.m.r.-spectroscopy. In solution metallotropic conversion of thecis-enolate chelates intotrans-enolates and C-forms occurs. The reactivity of these metal derivatives towards some alkylating and acylating reagents as well towards carbonyl compounds has been investigated.

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Diese Mitteilung ist z. T. Inhalt der Diplomarbeit vonI. Velinov, Univ. Sofia (1968).     

Schnelle Methoden zur Bestimmung der Hauptelemente in den Konzentraten und Mutterlaugen der Seesalzgewinnung

Zusammenfassung Es werden Methoden zur Bestimmung der Hauptelemente in den Mutterlaugen bei der Seesalzgewinnung beschrieben. Die Kationen und Anionen werden durch Ionenaustausch in einer Kolonne mit Wofatit KPS-200 in H-Form getrennt. Im Durchlauf werden Chlorid und Sulfat als Summe und Chlorid allein bestimmt. Sulfat wird als Differenz berechnet. Calcium, Magnesium und Eisen bestimmt man komplexometrisch. Die Summe Kalium und Natrium bestimmt man komplexometrisch als Magnesium nach lonenaustausch in einer Wofatit KPS-200-Säule in Mg²⁺-Form. Natrium wird als Natriumzinkuranylacetat bestimmt, und Kalium ergibt sich aus der Differenz.     

Benzthiazolderivate, 5. Mitt.: Dequartärisierung und nucleophile Substitution von Benzthiazoliumsalzen

Zusammenfassung Benzthiazoliumsalze (I) reagieren, wie an 20 Beispielen gezeigt wird, mit nucleophilen Partnern unter gleichzeitiger Labilisierung des Oniumsystems zu 2-substituierten 2,3-Dihydro-benzthiazolen (dequartärisierende nucleophile Substitution). Der Reaktionsverlauf wird von der Art der nucleophilen Komponente bestimmt: Freie Amino-(Hydrazino)-Verbindungen und I lassen sich im Molverhältnis 21, die Alkalisalze von Aminocarbonsäuren und-sulfosäuren im Molverhältnis 11 umsetzen. Verbindungen mit reaktiver Methylengruppierung reagieren glatt mit der äquivalenten Menge I, wenn in Gegenwart einer Base gearbeitet wird. Die verwendeten I-Verbindungen sind: 2-Äthoxy-3-methyl-benzthiazolium-tetrafluoroborat (VII) und 2-Methylmercapto-3-methylbenzthiazolium-methylsulfat (VIII).