Selective cleavage of the linear ether bond in benzyl glycidyl ether and triphenylmethyl glycidyl ether by potassium alkalide as two-electron-transfer reagent

The linear ether bond was exclusively cleaved in benzyl glycidyl ether and triphenylmethyl glycidyl ether under the influence of K⁻, K⁺(15-crown-5)₂ (1), whereas the strongly strained three-membered oxacyclic ring remained undisturbed. Potassium glycidoxide and benzylpotassium were found as the primary reaction products of benzyl glycidyl ether with 1. Subsequently, benzylpotassium reacted with benzyl glycidyl ether giving the next potassium glycidoxide molecule and bibenzyl. Benzyl phenyl ether was used as a model compound to explain the mechanism of bibenzyl formation. The reaction of triphenylmethyl glycidyl ether with 1 resulted in potassium glycidoxide and stable triphenylmethylpotassium. After treating with a quenching agent a new glycidyl ether or glycidyl ester was obtained from potassium glycidoxide. These results were found when the reaction occurred at the excess of glycidyl ether. In another case, i.e. at the excess of 1 further reactions took place with the participation of potassium anions and various new compounds were observed in the reaction mixture after benzylation or methylation. Thus, the method of substrates delivery influences the course of studied processes in a decisive way.     

Bestimmung von Mikromengen Schwefel nach Aufspaltung des S8-Ringes in Indium-, Blei-, Antimonund Wismutsulfiden mit Hilfe einer induzierten Reaktion von Natriumazid mit Jod

Zusammenfassung Die Bestimmungsmethode für Mikromengen elementaren, in Sulfiden enthaltenen Schwefels mit Natriumazid und Jod wurde modifiziert. Der Analyse geht die Aufspaltung des S₈-Ringes voraus, die man dank der nukleophilen Wirkung von N₃ ^– in DMF-Lösung erreicht. Diese Methode wurde auf die Bestimmung des Schwefels in Indium-, Blei-, Antimon- und Wismutsulfid angewandt. Sie ist einfach und empfindlich. Ihre Fehlergrenze liegt bei ± 4%.

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Determination of microamounts of sulfur after cleavage of the S₈ king in indium, lead, antimony and bismuth sulfides by means of an induced reaction of sodium azide with iodine

Summary The determination of microamounts of elemental sulfur contained in sulfides using sodium azide and iodine was modified. The analysis was preceded by cleavage of the S₈ ring, which is achieved by virtue of the nucleophilic action of N₃ ^– in DMF solution. This method was applied to the determination of sulfur in indium, lead, antimony and bismuth sulfides. It is simple and sensitive. Its limit of error is ±4%.

     

Limit distributions and one-parameter groups of linear operators on Banach spaces

Let = {U_t: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set (X) of all probability measures on X. By (Q; ) we denote the class of all limit measures of {U_tn(μ₁ * μ₂*…*μ_n)*δ_xn}, where {μ_n}Q, {x_n}X and measures U_tnμ_j (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes L_m( ) as follows: L₀( )= ( (X); ), L_m( )= (L_m−1( ); ) for m=1, 2,… and L_∞( )=_m=0^∞L_m( ). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from L_m( ), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators.     

On the definition of the Monge-Ampère operator in ℂ<Superscript>2</Superscript>

We show that if u is a plurisubharmonic function defined on an open subset of ² then the Monge-Ampère measure (dd^cu)² can be well defined if and only if u belongs to the Sobolev space W^1,2_loc().Partially supported by KBN Grant #2 P03A 028 19     

Linear Automorphisms that are Symplectomorphisms

Let K be the field of real or complex numbers. Let (X K²ⁿ,) be a symplectic vector space and take 0 < k < n,N =. Let L₁,...,L_N X be 2k-dimensionallinear subspaces which are in a sufficiently general position.It is shown that if F : X X is a linear automorphism whichpreserves the form ^k on all subspaces L₁,...,L_N, then F is an_k-symplectomorphism (that is, F^* = _k, where ). In particular, if K = R and k is odd then F mustbe a symplectomorphism. The unitary version of this theoremis proved as well. It is also observed that the set A_l,2r ofall l-dimensional linear subspaces on which the form has rank 2r is linear in the Grassmannian G(l,2n), that is, there isa linear subspace L such that A_l,2r = L G(l, 2n). In particular,the set A_l,2r can be computed effectively. Finally, the notionof symplectic volume is introduced and it is proved that itis another strong invariant.     

Generalization of the lineshape useful in magnetic resonance spectroscopy

A new lineshape function is derived from the Tsallis distribution to describe electron paramagnetic resonance (EPR) spectra, and possibly nuclear magnetic resonance (NMR) spectra as well. This lineshape generalizes the Gaussian and Lorentzian lineshapes that are widely used in simulations. The main features of this lineshape function are presented: the normalization, moments, and first derivative. A number of experimental EPR spectra are compared with the results of simulations employing the new lineshape function. The results show that the new lineshape often provides a better approximation of the experimental spectrum. It is also shown that the new parameter of the lineshape function can be used to quantify the intermolecular spin-spin interactions.     

Addition of dipropylamine to multiacrylate and its model compound catalyzed by lithium dipropylamide

The nucleophilic addition reaction of dipropylamine to vinyl groups of multiacrylate - poly(2-acryloyloxyethyl methacrylate) and to 2-butyrylethyl acrylate as model compound has been investigated. Based on the results obtained, it has been shown that the addition reaction rate of dipropylamine to multiacrylate and 2-butyrylethyl acrylate is proportional to [CH₂=CH-] and to [(C₃H₇)₂NLi] with the ratio [(C₃H₇)₂NH]_o/[(C₃H₇)₂NLi]_o = 20. Second-order addition reaction rate constants and activation energies for the systems under investigation have been determined. This revised version was published online in August 2006 with corrections to the Cover Date.