Reaction between piperidine-4-spiro-2′-oxiranes and nucleophilic reagents

An investigation was made into the opening of the epoxide ring of piperidine-4-spiro-2-oxiranes by N-, H-, C-, and P-nucleophiles, which yielded the corresponding 3,4-dihydroxy- and 3-hydroxypiperidine derivatives. When these epoxides were reacted with organomagnesium compounds, regrouping occurred, the piperidine ring reducing in size to a pyrrolidine ring and the latter being functionalized by a hydroxymethyl group.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1499–1503, November, 1993.     

Sulfur-containing derivatives of thiolan-1,1-dioxide 3. Reactions of salts of 2-(n,n-dialkyl)iminio-5,5-dioxoperhydrothieno[3,4-d]-1,3-dithiolans with bases

Salts of condensed 2-(N,N-dialkyl)iminio-1,3-dithiolan and 1,1-dioxothiolan rings are converted in alkaline media to 1,1-dioxothiolen esters of N,N-dialkyldithiocarbamic acids and into unsaturated bicyclic compounds. The latter are formed when the initial salts contain a bromine atom to the sulfonyl group.For Communication 2, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 40–47, January, 1993.     

Dispersity and kinetic characteristics of dissociation of mono- and hemiaquo adducts of copper N,N′-ethylenebis(acetylacetoniminate) under nonisothermal conditions

Using optical microscopy and thermogravimetry, we have established that determination of the kinetic characteristics of dissociation for the monoaquo adduct of copper N,N-ethylene-bis(acetylacetoniminate) with particle size 0.5–2 mm is hindered by self-dispersal processes. Using a piezoquartz microbalance, we have obtained the kinetic parameters for thermolysis for a phase whose crystal sizes are substantially smaller than the minimal size after self-dispersal of a block of a large crystal (0.5–2 m). For thermolysis of the hemiaquo adduct not accompanied by self-dispersal, the kinetic characteristics of the process for phases of dispersity 0.5–2 mm and 0.5–2 m are comparable.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 3, pp. 226–231, May–June, 1992.     

Diol-diisocyanate polymerization by gamma irradiation

Gamma irradiation has been used as an alternative way of curing diol-diisocyanate by means of specific catalysts and/or elevated temperatures. A mixture of toluene diisocyanate (TDI) and hydroxy terminated polybutadiene (HTPB) oligomer were irradiated over a dose range of 0–720 kGy using a 5 kCi⁶⁰Co -source. Various compositions were formulated and also suitable additives were incorporated. Disappearance of the isocyanate peak in the IR spectra was considered as a measure of its consumption. The conversion characteristics showed a profound influence of irradiation. A suitable mechanism is envisaged.     

Degenerate polynomial patches of degree 11 for almostGC 2 interpolation over triangles

We consider the problem of interpolating scattered data in ³ by analmost geometrically smoothGC ² surface, where almostGC ² meansGC ² except in a finite number of points (the vertices), where the surface isGC ¹. A local method is proposed, based on employing so-called degenerate triangular Bernstein-Bézier patches. We give an analysis of quintic patches forGC ¹ and patches of degree eleven for almostGC ² interpolation.     

On the spectrum of the sum of generators for a finitely generated group

Let Γ be a finitely generated group. In the group algebra ℂ[Γ], form the averageh of a finite setS of generators of Γ. Given a unitary representation π of Γ, we relate spectral properties of the operator π(h) to properties of Γ and π. For the universal representationπ _un of Γ, we prove in particular the following results. First, the spectrum Sp(π _un (h)) contains the complex numberz of modulus one iff Sp(π _un (h)) is invariant under multiplication byz, iff there exists a character such that η(S)={z}. Second, forS ⁻¹=S, the group Γ has Kazhdan’s property (T) if and only if 1 is isolated in Sp(π _un (h)); in this case, the distance between 1 and other points of the spectrum gives a lower bound on the Kazhdan constants. Numerous examples illustrate the results.