Rigidity and flexibility of virtual polytopes

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.     

On hyperbolic virtual polytopes and hyperbolic fans

Hyperbolic virtual polytopes arose originally as polytopal versions of counterexamples to the following A.D.Alexandrov’s uniqueness conjecture: Let K ⊂ ℝ³ be a smooth convex body. If for a constant C, at every point of ∂K, we have R ₁ ≤ C ≤ R ₂ then K is a ball. (R ₁ and R ₂ stand for the principal curvature radii of ∂K.) This paper gives a new (in comparison with the previous construction by Y.Martinez-Maure and by G.Panina) series of counterexamples to the conjecture. In particular, a hyperbolic virtual polytope (and therefore, a hyperbolic hérisson) with odd an number of horns is constructed. Moreover, various properties of hyperbolic virtual polytopes and their fans are discussed.     

Description of equilibrium bond lengths with the use of spectroscopic parametrization of the CNDO method including transition metals

Lensovet Leningrad Technological Institute. Plastpolimer Okhta Scientific-Production Association. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 4, pp. 22–28, July–August, 1991.     

Potentials of gas chromatography in the determination of reaction products in the catalytic oxidation of ammonia to nitrogen(II) oxide

Peculiarities of the determination of nitrogen oxides and ammonia in the reaction products of ammonia oxidation are studied by gas chromatography. Particular attention was paid to the sampling problem. It is shown that in the course of the transportation of samples containing nitrogen(II) oxide and oxygen, the oxidation of nitrogen(II) oxide to nitrogen(IV) oxide takes place in the vapor phase. The conditions were found for suppressing or even eliminating the gas-phase reaction of NO oxidation to NO₂. A procedure for the gas-chromatographic analysis of the reaction products in the catalytic oxidation of ammonia is proposed using several samples and packed columns, including the determination of NO with respect to NO₂ formed in the gas-phase oxidation of NO.     

Platinum(II) Diaquadiammine Complexes. Stable Hydrolysis Products by DFT Quantum-Chemical Calculations

The most stable hydrolysis products of cis-[Pt(NH₃)₂(H₂O)₂]^{2 +} were revealed by means of DFT quantum-chemical calculations of this complex and its deprotonated forms with full geometry optimization. The resulting force fields and normal mode vibrations were used to calculate thermodynamic characteristics for possible hydrolysis stages and equilibrium constants for proton-transfer processes in the gas phase and in aqueous solutions. The hydroxo-bridged dimers [Pt(NH₃)₂(-OH)]₂ ^{2 +} with short Pt+++Pt distances are the hydrolysis products of platinum(II) cis-diaquadiamminates in the aqueous medium.     

Gas chromatography on macroporous sulfonated cation exchangers

Chromatographia - The retention of compounds of various classes on macroporous sulfonated cation exchangers in the form of the fourth period elements in Mendeleev's table (i. e. in the K, Ca,...     

Redox Properties of Rhodium(III) Oxo-Bridged Carboxylate Complexes

Chemical and electrochemical oxidation of rhodium (III) oxo-bridged carboxylate complexes was studied. The chemical [with O₃ and Ce(IV) salts] or electrochemical (at potentials of 1.00-1.20 V) oxidations of the binuclear complexes [Rh₂(-O)(-O₂CCH₃)₂(H₂O)₆]^{2 +} and [Rh₂(-O)(-O₂CCF₃)₂(H₂O)₆]^{2 +} leads to the superoxo complexes [Rh₂(-O)(O₂-)(-O₂CCH₃)₂(H₂O)₅]⁺ and [Rh₂(-O)(O₂ ^-)(-O₂CCF₃)₂(H₂O)₅]⁺ with terminal coordination of O₂-. The trinuclear acetate [Rh₃(₃-O)(-O₂CCH₃)₆(H₂O)₃]⁺, unlike its trifluoroacetate analog [Rh3(₃-O)(-O₂CCF₃)₆(H₂O)₃]⁺, is oxidized only electrochemically at a potential of 1.38 V. The oxidation of [Rh₃(₃-O)(-O₂CCH₃)₆(H₂O)₃]⁺ is reversible and involves formation of an unstable superoxo group O₂ ^- between two Rh₃III(₃-O) cores.     

Saponins of dioscorea XV. Caucasosaponin and caucasoprosapogenin fromD. caucasica

Summary Two new saponins have been isolated from the rhizomes ofD. caucasica: the water-soluble caucasosaponin—a rhamnosotriglucoside of 25 D-22-spirost-22-en-3-ol—and the water insoluble caucasoprosapogenin—a glucosotrioside of 25 D-22-spirost-5-en-3-ol-, and also the previously known rhamnosidodiglucoside of 25 D-22-spirost-5-en-3-ol—gracillin.Khimiya Prirodnykh Soedinenii, Vol. 3, No. 4, pp. 237–241, 1967     

Effect of surface recombination on the amplitude spectrum of variable bias γ-counters

The form of the amplitude spectrum of a photoresistive counter is found by solution of the continuity equation for an infinite semiconductive plate with an instantaneous point source of nonequilibrium charge carriers and a specified surface recombination rate for these carriers and an additional assumption as to the character of -quantum absorption by the photoresistor material. It is thus shown to be possible to construct the spectrum with use of the response function formalism of [1, 2] for each of the signal formation processes (e-p pair generation, photoconductivity kinetics, imposition of equipment noise).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 97–100, September, 1982.