Degrees of Real Wronski Maps

Abstract. We study the map which sends vectors of polynomials into their Wronski determinants. This defines a projection map of a Grassmann variety which we call a Wronski map. Our main result is computation of degrees of the real Wronski maps. Connections with real algebraic geometry and control theory are described.     

Kinetics of carbon dioxide absorption from air in a flow reactor with a fixed bed of K<Subscript>2</Subscript>CO<Subscript>3</Subscript>-based sorbent

Sorption of carbon dioxide from air in a flow reactor with a bulky fixed bed of the K₂CO₃/Al₂O₃ composite sorbent was studied. The dynamic sorption capacity of the material was shown to depend on the relative humidity of the inlet air. A numerical model was constructed for evaluating the profile of СО₂ concentration in the layer and kinetic curves of CO₂ breakthrough at the outlet of the reactor. The results of simulation allowed us to adequately describe the experimental kinetic curves at 20–40% humidity.     

Nanodiamonds thermoluminescence

Nanodiamonds thermoluminescence was studied. It was compared with thermoluminescence of synthetic diamonds of relative purity, weakly and strongly boron-doped. A dependence of the nanodiamond thermoluminescence on an irradiation dose was examined.     

Calculating the characteristics of neutron-deuteron and proton-deuteron systems in a two-body potential model

³H and ³He nuclei are considered in a two-body model (³H = n + d; ³He = p + d). Two independent approaches are used: in the first, interaction is described by the folding potential, while NN potentials are taken in the Hulthen form with allowance for violations of isotopic invariance. The second approach features phenomenological Hulthen and Yukawa Nd potentials used as Nd interaction. In both approaches, the binding energies, vertex constants, and asymptotic normalization coefficients in the N+d channel are calculated.     

New dinuclear palladium complex with a Chinese-lantern structure

The new dinuclear palladium complex Pd₂(-S,N-SC₇H₅N₂)₄ with a Chinese-lantern structure was synthesized by the reaction of K₂PdCl₄ with 2-mercaptobenzimidazole and structurally characterized by X-ray diffraction analysis.     

Half-sandwich complexes of lanthanides with tridentate ligands [RCH2CH(O)CH2OBun]2– (R = C5H4, 1-C9H6): synthesis,structures, and properties. The crystal structure of the complex {[(η5-C5H4)CH2CH(μ2:η1-O)CH2OBun]LaN(SiMe3)2}2

The oxirane-ring opening of butyl glycidyl ether with cyclopentadienylsodium or indenylsodium afforded cyclopentadienyl- and indenyl-substituted alcohols RHCH₂CH(OH)CH₂OBuⁿ (R = C₅H₄ (1) or 3-C₉H₆ (2), respectively), which were used as tridentate ligands. The reactions of these compounds with Ln[N(SiMe₃)₂]₃ produced the lanthanide complexes {[(⁵-R)CH₂CH(²:¹-O)CH₂OBuⁿ]LnN(SiMe₃)₂}₂ (R = C₅H₄, Ln = La (3), Pr (4), Er (5), Lu (6); or R = 1-C₉H₆, Ln = La (7)). The coordination spheres of the metal atoms in these complexes involve simultaneously the ⁵-cyclopentadienyl (indenyl), bridging alkoxide, and terminal amide ligands. The complexes were characterized by microanalysis, IR and NMR spectroscopy, and magnetochemistry. The crystal and molecular structure of complex 3 was established by single-crystal X-ray diffraction analysis.     

Thermal activation of complexation reaction on aerosil surface

The influence of temperature in the 20–100°C range on processes of bimolecular interaction in the aerosil-phenanthrene-trinitrobenzene system has been studied. Temperature-stimulated CTC accumulation on the surface is found. Activation energies of complex formation are estimated. Quenching of phenanthrene fluorescence by acceptor has a mixed static and dynamic character.     

Cubane derivatives 1. Synthesis and molecular structures of the esters of 1,4-cubanedicarboxylic acid

An effective method of esterification of 1,4-cubanedicarboxylic acid with alkylsulfuric acids is proposed. The derivatives of alkanols with substantially different pK_a Valus are obtained in high yields. Molecular structures of the esters obtained are confirmed by various methods. The X-ray study showed a remarkable effect of the nature of an alkyl radical on the geometry of the cubane core.Translated fromIzyestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp.668–672, April, 1994.The authors thank Dr. G. V. Lagodzinskaya for analyzing the NMR spectra and for useful discussions.     

Synthesis, structure, and antimetastatic activity of thetrans-[Pt(NC5H4C(O)NHC2H4ONO2)2Cl2] complex

Thetrans-[Pt(NC₅H₄C(O)NHC₂H₄ONO₂)₂Cl₂] complex (2) was prepared by the reaction of nicorandyl (N-nitroethoxynicotinamide), which is widely used in cardiology, with K₂PtCl₄ in water. The structure of2 was established by X-ray structural analysis. It was found that complex2 exhibits high antitumor activity, in particular, antimetastatic activity, unlike the analogous Cu^II complex with bromine atoms. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1672–1675, September, 1997.