Operator conditions for ℂ-differentiability

The concepts of dilation and rotation operators are introduced for maps of domains of infinite-dimensional Hibert spaces. Sufficient conditions for -differentiability along subspaces are established and theorems on operator conditions for IR-differentiable maps to be monogenic and holomorphic are proved.Translated from Ukrainskii Matematicheskii Zhurnal,42, No. 11, pp. 1448–1454, November, 1990.     

Representation of the local general solution of a certain class of differential-functional equations

For the differential-functional equation of neutral type x(a t)+tb(t)x(t)+ c(t)x(at)+d(t)x(t)=0,0<<1,a>1, in the neighborhood of the singular critical point t=0, the representation of the general solution is constructed; it is shown that the general solution depends on an arbitrary constant and an arbitrary periodic function.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 206–210, February, 1990.     

P(IV)-P(V) Coordinational Isomerism of Phosphorus N-α-Haloethylimines

The semiempirical MNDO-PM3 method in supramolecular approximation was used to study the structure of (N--haloethylimino)chloro(o-phenylenedioxy)phosphoranes R¹ ₃CR²X-N-P(Cl)O₂C₆H₂(R³-m)₂, where R¹ = H, Cl, F, R² = R³ = H, Cl, and X = F, Cl, Br, and of their 1:2 solvates with chloroform, as well as alternative mechanisms of the P(IV)-P(V) holotropic rearrangement. It was found that the activation barrier of the sigmatropic rearrangement increases in the order Br < Cl < F, in parallel with increasing thermodynamic stability of a more stable phosphorane isomer with an axial-equatorial arrangement of the dioxaphos- phole ring. It was shown that the most favorable pathway of the phosphorus-carbon halotropic rearrangement of a phosphorus N--haloethylimine, both nonsolvated and solvated with two molecules of chloroform, is the sigmatropic transformation.     

Synthesis and structures of five-coordinate bis-o-iminobenzosemiquinone complexes M(ISQ-R)2X (X = Cl, Br, I, or SCN; M = CoIII, FeIII, or MnIII)

New five-coordinate complexes Co(ISQ-Prⁱ)₂Cl, Co(ISQ-Me)₂Cl, Co(ISQ-Me)₂I, Co(ISQ-Me)₂(SCN), Mn(ISQ-Prⁱ)₂Cl, and Fe(ISQ-Me)₂Br (ISQ-Prⁱ and ISQ-Me are the 4,6-di-tert-butyl-N-(2,6-diisopropylphenyl)-and 4,6-di-tert-butyl-N-(2,6-dimethylphenyl)-o-iminobenzosemiquinone radical anions, respectively) were synthesized. The complexes were characterized by UV-Vis and IR spectroscopy and magnetochemistry. The molecular structures of the Fe(ISQ-Me)₂Br and Mn(ISQ-Prⁱ)₂Cl complexes were established by X-ray diffraction. The singlet ground state (S = 0) of the cobalt complexes is caused by antiferromagnetic coupling between the unpaired electrons of the radical ligands (S = 1/2) through the fully occupied atomic orbitals of low-spin cobalt(III) (d⁶, S = 0). The effective magnetic moments of the complexes at 10 K are 0.18 μ_B for Co(ISQ-Prⁱ)₂Cl and 0.16 μ_B for Co(ISQ-Me)₂I. The ground state of the manganese complex is triplet (S = 1). Two unpaired electrons of the o-iminobenzosemiquinone ligands are strongly antiferromagnetically coupled with two of four unpaired electrons of high-spin manganese(III) (d⁴, S = 2). Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 43–51, January, 2006.     

Problem of a wide variety of products in the Cu(hfac)2-nitroxide system

The stereochemically flexible Cu(hfac)(2) metal-ligand system when combined with polyfunctional nitroxides leads to a variety of solids with varying structure and composition. While investigating the products of Cu(hfac)(2) interaction with spin-labeled pyrazole 4,4,5,5-tetramethyl-2-(1-methyl-1H-pyrazol-4-yl)-imidazoline-3-oxide-1-oxyl, we have isolated a family of (12) heterospin compounds differing in structure and composition in the solid state. In synthetic systems, these compounds often cocrystallize and must be separated mechanically. It is also shown that minor variation of the structure of the solid heterospin complex can substantially change the magnetic properties of compounds.     

Bidentate-bridging butyleneglycol in a framework structure with A Co(II) mixed-ligand complex of an imidazoline nitroxyl

Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated from Zhurnal Strukturnoi Khimii, Vol. 33, No. 2, pp. 118–125, March–April, 1992.     

Unexpected results in the heterocyclization of 5-acetylenylpyrazole-4-carboxylic acid hydrazides under the influence of CuCl: formation of a diazepinone and dehydrodimerization into the corresponding bis(pyrazolo[4,3-d][1,2]diazepinone)

The simple reaction of cyclization of hydrazides of vic-acetylenylbenzoic and acetylenylpyrazole carboxylic acid can lead to four different compounds: five-membered N-aminolactams, six-membered N-aminolactams, six-membered diazinones and diazepinones, but only the first three have been described. In this paper we report the unexpected formation of a bis(pyrazolo[4,3-d][1,2]diazepinone, the structure of which has been established by X-ray crystallography.     

Simulation of Asymmetric Peak-Shaped Analytical Signals by the Frame Representation of Their Shape Using Stripping Voltammetry as an Example

To simulate peak-shaped analytical signals, the shape characteristics and geometrical properties of four asymmetric basic functions (the derivative of the logistic function, the Gaussian function, the Cauchy function modified by Fraser and Suzuki, and the Poisson function with the Stromberg correction) are systematically studied. The frame representation, which was proposed earlier by the two authors of this paper, is used to characterize the peak shape. Some regularities are found in peak properties expressed in terms of the frame parameters and considered as functions of the coefficient of skewness b. Peak shapes are compared using two approaches to obtaining dimensionless frame parameters: one using relative parameters and another using parameters of the unit frame. It is shown that the frame representation of the peak shape can be used in the phenomenological simulation of metal peaks in stripping voltammetry. The practical use of information on the shape of the analytical signal in the solution of various problems of analytical chemistry is discussed.     

4-Aryl-5-(pyrimidin-2′-yl)-1,4-dihydropyridines,-1,4-di- and -1,2,3,4-tetrahydropyrimidines

2-Acetonylpyrimidines readily undergo the Hantzsch—Biginelli cyclocondensation. This method was used to obtain derivatives of 1,4-dihydropyridine and 1,4-di- and 1,2,3,4-tetrahydropyrirrzidines, containing the pyrimidine fragment in the 5 position of the heterocycle.Institute of Bioorganic Chemistry and Petroleum Chemistry, Ukrainian Academy of Sciences, Kiev 253660. Translated from Khimiya Geterotsiklcheskikh Soedinenii, No. 5, pp. 679–685, May, 1994. Original article submitted January 20, 1994.     

Synthesis of 1,2,4-triazolo[3,4-b]-1,3,4-thiadiazepines and 4-amino-3-acylvinylthio-1,2,4-triazoles by reaction o acylacetylenes with 4-amino-3-mercapto-1,2,4-triazole

1,2,4-Triazolo[3,4-b]-1,3,4-thiadiazepines have been prepared by treating -acetylenic ketones with 4-amino-3-mercapto-1,2,4-triazole in glacial acetic acid. Terminal acetylenic ketones react with the triazole to form 4-amino-3-acylvinylthio-1,2,4-triazoles. Heating the latter with hydrazine hydrate in alcohol yields substituted pyrazoles.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 990–994, July, 1991.