Weierstrass Multiplicative Points on a Compact Riemann Surface

We introduce Weierstrass multiplicative points and develop the theory of Weierstrass multiplicative points for multiplicative meromorphic functions and Prym differentials on a compact Riemann surface. We prove some analogs of the Weierstrass and Noether theorems on the gaps of multiplicative functions. We obtain two-sided estimates for the number of Weierstrass multiplicative points and q-points. We propose a method for studying the Weierstrass and Noether gaps and Weierstrass multiplicative points by means of filtrations in the Jacobi variety of a compact Riemann surface.     

Adsorption phenomena at high pressures and temperatures 4. Isotherms of excess and absolute adsorption of Kr on NaA zeolite

The problem of conversion of an isotherm of excess adsorption measured experimentally into values of the total amount of the adsorbate (absolute adsorption) has been formulated. Five isotherms of excess adsorption of krypton on NaA zeolite were measured (at 334–500 K) at equilibrium pressures of -160 MPa. The corresponding isotherms of the total amount were calculated and the temperature dependences of the parameters of an equation describing the isotherms of excess adsorption were identified. It was shown that at high temperatures and pressures, krypton atoms diffuse into the -cavities of the NaA zeolite.For Part 3, seeRuss. Chem. Bull., 1996, 45, 534 (Engl. Transl.).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1138–1142, May, 1996.     

Adsorption phenomena at high pressures and temperatures 5. Heats of excess and total adsorption of krypton on zeolite NaA

Thermodynamic principles for the calculation of differential heats of excess and absolute adsorption were considered. A set of isosteres of excess adsorption of krypton on zeolite NaA are presented, from which the coverage and temperature dependences of the heats of excess adsorption are calculated and analyzed. The reasons for infinitely high values of the excess heats at finite values of adsorption are discussed. The problems of recalculation of the excess adsorption to absolute adsorption are considered.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1946–1950, August, 1996.     

Meso-trans-diaryldihexadecyltetrabenzoporphyrins and their zinc complexes: Synthesis and spectra

3-[(1-Oxo-1H-isoindol-3-yl)(phenyl)methylidene]-2,3-dihydro-1H-isoindol-1-one, 3-[(1-oxo-1H-isoindol-3-yl)(1-naphthyl)methylidene]-2,3-dihydro-1H-isoindol-1-one, and 3-[(1-oxo-1H-isoindol-3-yl)(9-anthryl)methylidene]-2,3-dihydro-1H-isoindol-1-one were prepared by the reactions of phthalimide with phenylacetic, 1-naphthylacetic, and 9-anthrylacetic acids, respectively. Heating of these precursors with stearic acid in the presence of zinc oxide yielded zinc complexes of meso-trans-diphenyldihexadecyltetrabenzoporphyrin, meso-trans-di(1-naphthyl)dihexadecyltetrabenzoporphyrin, and meso-trans-di(9-anthryl)dihexadecyltetrabenzoporphyrin, respectively. Treatment of the metal complexes with HCl yielded the porphyrin bases. The spectral properties of the compounds were studied.     

A Study of the Linear Tension Effect on the Polystyrene Microsphere Wettability with Water

A technique aimed at measuring contact angles for microparticles and suitable for determining the linear tension is developed. The technique is based on determining the equilibrium position of the microsphere (where the sum of forces acting on the microsphere is zero) at the liquid–gas interface. This position is unambiguously determined from the experimental force–distance curve obtained for the microparticle–interface interaction. The measurements are performed using an original setup based on the operating principle of the atomic force microscope. The advancing and receding contact angles of water are measured for individual polystyrene microspheres with radii from 1 to 5 m. The contact angles are shown to increase with a decreasing microsphere radius, whereas the hysteresis of the contact angle decreases. The results indicate the existence of a negative linear tension in the case of the rough surface of polystyrene microspheres, which is deformed along the three-phase contact line.     

Fredholm property of boundary value problems for a fourth-order elliptic differential-operator equation with operator boundary conditions

In a Hilbert space H, we study the Fredholm property of a boundary value problem for a fourth-order differential-operator equation of elliptic type with unbounded operators in the boundary conditions. We find sufficient conditions on the operators in the boundary conditions for the problem to be Fredholm. We give applications of the abstract results to boundary value problems for fourth-order elliptic partial differential equations in nonsmooth domains.     

Metal complexes of 1-methyltetrabenzooctadehydrocorrin

In reaction of 2,3-dihydro-3-[(1-hydroxy-1-methyl-1H-isoindol-3-yl)methylene]-1H-isoindol-1-one with hydrazine hydrate in the presence of a template agent (metal acetates) in butanol environment metal complexes formed of 1-methyltetrabenzooctadehydrocorrin. A scheme of formation of these compounds was suggested and their spectral characteristics were investigated.