Convexity preserving interpolation by algebraic curves and surfaces

The problem of interpolation by a convex curve to the vertices of a convex polygon is considered. A natural 1-parameter family ofC algebraic curves solving this problem is presented. This is extended to a solution, of a general Hermite-type problem, in, which the curve also interpolates to one or two prescribedtangents at any desired vertices of the polygon. The construction of these curves is a generalization of well known methods for generatingconic sections. Several properties of this family of algebraic curves are discussed. In addition, the method is generalized to convexC interpolation of strictly convex data sets inR ³ by algebraicsurfaces.     

Magnetic field value in the weak energy release region of the solar corona

Spectrographic data from observations of the polarized weak steplike (with relatively sharp growth t 3 sec and slow decay t 10² sec) solar continuum radioemission are analyzed below. The main results are found using a sweeping spectrograph in the 8–12 GHz frequency range (sweep rate 1 sample per second and frequency resolution 120 MHz) and using the RT-22 radio telescope at the Crimean Astrophysical Observatory (angular resolution 4–6). In a series of events at the leading edge of the continuum a narrow-band frequency drifting emission termed blip-type is found. The degree of continuum circular polarization (p<10%) is low compared to that of the narrow-band component (p20%). Both components of the aforementioned events should be radiating on the second harmonic of the local plasma frequency in the context of a plasma generating mechanism. Based on the model proposed and using the observed degree of circular polarization of each component, we can estimate the strength of the magnetic field within the area of the source and the width of the angular spectrum from the radiating plasma turbulence. The results of analysis of the real microwave events are given below.Radiophysical Research Institute, Nizhnii Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 7, pp. 874–882, July, 1994.     

One-stage conversion of aromatic carboxylic acids into 2, 5-diaryl-1, 3, 4-oxadiazoles

A method has been developed for the one-stage conversion of aromatic carboxylic acids into symmetrical 2, 5-diaryl-1, 3, 4-oxadiazoles by heating them with hydrazine hydrochloride in polyphosphoric acid.     

Effect of Peptization on Texture and Physicomechanical Properties of Aluminum Hydroxides

The method of low-temperature adsorption of nitrogen was applied to study structural characteristics of commercial peptized aluminum hydroxides. An increase or decrease in the porometric volume, depending on the nature and concentration of the peptizing agent, was analyzed. The phenomena observed are explained in terms of the mechanism suggested for formation of the pore system in commercial aluminum hydroxides. The dependence of the physicomechanical properties of active aluminum oxide on synthesis conditions and texture characteristics of commercial aluminum hydroxides was studied.     

Correlation between stereochemistry and sign of cotton effects for degenerate transitions in spectra of binuclear clusters of molybdenum(II)

A correlation between the stereochemistry and sign of the Cotton effect for ^* transition in the spectra of dimolybdenum tetracarboxylates and related compounds has been accomplished by constructing, within the framework of a one-electron model of optical activity, a 32-sector rule based on data from x-ray structure analysis and circular dichroism for dimolybdenum tetra-(R)-mandelate. It has been shown that a positive value of the pseudoscalar function xyz(x²–y²)(a²-z²) corresponds to a negative Cotton effect for the ^* transition in the case in which the dominant contribution to this effect comes from R_x components of the rotator strength of the transition.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1783–1785, August, 1990.