The Möbius Transformation and Smirnov’s Inequality for Polynomials

Differential inequalities for polynomials generalizing the well-known Smirnov, Rahman, Schmeisser, and Bernstein inequalities are obtained.

     

Synthesis of pyrophosphatotetraamminediplatinum(II) complex and its transformations in hydrochloric acid solutions

A new method for the synthesis of [Pt₂(NH₃)₄P₂O₇] is proposed. Its transformations in a hydrochloric acid medium are described.     

Study of the Structure and Reactions of Bis(μ-Oxalato)tetramminediplatinum(II) in Aqueous Chloride Solutions

A comparison study of the bis(-oxalato)tetramminediplatinum(II) dimer [Pt₂(NH₃)₄(-C₂O₄)₂] and the oxalatodiammineplatinum(II) chelate [Pt(NH₃)₂C₂O₄] is performed. The kinetics and mechanism of substitution of C₂O^2– ₄ for Cl^– in aqueous chloride solutions are studied by photoelectronic spectroscopy, gravimetry, and chemical phase analysis within the 1.0–6.7 pH range at 75°C. The rate constants of substitution and the equilibrium constants for a two-step protonation for the dimeric and chelate complexes are calculated. Their solubility in 1 M KCl at 75°C; is determined. The unit cell parameters for [Pt₂(NH₃)₄(-C₂O₄)₂] are determined: a = 3.858 Å, b = 10.704 Å, c = 6.795 Å, = 94.35°. The IR spectra of [Pt(NH₃)₂C₂O₄], [Pt₂(NH₃)₄(-C₂O₄)₂], and their deuterated analogs are studied.     

Determination of the energy measurement accuracy for charged particles by their range in nuclear photoemulsion

Ranges of monochromatic muons in nuclear photoemulsion, produced in the ?? ?? ??? _?? decay, are measured by the coordinate method to determine their energy by the range. The variance of the muon energymeasured by this method ?? _?? = (0.11±0.01) MeV, which corresponds to the accuracy of the determination of the charged particle energy by the range in nuclear emulsion ??3.1%. The developed technique will allow electron energy measurements in the 2??-decay (??3 MeV)with an accuracy of (5?C6)%.     

Reaction of cis-diamminedichloroplatinum(II) with arabinogalactan. The identification and therapeutic effect of the product obtained

A reaction of cis-diamminedichloroplatinum(II) with the natural polysaccharide arabinogalactan gave a product characterized by X-ray powder diffraction, IR spectroscopy, UV spectrophotometry, and thermogravimetry. It was demonstrated that cis-diamminedichloroplatinum(II) is bound to arabinogalactan by a linkage between its -C-O-C- bond and the hydrogen atom of the NH₃ group of the starting complex. The product can suppress tumor growth with no toxic effect on the organism.     

Bounding a domain containing all compact invariant sets of the permanent-magnet motor system

In this paper we characterize a locus of compact invariant sets of the system describing dynamics of the permanent-magnet synchronous motor (PMSM). We establish that all compact invariant sets of this system are contained in the intersection of one-parameter set of ellipsoids and compute its parameters. In addition, localizations by using a parabolic cylinder, an elliptic paraboloid and a hyperbolic cylinder are obtained. Simple polytopic bounds are derived with help of these localizations. Most of localizations mentioned above remain valid for more specific motor systems; namely, for the interior magnet PMSM and for the surface magnet PMSM. Yet another localization set for the interior magnet PMSM is described. Examples of localization of chaotic attractors existing for some values of parameters of PMSMs are presented as well.     

Study of the charge distribution of galactic cosmic rays and search for superheavy nuclei traces in olivine crystals from meteorites

The search for and identification of energetic nuclei of superheavy elements of cosmic rays in olivine crystals frommeteorites, currently performedwithin the Olympia project [1], are based on measurements of dynamic and geometrical parameters of tracks, i.e., chemically etchable regions of the traces of slowing down of these nuclei before their stop, using the fully automated PAVIKOM measuring system [2].     

Asymptotic Solution of the Problem on an Accelerated Source of High-Frequency Oscillations

The problem of the wave field of a source moving in an inhomogeneous medium is considered. It is assumed that the velocity of the source is less than the velocity of sound for t < 0 and is greater than this velocity for t > 0 (subsonicsupersonic transition). An asymptotic expansion for the wave field in a neighborhood of the source is constructed on the basis of the well-known Hadamard ansatz. The expansion derived is uniform with respect to the velocity of the source and contains new special functions. These functions are generalizations of the Hankel and Bessel functions and possess some remarkable properties. Bibliography: 7 titles.