Enhancement of local superconductivity in ferromagnetic FeCrB metallic glass by Ar+ ion irradiation

We have reinforced local superconductivity in ferromagnetic Fe(67)Cr(18)B(15) metallic glasses by ion irradiation. Superconductivity in this medium appears due to the presence of large-scale layered clusters of metallic Fe-Cr phase, 150-230 ? in size, with a ferromagnetic (or superparamagnetic) Fe-rich core and nonmagnetic Cr-rich superconducting shell. Here we show that due to the intensification of concentration phase separation in the Fe-Cr clusters under ion (Ar(+)) irradiation, the volume of the superconducting phase increases from the initial 0.4-0.5% up to 7-8%. After irradiation, the resistivity jump Δρ/ρ in the temperature range T=3.1-3.6 K increases ～14 times, reaching 19%, as compared to 1.36% for the initial sample. In the interval of T=3.1-3.6 K, the rate of resistance change reaches 79% K(-1) for the irradiated sample instead of 3.6% K(-1) for the initial sample. In the same temperature interval, the rate of magnetoresistance change increases from 3% K(-1) for the initial sample up to 70% K(-1) after irradiation.     

Ethylene polymerization and ethylene-1-hexene copolymerization over immobilized metallocene catalysts

Ethylene polymerization and ethylene-1-hexene copolymerization in the presence of metallocene catalysts based on Cp₂ZrCl₂, rac-Et(Ind)₂ZrCl₂, rac-Me₂Si(2-Me-4-Ph-Ind)₂ZrCl₂, and rac-Me₂Si(2-Me-4-Ph-Ind)₂HfCl₂ been investigated. The catalysts have been immobilized on montmorillonite (MMT) containing methylaluminoxanes (MMT-H₂O)/AlMe₃ or isobutylaluminoxanes (MMT-H₂O)/ Ali-Bu₃ synthesized directly on the support surface. The immobilized catalysts, with the general formula (MMT-H₂O)/AlR₃/Zr(Hf)-cene, show a high activity comparable with the activity of the respective homogeneous systems, which depends on the nature of the metal and on the metallocene composition and structure. The catalytic properties of the metallocene systems depend strongly on the nature of the activator as a component of the catalytic complex. (MMT-H₂O)/Ali-Bu₃ is a more effective activator of the hafnocene precatalyst in the polymerization processes than oligomeric methylaluminoxane or methylaluminoxane synthesized on the support. The immobilization of the metallocenes on (MMT-H₂O)/AlR₃ leads to an increase in the molar mass of polyethylene and ethylene-1-hexene copolymers relative to the molar mass of the polymers synthesized using the respective homogeneous systems. The immobilized metallocene catalysts display high selectivity toward the insertion of a higher α-olefin (1-hexene) into the polymer chain, retaining this important property of their homogeneous counterparts.     

Generalized solutions of impulse systems and the phenomenon of pulsations

For systems of differential equations with impulse action at nonfixed moments of time, the concept of a generalized solution is presented. On its basis a classification of impulse systems is proposed and conditions are indicated sufficient for the impulse system to belong to one class or another.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 657–663, May, 1991.     

Unbounded functions with almost periodic differences

The structure of continuous real-valued functions F(t) on the real line, such that for any fixed y the difference F(t+y)–F(t) is an almost periodic Bohr function, is investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1409–1413, October, 1991.     

Conditions for Synchronization of One Oscillation System

Using methods of perturbation theory, we investigate the global behavior of trajectories on a toroidal attractor and in its neighborhood for a system of differential equations that arises in the study of synchronization of oscillations in the mathematical model of an optical laser. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 922–945, July, 2005.     

Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds

We investigate S¹-invariant Hamiltonian systems on compact 4-dimensional symplectic manifolds with free symplectic action of a circle. We show that, in a rather general case, such systems generate ergodic flows of types (quasiperiodic and nilpotent) on their isoenergetic surfaces. We solve the problem of straightening of these flows. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 1, pp. 122–140, January, 1997.     

Study of a discrete dynamic system in a neighborhood of a quasi-periodic trajectory

We study a discrete system in a neighborhood of a quasi-periodic trajectory. We obtain conditions for reducing a system in this neighborhood to a system with quasi-periodic coefficients. We determine the behavior of this system under the action of small perturbations.This work was prepared with the financial support of the Ukrainian State Committee on Science and Technology.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 12, pp. 1702–1711, December, 1992.     

Linear Noetherian boundary value problems for differential systems with an impulse action

A solvability criterion of linear nonhomogeneous boundary value problems is obtained for systems of ordinary differential equations with impulse action in the general case when the number of boundary conditions does not coincide with the order of the differential system (Noetherian problems). The generalized Green operator of such boundary value problems is constructed. Its connection with the generalized inverse operator of the operator of the original boundary value problem is shown.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 564–568, April, 1992.     

Investigation of a dynamical system in a neighborhood of an invariant toroidal manifold in the general case

A dynamical system is studied in the neighborhood of an invariant toroidal manifold for the most general relationship between the dimensionality of the phase space and the dimensionality of the manifold.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1399–1408, October, 1994.