Random summation of independent identically distributed random vectors with zero means

Translated from:Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 20–26.     

Investigation of the fundamental properties of a Coulombian plasma by the method of many-particle dynamics

It is shown that a completely ionized, classical, Coulombian plasma, placed in an adiabatic enclosure, possesses a stationary state. At the same time, a plasma placed in a thermostat recombines through triple collisions, with a velocity satisfactorily accounted for by well-known theoretical results. The results obtained by numerical modeling have shown that, for a plasma placed in an adiabatic enclosure, the ergodic assumption is not valid. Various possible kinetic mechanisms, ensuring the existence of a stationary state of the adiabatically enclosed plasma, are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 3–34, November, 1991.     

Bound states and resonances ofN-particle discrete Schrödinger operator

The existence of bound states and resonances of the Hamiltonian of a system ofN different quantum lattice particles with nonvanishingN-particle short-range interaction is proved. The dependence of the bound states and the resonances on the coupling constant and the quasimomentum is studied.Samarkand State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 51–65, April, 1992.     

Banach-Saks operators on spaces of continuous functions

Summary Let K be a compact Hausdorff space and let E be a Banach space. We denote by C(K, E) the Banach space of all E-valued continuous functions defined on K, endowed with the supremum norm. We study in this paper Banach-Saks operators defined on C(K, E) spaces. We characterize these operators for a large class of compacts K (the scattered ones), or for a large class of Banach spaces E (the superreflexive ones). We also show by some examples that our theorems can not be extended directly.Partially supported by C.A.I.C.Y.T. grant 0338-84. The author wishes to thank Professor F.Bombal for his encouragement.     

Manifolds with invariant semi-Riemannian almost product structure

A manifold M with semi-Riemannian almost product structure invariant relative to a transformation group G is considered. A connection with special G-invariance property is constructed in the corresponding bundle of frames.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 926–931, July, 1992.     

某些查耳酮化合物的发光

本文叙述了两个同质查耳酮系列的合成.一个带有查耳酮中心链(系列Ⅰ),另一个是系列Ⅰ的酯类(系列Ⅱ).研究了每个系列中三种化合物的发光,发现两个系列的所有化合物都能见到发光.系列Ⅰ中的化合物在峰值为360nm处可见到发光,而系Ⅱ列中的化合物未能观测到这一波长的发光.然而,在峰值为470nm处两者均可见到发光.得出的结论是,消除非键电子微扰作用的氢键是系列Ⅰ中的化合物在360nm处出现发光的原因.     

Resistance of composite flywheel rim to radial tensile stresses from centrifugal forces based on results of pure bending of a rim segment

A method is proposed for evaluating the resistance of a flywheel rim to radial stresses in free rotation. The method is based on loading a rim segment in pure bending and calculating the limiting moment and the corresponding limiting angular velocity. Applicability of the method is substantiated theoretically by investigating the similarity of the radial stress diagrams in rotation and pure bending. The method is verified experimentally for the strained state of a rim segment in pure bending.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 521–526, July–August, 1993.