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Vladikavkaz Mathematical Journal

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January-March, 2000

Volume 2, Issue 1

On Combined Nonstandard Methods in Functional Analysis
A.G. Kusraev (Vladikavkaz) and S.S. Kutateladze (Novosibirsk)
UDC 517.98

The main nonstandard tool-kits are known as infinitesimal analysis (Robinson's nonstandard analysis) and Boolean-valued analysis (see [1] and the references there in). Sharp distinctions between these two versions of nonstandard analysis in content and technique notwithstanding, many ways are open to their simultaneous application [2, 3]. One of the simplest approaches consists in successive application of different nonstandard methods [4, 5]. A few examples below demonstrate that combining is often useful in settling the problems of functional analysis which stem mainly from the theory of vector lattices. We believe firmly in importance of constructing a synthetic theory that utilizes both nonstandard ways of mathematical reasoning.

Article (eng.) - [pdf] [zip-pdf]

Cyclically Compact Operators in Banach Spaces
A. G. Kusraev (Vladikavkaz)
UDC 517.98

The Boolean-valued interpretation of compactness gives rise to the new notions of cyclically compact sets and it operators which deserves an independent study. A part of the corresponding theory is presented in this work. The necessary information from the theory of Boolean-valued models can be found in [1] and [2].

Article (eng.) - [pdf] [zip-pdf]

Mathematical Modeling of Internal Gravity Waves in Water Basin at a Selective Water Intake
I. D. Мuzaev, J. D. Tuaeva (Vladikavkaz)
UDC 532 (075.8)

The contact problem of oscillation of interface of different density of layers of water is resolved at a selective water intake from high layer. The linear theory of surface and internal gravity waves of small amplitude utilised. The depthes of layers are final values. At the solution of a problem are allowed wavemaking on a surface of high layer. The expression, which one allows to place the lower stand of interface of layers, is obtained. The schedules of oscillation of interface are adduced depending on the design characteristics of a window of water intake of facility.

Article (rus.) - [pdf] [zip-pdf]

The Fundumental Function of Non-linear Temperature Field
Т. Z. Chochiev (Tskhinval)
UDC 539.377

The problem of non-linear field of temperature for uniform and resilient half-space is considered in the article. The function, from which the linearity of temperature field is depended, relates with linear field of temperature. Because of this connection the relation which helps us to define the non-linear field of temperature using linear field of temperature, have been constructed. It is interesting to consider the case of p(x,t) is unknown. In this article we proclaim the features of this function and the statute of alteration.

Article (rus.) - [pdf] [zip-pdf]

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