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Byline: S. N. Il'in (1) Abstract: Infinite limitedly Toeplitz extensions of a finite rectangular Toeplitz matrix are considered. Conditions necessary and sufficient for such an extension of smallest rank to be unique are established. Bibliography: 2 titles. Author Affiliation: (1) Kazan' State University, Kazan', Russia Article History: Registration Date: 22/11/2005 Received Date: 06/05/2004 Article note: Published in Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 30--39.

It is commonly agreed that students' ways of thinking should be taken into account when planning instruction and that teachers should choose or construct sequences of instruction for use and […]

Abstract: The self-adjoint elliptic boundary-value problem in a domain with cylindrical outlets to infinity is considered. The notion of an augmented scattering matrix is introduced on the basis of artificial radiation conditions. Properties of the augmented scattering matrix are studied, and the relationship with the classical scattering matrix is demonstrated. The central point is the possibility of calculating the number of linearly independent solutions of a homogeneous problem with fixed rate of decrease at infinity by analyzing the spectrum of the augmented scattering matrix. This property is applied to the problem on diffraction on a periodic boundary as an example. Bibliography: 21 titles. Article History: Registration Date: 21/10/2004

Byline: V. V. Perepichka (1), I. P. Shats'kyi (1) Abstract: We reduce the problem on bending of a semiinfinite plate containing a periodic system of parallel internal cuts (cracks) perpendicular to the free edge to an integral equation. Numerical calculations are performed and their analysis is presented. Author Affiliation: (1) Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv Article History: Registration Date: 09/10/2004

Byline: S. A. Nazarov (1) Abstract: The NavieraStokes problem in a plane domain with two angular outlets to infinity is provided, as usual, either with the flux condition or with the pressure drop one. For small data it is proved that there exists a solution with the decay O(|x|.sup.-1) of the velocity field as |x| [right arrow] [infinity] (if one of the angles is equal to or greater than [pi], then additional symmetry assumptions are needed). Since the nonlinear and linear terms are asymptotically of the same power, the results are based on a complete investigation of the linearized Stokes problem in weighted spaces with a detached asymptotics (the angular parts in the representations are not fixed). Bibliography: 16 titles. Author Affiliation: (1) The Mechanical Engineering Institute of the Russian Academy of Sciences, Russia Article History: Registration Date: 12/10/2004

Byline: D. Khmelev (1), E. Spodarev (2) Author Affiliation: (1) Moscow State University, Vorob'yovy Gory, 119899, Moscow, Russia (2) Friedrich--Schiller Universitat Jena, Jena, Germany Article History: Registration Date: 20/10/2004

Byline: G. B. Di Masi (1), A. Stettner (2) Author Affiliation: (1) Universita di Padova and CNR--LADSEB, Padova, Italy (2) Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-950, Warsaw, Poland Article History: Registration Date: 20/10/2004

Byline: R. M. Kushnir (1), Ya. D. P'yanylo (1) Abstract: By using the Laplace integral transformation, we determine and investigate the thermostressed state of a three-layer structure compressed at infinity in the case of nonideal thermal contact at interfaces. Such a structure models a piecewise-homogeneous friction assembly. The contact interaction between the components of the structure under study and their relative motion with friction result in an increase in temperature, which induces thermoelastic displacements. We present the results of a numerical calculation of the dependence of these parameters on time and the spatial coordinate. Author Affiliation: (1) Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv Article History: Registration Date: 11/10/2004

Abstract: An empirical study of Smarandache k-k additive relationships and related data is tabulated and analyzed. It leads to the conclusion that the number of Smarandache 2-2 additive relations is [...]

Abstract: An analysis of the number of relations of the type S(n)-S(n+1)-S(n+2)-S(n+3) for n This brief note on Smarandache 2-2 subtractive relationships should be seen in relation to the article [...]

In his recent paper[1], Sastry defines two triangles T(a, b, c) and T(a', b', c') to be Smarandache related if S(a) = S(a'), S(b) = S(b') and S(c) = S(c'). [...]

Byline: A. W. Moore (1) Keywords: Infinity; Paradoxes; Set theory; Aristotle; Cantor Abstract: For over two thousand years thought about the infinite was dominated by Aristotelian hostility to the idea that the infinite could be a legitimate object of mathematical study. Then Cantor's work late in the nineteenth century seemed to overturn this orthodoxy. However, by highlighting ways in which infinitude still could not be brought under the control of mathematicians, Cantor's work may in fact have reinforced the orthodoxy. Author Affiliation: (1) St. Hugh's College, Oxford, Ox2 6le, England Article History: Registration Date: 15/10/2004

Time-neutrality and impatience in a finite horizon context are well-understood economic concepts. However, time-neturality on the set of bounded infinite utility streams remains undefined. Time-neutrality in an infinite horizon results from the repeated application of time-neutrality's finite version. Research shows that time-neutrality's infinite version can be defined as invariance under bounded permutations.

Abstract In this paper, we use the elementary methods to study the properties of the infinity series [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1 [n.sup.s], where A denotes the set [...]

A study which analyzes the texts of Rene Descartes that speak about real bodies suggests that when Descartes speaks about the divisibility of matter into imperceptible parts to infinity, he is not talking about the existence of mind-independent material substances to infinity. It is argued that Descartes rather talks about a single material substance, or essence, apprehensible by the mind alone, in virtue of which an indivisible material thing is inconceivable, thereby proving the Eleatic Descartes has remained intact.

ABSTRACT Professor Anthony Begay of Navajo Community College influenced me in writing this paper. I enjoyed the Smarandache concatenation. The sequences shown here have been extracted from the Arizona State [...]