# WHITNEY'S EXTENSION PROBLEMS AND INTERPOLATION OF DATA

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In the present paper, conditions of embedding for a quadratic extension of an algebraic number field into a cyclic 2-extension are presented. An example of an unsolvable embedding problem for which the compatibility condition is fulfilled is constructed. Bibliography: 7 titles.

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Let K be a finite extension of â„š and let S = {v} denote the collection of normalized absolute values on K. Let VK+ denote the additive group of adeles over K and let c : VK+ â†’ â„ â‰¥ 0 denote the content map defined as c({av}) = Î vâˆˆS (av) for {av} âˆˆ VK+. A...

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We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h( d) of the real quadratic field $$ \mathbb{Q}{\left( {{\sqrt d }} \right)} $$. In particular, we give a new proof of the result of Hasse,...

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Let G be a reductive group over a local field of characteristic zero or a finite central cover of such a group. We present a conjecture that enables one to define formal degree for all unitary representations of G. The conjecture is proved for GLn and over real and p-adic fields, together with a...

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The distribution of special algebraic numbers is studied, and an optimal regular system is constructed. Bibliography: 11 titles.

- algebraic numbers. // Hutchinson Dictionary of Scientific Biography;2005, p1
In mathematics, numbers that satisfy a polynomial equation with rational coefficients: for example, âˆš2 solves x2 - 2 = 0. Real numbers that are not algebraic are called

trancendental numbers . Although there is an infinity of algebraic numbers, there is... - Kings in Hypertournamentsâ€”Survey. Brcanov, Dejan; Petrovic, Vojislav; Treml, Miroslav // AIP Conference Proceedings;9/30/2010, Vol. 1281 Issue 1, p906
A vertex Î½ is an s-king of an hypertournament T if the distance from Î½ to every other vertex of T is at most s. We consider 1-kings and 2-kings of hypertournaments. In some properties they follow corresponding kings of ordinary tournaments. In some other they are completely different.

- On Archimedean Fields. Schleiermacher, Adolf // Journal of Geometry;2009, Vol. 92 Issue 1/2, p143
In this note we consider formally real fields that admit only of Archimedean orderings. Such fields will be called Archimedean. We establish necessary and sufficient conditions for a formally real field to be Archimedean. We also characterize in terms of convexity the positive cones of...

- The embedding problem with non-Abelian kernel for local fields. Ishkhanov, V.; Lur�e, B. // Journal of Mathematical Sciences;Sep2009, Vol. 161 Issue 4, p553
The embedding problem of local fields with p-groups is equivalent to its associated Abelian problem if the inequality d = r + 2 is valid; here d and r are the numbers of generators of the Demushkin group and of the Galois group of an embedded field. Bibliography: 6 titles.