Let Q(ζm) be the mth cyclotomic field, where ζm is a primitive mth root of unity for an integer m ≥ 1. Let hm denote the class number of Q(ζm) and hm be the class number of its maximal real subfield Q(ζm + ζ −1 m ). Kummer proved that the relative class number hm = hm/h + m is an integer, and in 1851 he claimed ([7], pg. 473) that the rule for the asymptotic growth of hp as the prime p → ∞ is g...

Let K be a field with a valuation satisfying the following conditions: both K and the residue field k have characteristic zero; the value group is not 2-divisible; there exists a maximal subfield F in the valuation ring such that Gal(F̄ /F ) and Gal(k̄/k) have the same 2-cohomological dimension and this dimension is finite. Then Hilbert’s Tenth Problem has a negative answer for any function field...

Let F be a number field with ring of integers OF and D a division F -algebra with a maximal cyclic subfield K. We study rings occurring as quotients of a natural OF -order Λ in D by two-sided ideals. We reduce the problem to studying the ideal structure of Λ/qΛ, where q is a prime ideal in OF , s ≥ 1. We study the case where q remains unramified in K, both when s = 1 and s > 1. This work is mot...

Given polar spaces (V, β) and (V, Q) where V is a vector space over a field K, β a reflexive sesquilinear form and Q a quadratic form, we have associated classical isometry groups. Given a subfield F of K and an F -linear function L : K → F we can define new spaces (V, Lβ) and (V, LQ) which are polar spaces over F . The construction so described gives an embedding of the isometry groups of (V, ...

This paper presents the results of an investigation specific types of information found in sentences of subfield articles, though a priori semantic categories are not used. The method of sublanguage grammars for obtaining information formats is described. Illustrations are drawn from a sublanguage grammar written for a subfield of pharmacology. Parts of the procedure are computerized or are bei...

Let $K$ be a global or local field, $E/K$ Galois extension, and Br$(E)$ the Brauer group of $E$. This paper shows that if is $v$ its natural discrete valuation, $v'$ valuation $E$ extending $v$, $q$ characteristic residue field $\widehat E$ $(E, v')$, then Br$(E) = \{0\}$ only following conditions hold: contains as subfield maximal $p$-extension K$, for each prime $p \neq q$; an algebraically c...

Recent studies suggested that sestrin2 is a crucial modulator for the production of reactive oxygen species (ROS). In addition, sestrin2 may also regulate ribosomal protein S6 (RpS6), a molecule important for protein synthesis, through the effect of mammalian target of rapamycin (mTOR) complex that is pivotal for longevity. However, the roles of sestrin2 in cerebral ischemia, in which oxidative...

Space-time coding is used for reliable high rate transmission over wireless digital channels with multiple antennas at both the transmitter and receiver ends. From a mathematical point of view, a space-time block code (STBC) consists of a family of matrices with complex entries (the codebook) that satisfies a number of properties which determine how well the code performs. The first aim is to f...