On the behaviour of Brauer pp-dimensions under finitely-generated field extensions

The present paper shows that if $q \in \mathbb P$ or $q = 0$, where $\mathbb P$ is the set of prime numbers, then there exist characteristic $q$ fields $E _{q,k}\colon \ k \in \mathbb N$, of Brauer dimension Brd$(E _{q,k}) = k$ and infinite absolute Brauer $p$-dimensions abrd$_{p}(E _{q,k})$, for all $p \in \mathbb P$ not dividing $q ^{2} - q$. This ensures that Brd$_{p}(F _{q,k}) = \infty$, $p \dagger q ^{2} - q$, for every finitely-generated transcendental extension $F _{q,k}/E _{q,k}$. We also prove that each sequence $a _{p}, b _{p}$, $p \in \mathbb P$, satisfying the conditions $a _{2} = b _{2}$ and $0 \le b _{p} \le a _{p} \le \infty$, equals the sequence abrd$_{p}(E), {\rm Brd}_{p}(E)$, $p \in \mathbb P$, for a field $E$ of characteristic zero.Comment: LaTeX, 14 pages: published in Journal of Algebra {\bf 428} (2015), 190-204; the abstract in the Metadata updated to fit the one of the pape

Magnetic translation groups in n dimensions

Magnetic translation groups are considered as central extensions of the translation group T=Z^n by the group of factors (a~gauge group) U(1). The obtained general formulae allow to consider a magnetic field as an~antisymmetric tensor (of rank 2) and factor systems are determined by a transvection of this tensor with a tensor product t \otimes t'.Comment: 15 pages, Latex 2.09 Presenetd at Symp. "Quant. Group & Their Appl. in Phys.", Poznan, Oct. 17-20 199

Obstructions to nonpositive curvature for open manifolds

We study algebraic conditions on a group G under which every properly discontinuous, isometric G-action on a Hadamard manifold has a G-invariant Busemann function. For such G we prove the following structure theorem: every open complete nonpositively curved Riemannian K(G,1) manifold that is homotopy equivalent to a finite complex of codimension >2 is an open regular neighborhood of a subcomplex of the same codimension. In this setting we show that each tangential homotopy type contains infinitely many open K(G,1) manifolds that admit no complete nonpositively curved metric even though their universal cover is the Euclidean space. A sample application is that an open contractible manifold W is homeomorphic to a Euclidean space if and only if the product of W and a circle admits a complete Riemannian metric of nonpositive curvature.Comment: 29 page

A representação da natureza e do homem nas metáforas das obras da Aipin

This study analyzes the metaphors in such works of contemporary Khanty writer as Yeremei Aipin “Khanty, or the Morning Star Dawn” and “Mother of God in the Bloody Snows”. The metaphors under study reflect the essence of interaction of man and nature and are presented by the author in the form of metaphorical schemes. As a result of the study, the conclusion is made that in the minds of the characters presented in the author’s works, nature and man have a close connection, which is reflected in the use of metaphors that correspond to iconic cognitive schemes: the source sphere “nature” – the target sphere “man”, the source sphere “man” – the target sphere “nature”. The results can be applied in the regional studies, in teaching such courses as “Linguistic Worldview of the Small-numbered Peoples”, and in the works devoted to the creative writing style of Ye.D. Aipin.Este estudio analiza las metáforas en obras del escritor contemporáneo de Khanty como Yeremei Aipin “Khanty, or the Morning Star Dawn” y “Mother of God in the Bloody Snows”. Las metáforas en estudio reflejan la esencia de la interacción del hombre y la naturaleza y son presentadas por el autor en forma de esquemas metafóricos. Como resultado del estudio se concluye que en la mente de los personajes presentados en las obras del autor, la naturaleza y el hombre tienen una estrecha conexión, lo que se refleja en el uso de metáforas que corresponden a esquemas cognitivos icónicos: la esfera fuente. “naturaleza” – la esfera de destino “hombre”, la esfera de origen “hombre” – la esfera de destino “naturaleza”. Los resultados se pueden aplicar en los estudios regionales, en la enseñanza de cursos como "Cosmovisión lingüística de los pueblos pequeños", y en los trabajos dedicados al estilo de escritura creativa de Ye.D. Aipín.Este estudo analisa as metáforas em obras do escritor contemporâneo Khanty como Yeremei Aipin “Khanty, or the Morning Star Dawn” e “Mother of God in the Bloody Snows”. As metáforas em estudo refletem a essência da interação do homem com a natureza e são apresentadas pelo autor na forma de esquemas metafóricos. Como resultado do estudo, conclui-se que na mente dos personagens apresentados nas obras do autor, natureza e homem possuem uma estreita ligação, o que se reflete no uso de metáforas que correspondem a esquemas cognitivos icônicos: a esfera fonte “natureza” – a esfera alvo “homem”, a esfera fonte “homem” – a esfera alvo “natureza”. Os resultados podem ser aplicados nos estudos regionais, no ensino de cursos como “Linguistic Worldview of the Small-numbered Peoples”, e nos trabalhos dedicados ao estilo de escrita criativa de Ye.D. Aipin

Economical adjunction of square roots to groups

How large must an overgroup of a given group be in order to contain a square root of any element of the initial group? We give an almost exact answer to this question (the obtained estimate is at most twice worse than the best possible) and state several related open questions.Comment: 5 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2: minor correction

Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and diffeomorphisms relative to which they are generalized Lie groups or topological groups. Among such topologies pairwise incomparable are found as well. Topological perfectness of the diffeomorphism group relative to certain topologies is studied. There are proved theorems about projective limit decompositions of these groups and their compactifications for compact manifolds. Moreover, an existence of one-parameter local subgroups of diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad

BORON ENRICHMENT BY 10B ISOTOPE IN GAS CENTRIFUGE

Though, the boron isotope 10B is used as a neutron absorber for nuclear reactors. Therefore, it is of interest to consider that by means of gas centrifuges. Unlike the enrichment of uranium hexafluoride, in the separation of boron trifluoride it is necessary to take into account the friction of rotating gas against motionless central body. It has been found that the interaction between gas and real size central body slightly reduces the separating power, providing the possibility of boron isotopes production by centrifuges

On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids

Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics, respectively. In the first part of this paper, we present a result on separation of simplices and balls (up to affine equivalence) among all compact convex sets in two- and three-dimensional Euclidean spaces, which focuses on the set of extreme points and the action of affine transformations on it. Regarding the above-mentioned axiomatization of quantum physics, our result corresponds to the case of simplest (2-level) quantum system. We also discuss a possible extension to higher dimensions. In the second part, towards generalizations of the framework of general probabilistic theories and several existing results including ones in the first part from the case of compact and finite-dimensional physical systems as in most of the literatures to more general cases, we study some fundamental properties of convex sets and affine maps that are relevant to the above subject.Comment: 25 pages, a part of this work is to be presented at QIP 2011, Singapore, January 10-14, 2011; (v2) References updated (v3) Introduction and references updated (v4) Re-organization of the paper (results not added

Experimental study of extended timescale dynamics of a plasma wakefield driven by a self-modulated proton bunch

Plasma wakefield dynamics over timescales up to 800 ps, approximately 100 plasma periods, are studied experimentally at the Advanced Wakefield Experiment (AWAKE). The development of the longitudinal wakefield amplitude driven by a self-modulated proton bunch is measured using the external injection of witness electrons that sample the fields. In simulation, resonant excitation of the wakefield causes plasma electron trajectory crossing, resulting in the development of a potential outside the plasma boundary as electrons are transversely ejected. Trends consistent with the presence of this potential are experimentally measured and their dependence on wakefield amplitude are studied via seed laser timing scans and electron injection delay scan