Fluctuations and Instabilities of Ferromagnetic Domain Wall pairs in an External Magnetic Field

Soliton excitations and their stability in anisotropic quasi-1D ferromagnets are analyzed analytically. In the presence of an external magnetic field, the lowest lying topological excitations are shown to be either soliton-soliton or soliton-antisoliton pairs. In ferromagnetic samples of macro- or mesoscopic size, these configurations correspond to twisted or untwisted pairs of Bloch walls. It is shown that the fluctuations around these configurations are governed by the same set of operators. The soliton-antisoliton pair has exactly one unstable mode and thus represents a critical nucleus for thermally activated magnetization reversal in effectively one-dimensional systems. The soliton-soliton pair is stable for small external fields but becomes unstable for large magnetic fields. From the detailed expression of this instability threshold and an analysis of nonlocal demagnetizing effects it is shown that the relative chirality of domain walls can be detected experimentally in thin ferromagnetic films. The static properties of the present model are equivalent to those of a nonlinear sigma-model with anisotropies. In the limit of large hard-axis anisotropy the model reduces to a double sine-Gordon model.Comment: 15 pages RevTex 3.0 (twocolumn), 9 figures available on request, to appear in Phys Rev B, Dec (1994

Note on power hypergraphs with equal domination and matching numbers

We present some examples that refute two recent results in the literature concerning the equality of the domination and matching numbers for power and generalized power hypergraphs. In this note we pinpoint the flaws in the proofs and suggest how they may be mended.Comment: 7 pages, 1 figure, XIII Encuentro Andaluz de Matem\'atica Discreta, (C\'adiz) Spain, july, 202

The mRNA degradation factor Xrn1 regulates transcription elongation in parallel to Ccr4

Co-transcriptional imprinting of mRNA by Rpb4 and Rpb7 subunits of RNA polymerase II (RNAPII) and by the Ccr4–Not complex conditions its posttranscriptional fate. In turn, mRNA degradation factors like Xrn1 are able to influence RNAPII-dependent transcription, making a feedback loop that contributes to mRNA homeostasis. In this work, we have used repressible yeast GAL genes to perform accurate measurements of transcription and mRNA degradation in a set of mutants. This genetic analysis uncovered a link from mRNA decay to transcription elongation. We combined this experimental approach with computational multi-agent modelling and tested different possibilities of Xrn1 and Ccr4 action in gene transcription. This double strategy brought us to conclude that both Xrn1-decaysome and Ccr4–Not regulate RNAPII elongation, and that they do it in parallel. We validated this conclusion measuring TFIIS genome-wide recruitment to elongating RNAPII. We found that xrn1Δ and ccr4Δ exhibited very different patterns of TFIIS versus RNAPII occupancy, which confirmed their distinct role in controlling transcription elongation. We also found that the relative influence of Xrn1 and Ccr4 is different in the genes encoding ribosomal proteins as compared to the rest of the genome

Time Series on Functional Service Life of Buildings using Fuzzy Delphi Method

The functional service life of heritage buildings, defined as the time period during which the building fulfils the requirements for which it was designed, is a complex system that has still not been fully resolved and continues to be the object of research regarding its social, economic and cultural importance. This paper presents an application for analysing time series that reflect the state of building performance over time. To this end, historical time records are used that provided data that could be interpreted by experts in the field. The latter can then evaluate the input variables (vulnerability and risk) using the expert system for predicting the service life of buildings, Fuzzy Building Service Life (FBSL), this methodology put together the fuzzy logic tools and Delphi method. This model provides output data on the state of functionality or performance of each buildings at each moment in time whenever information records are available. The Delphi Method is used to eliminate expert subjectivity, establishing an FDM-type assessment methodology that effectively quantifies the service life of buildings over time. The application is able to provide significant data when generating future preventive maintenance programmes in architectural-cultural heritage buildings. It can also be used to optimise the resources invested in the conservation of heritage buildings. In order to validate this system, the FDM methodology is applied to some specific building examples.Ministerio de Economía y Competitividad de España, Project ART-RISK - BIA2015-64878-RMinisterio de Economía y Competitividad de España MTM 2015-65397-

Irreducible triangulations of the Möbius band

A complete list of irreducible triangulations is identified on the Möbius band.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia e Innovació

Generating punctured surface triangulations with degree at least 4

As a sequel of a previous paper by the authors, we present here a generating theorem for the family of triangulations of an arbitrary punctured surface with vertex degree ≥ 4. The method is based on a series of reversible operations termed reductions which lead to a minimal set of triangulations in such a way that all intermediate triangulations throughout the reduction process remain within the family. Besides contractible edges and octahedra, the reduction operations act on two new configurations near the surface boundary named quasi-octahedra and N-components. It is also observed that another configuration called M-component remains unaltered under any sequence of reduction operations. We show that one gets rid of M-components by flipping appropriate edges

Periodos asociados a los isotopismos de un cuadrado latino

En Criptografía, la eficacia de un generador de secuencias pseudo-aleatorias viene determinada por el periodo de crecimiento en la secuencia generada. En el caso concreto de generadores basados en elementos líderes y cuadrados latinos, existen diversos análisis estadísticos que confirman la importancia que adquiere una óptima elección del cuadrado latino en el que se basa el generador, si bien limitan su estudio a un único líder, que determina a su vez la secuencia de partida. En el presente trabajo, se desarrolla una alternativa al análisis del periodo de crecimiento, atendiendo a todo el conjunto de líderes y ampliando el de secuencias de partida, al mismo tiempo que se analiza la influencia que ejercen en dicho periodo las estructuras cíclicas de las simetrías de un cuadrado latino. Atendiendo a dicho análisis se obtiene explícitamente una clasificación de los cuadrados latinos de orden menor o igual a 5

Irreducible triangulations of the once-punctured torus

A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of combinatorial structures of irreducible triangulations is made by hand for the once-punctured torus, consisting of exactly 297 non-isomorphic triangulations.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia e Innovació

Geometric Realization of Möbius Triangulations

A Möbius triangulation is a triangulation on the Möbius band. A geometric realization of a map M on a surface $\Sigma$ is an embedding of $\Sigma$ into a Euclidean 3-space $\mathbb{R}^3$ such that each face of M is a flat polygon. In this paper, we shall prove that every 5-connected triangulation on the Möbius band has a geometric realization. In order to prove it, we prove that if G is a 5-connected triangulation on the projective plane, then for any face f of G, the Möbius triangulation $G-f$ obtained from G by removing the interior of f has a geometric realization