Time kink: modeling change of metric signature

The model of a signature change of a metric from the Lorenztian to Euclidean one with the use of a time dependent kink as $g_{00}$ component of the metric is considered. The metric which describes the continuous change of the signature of this type on a hypersurface is constructed and corresponding Einstein equations are solved in both regions of the space-time. The discontinuities of the Einstein tensor components on the hypersurface are discussed as well as junction conditions for the parameters of the solutions. Additionally, the properties of simple cosmological model are discussed in the model, the presence of an inflation in the model is demonstrated as a consequence of the signature change without any additional fields need. The possible appearance of this type of solution for the metric in the form of the scalar field in the framework of the Einstein-Cartan gravity is described. The Lagrangian for that field and it's properties are obtained as well as a time dependent potential of the field which separate the Lorentzian and Euclidean regions of the space-time

Vortex Filament Equation for a regular polygon in the hyperbolic plane

The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and both of its ends grow exponentially, which makes the problem more challenging from a numerical point of view. However, with fixed boundary conditions, a finite difference scheme and a fourth-order Runge--Kutta method in time, we show that the numerical solution is in complete agreement with the one obtained from algebraic techniques. Second, as in the Euclidean case, we claim that, at infinitesimal times, the evolution of VFE for a planar polygon as the initial datum can be described as a superposition of several one-corner initial data. As a consequence, not only can we compute the speed of the center of mass of the planar polygon, but the relationship also allows us to compare the time evolution of any of its corners with that in the Euclidean case

On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion

In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical simulations, we show that the solutions are polygons at rational times, as in the zero-torsion case. However, unlike in that case, the evolution is not periodic in time; more- over, the multifractal trajectory of the point X(0,t) is not planar, and appears to be a helix for large times. These new solutions of VFE can be used to illustrate numerically that the smooth solutions of VFE given by helices and straight lines share the same instability as the one already established for circles. This is accomplished by showing the existence of variants of the so-called Rie- mann’s non-differentiable function that are as close to smooth curves as desired, when measured in the right topology. This topology is motivated by some recent results on the well-posedness of VFE, which prove that the selfsimilar solutions of VFE have finite renormalized energy

A technical note: The role of liliequist membrane fenestration during the pterional approach for anterior circulation aneurysm clipping

The Liliequist membrane is a critical membrane located at the base of the brain separating the supratentorial from the infratentorial cisterns. The advantages of Liliequist membrane fenestration as a critical part of the pterional trans-Sylvian approach for ruptured anterior circulation aneurysm clipping is not well established. We demonstrated that the fundamental role of Liliequist membrane fenestration is brain relaxation through the egress of CSF that is not usually gained from other modalities (e.g., placement of a lumbar drain, fenestration of lamina terminalis) in this specific setting

Unraveling beam self-healing

We show that, contrary to popular belief, non only diffraction-free beams may reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon Shack-Hartmann wave front reconstruction. We believe that these results can open new avenues in this field

Stability of the selfsimilar dynamics of a vortex filament

In this paper we continue our investigation about selfsimilar solutions of the vortex filament equation, also known as the binormal flow (BF) or the localized induction equation (LIE). Our main result is the stability of the selfsimilar dynamics of small pertubations of a given selfsimilar solution. The proof relies on finding precise asymptotics in space and time for the tangent and the normal vectors of the perturbations. A main ingredient in the proof is the control of the evolution of weighted norms for a cubic 1-D Schr\"odinger equation, connected to the binormal flow by Hasimoto's transform.Comment: revised version, 36 page

Travelling ionospheric disturbances over Kharkiv, Ukraine, accompanying the operation of EISCAT heater facility

We have detected the travelling ionospheric disturbances (TIDs) over Kharkiv with periods of 40–80 min occurring in the time range between 09:00 and 10:30 UT on November 22 and between 10:00 and 12:00 UT on November 23, 2012 during and after the operation of the EISCAT heater facility. The duration of these disturbances were less than 120–180 min. The relative amplitudes of the TIDs in electron density ranged from 0.05 to 0.15 and those in electron and ion temperatures were about 0.02 – 0.05. Assuming that these TIDs have been generated in the heated region, we described the possible mechanisms of their generation.Виявлено рухомі іоносферні збурення (РІЗ) над Харковом з періодами 40–80 хв., що мали місце впродовж 09:00 – 10:30 UT 22 листопада та з 10:00 до 12:00 UT 23 листопада 2012 р. в період і після роботи нагрівного стенда EISCAT. Тривалість цих збурень не перевищувала 120–180 хв. Відносні амплітуди РІЗ концентрації електронів складали 0.05 – 0.15, а РІЗ температур електронів та іонів дорівнювали 0.02 – 0.05. За припущення, що ці РІЗ були згенерровані в нагрітій області, описано можливі механізми їх генерації

Metodología de Análisis Envolvente de Datos (DEA) - GLMNET para la Evaluación y Pronóstico de Eficiencia Financiera en una Zona Franca Industrial - Colombia.

This research work proposes a methodology for evaluation and forecasting for companies located in the Industrial Port Zone of the city of Barranquilla, Colombia. Based on an empirical and rational analysis, supported by the concepts of technical efficiency, purely technical efficiency, additive efficiency, efficiency of scale and of mixing, as well as in the algorithm for machine learning GLMNET. Work was done with 29 companies that presented their complete financial statements for the year 2017 in the Chamber of Commerce of Barranquilla - Colombia. As a result, it was found an average technical efficiency of 72.79%, a purely technical efficiency of 82.54% and an additive efficiency of 59.45%. In addition, the projections required to make inefficient organizations achieve efficiency are contributed. From the study, it can also be observed that 11 companies were constituted as benchmarks to measure the companies of the Free Zone of the Port of Barranquilla. It is noteworthy that the algorithm GLMNET delivered a good result in the prediction of group membership of efficient and inefficient enterprises, with an accuracy of 93.1%. © 2019 Centro de Informacion Tecnologica. All rights reserved.Department of Environmental Affairs, DEATeniendo en cuenta que las exportaciones generan un incremento de la productividad como lo señalan diferentes autores (Pardo y García, 1999), esta variable se estudia en esta investigación toda vez que se aportan las directrices para que las empresas ineficientes de la zona franca en estudio alcancen la eficiencia empresarial. En términos financieros con esta investigación se analiza las magnitudes en términos de ingresos y utilidad neta de tal forma que las empresas ineficientes incrementen su eficiencia frente a los recursos que utilizan. Lo anterior permite generar una serie de decisiones en el contexto analizado que permite dinamizar y direccionar las acciones para alcanzar los resultados que permita a las organizaciones ineficientes ser competitivas en el sector. Existen investigaciones previas sobre el uso del análisis DEA y el aprendizaje automático, en (Hong et al., 1999) clasifican empresas eficientes y no eficientes utilizando DEA para luego predecir el estado de eficiencia de nuevas empresas, por otro lado (Lin, Hu, y Tsai, 2012) revisan en un periodo de cinco años la implementación del aprendizaje automático y los modelos DEA para la modelación del riesgo de quiebra en las empresas, a su vez otras investigaciones realizan procesos de clasificación paralelas utilizando la técnica de Support Vector Machines (Yeh, Chi, y Hsu, 2010), además de valoraciones empresariales en sectores específicos, como cadenas de suministro ( Wong y Wong, 2007) y desempeño corporativo (Mirhedayatian, Azadi y Saen, 2014)

Looking for signatures of the Left-Right Twin Higgs model with the ATLAS detector at the LHC

The twin Higgs mechanism has recently been proposed to solve the little hierarchy problem. The phenomenology of this model is presented, and the possibility to observe some of the signatures predicted by this model using the ATLAS detector at the LHC is discussed