The on-line width of various classes of posets.

An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemer\\u27edi proved that any on-line algorithm could be forced to use $\binom{w+1}{2}$ chains to partition a poset of width $w$. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In the survey paper by Bosek et al., variants of the problem were studied where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size $d$. We prove two results for this problem. First, we prove that any on-line algorithm can be forced to use $(2-o(1))\binom{w+1}{2}$ chains to partition a $2$-dimensional poset of width $w$. Second, we prove that any on-line algorithm can be forced to use $(2-\frac{1}{d-1}-o(1))\binom{w+1}{2}$ chains to partition a poset of width $w$ presented via a realizer of size $d$. Chrobak and \\u27Slusarek considered variants of the on-line chain partitioning problem in which the elements are presented as intervals and intersecting intervals are incomparable. They constructed an on-line algorithm which uses at most $3w-2$ chains, where $w$ is the width of the interval order, and showed that this algorithm is optimal. They also considered the problem restricted to intervals of unit-length and while they showed that first-fit needs at most $2w-1$ chains, over $30$ years later, it remains unknown whether a more optimal algorithm exists. We improve upon previously known bounds and show that any on-line algorithm can be forced to use $\lceil\frac{3}{2}w\rceil$ chains to partition a semi-order presented in the form of its unit-interval representation. As a consequence, we completely solve the problem for $w=3$. We also consider entirely new variants and present the results for those

Lagrangian analysis of the northern stratospheric polar vortex split in april 2020

The present study examines the northern stratosphere during April 2020, when the polar vortex split into two cyclonic vortices during a winter-early spring period with the strongest ozone depletion on record. We investigate the dynamical evolution leading to the split at middle stratospheric levels, including the fate of fluid parcels on the vortex boundary during its rupture and the distribution of ozone between the vortices resulting from the split. We also illustrate the vertical structure of the vortices after the split. The findings obtained with Lagrangian methods confirm the key role for the split played by a flow with a special configuration of barriers to the motion of parcels. A trajectory analysis clarifies how the ozone distribution between vortices was such that ozone poorest air remained in the main vortex. The offspring vortex had a deep structure from the troposphere and later decayed to vanish by the end of April.Peer ReviewedObjectius de Desenvolupament Sostenible::13 - Acció per al ClimaPostprint (published version

Can universe exit from phantom inflation due to gravitational back reaction?

The effects of the gravitational back reaction of cosmological perturbations are investigated in a phantom inflation model. The effective energy-momentum tensor of the gravitational back reaction of cosmological perturbations whose wavelengths are larger than the Hubble radius is calculated. Our results show that the effects of gravitational back reaction will counteract that of the phantom energy. It is demonstrated in a chaotic phantom inflation model that if the phantom field at the end of inflation is larger than a critical value determined by the necessary e-folds, the phantom inflation phase might be terminated by the gravitational back reaction.Comment: 9 pages, Revtex4, to appear in JCA

A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex

In this work, we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the exceptional sudden Stratospheric warming event that took place during September 2002. Our focus is on constructing a simple kinematic model that retains the fundamental mechanisms responsible for complex fluid parcel evolution, during the polar vortex breakdown and its previous stages. The construction of the kinematic model is guided by the Fourier decomposition of the geopotential field. The study of Lagrangian transport phenomena in the ERA-Interim reanalysis data highlights hyperbolic trajectories, and these trajectories are Lagrangian objects that are the kinematic mechanism for the observed filamentation phenomena. Our analysis shows that the breaking and splitting of the polar vortex is justified in our model by the sudden growth of a planetary wave and the decay of the axisymmetric flow

A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex

In this work, we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the exceptional sudden Stratospheric warming event that took place during September 2002. Our focus is on constructing a simple kinematic model that retains the fundamental mechanisms responsible for complex fluid parcel evolution, during the polar vortex breakdown and its previous stages. The construction of the kinematic model is guided by the Fourier decomposition of the geopotential field. The study of Lagrangian transport phenomena in the ERA-Interim reanalysis data highlights hyperbolic trajectories, and these trajectories are Lagrangian objects that are the kinematic mechanism for the observed filamentation phenomena. Our analysis shows that the breaking and splitting of the polar vortex is justified in our model by the sudden growth of a planetary wave and the decay of the axisymmetric flow

New Isotropic and Anisotropic Sudden Singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.Comment: Typos corrected. Published versio

Crossing the phantom divide without phantom matter

A class of braneworld models can lead to phantom-like acceleration of the late universe, but without the need for any phantom matter. In the simplest models, the universe contains only cold dark matter and a cosmological constant. We generalize these models by introducing a quintessence field. The new feature in our models is that quintessence leads to a crossing of the phantom divide, $w=-1$. This is a purely gravitational effect, and there is no phantom instability. Furthermore, the Hubble parameter is always decreasing, and there is no big rip singularity in the future.Comment: 5 pages, 5 figures, revtex

Evaluación bioeconómica de alternativas ganaderas a la producción de leche en las sabanas infértiles del norte de Camagüey

Livestock alternatives to milk production were evaluated with the improvement of the native pasture from an association of Andropogon gayanus cv. CIAT 621 and Centrosema pubescens, which had shown good adaptation to the edaphic and climatic conditions of the savannas in the north of the province of Camagüey, Cuba, where Fersialitic Red Parduzco Mullido Ferromagnesial soils predominate, with low fertility. The alternatives were bovine fattening and dairy accompanied by sheep farming. The stage was a farm located in the area with typical characteristics of that place. Forage and food balances were carried out to obtain the productive response to the planting of grass and supplementation and the partial budget analysis for the net change of utilities of each variant. The calculations were made in USD according to the costs and prices in force in 2003. Within the variants of fattening the planting of the association in 25 and 40% of the area with or without supplement achieved the greatest net changes in profits with respect to Dairy activity, while in the case of diversified dairy with sheep farming, the greatest advantages are obtained for the 40% improvement of the native pasture in both cases. According to the results, for the region the best options of livestock exploitation and improvement of the native pasture from the association with respect to the dairy would be the bovine fattening with 25 and 40% improvement with and without supplementation and the diversified dairy with sheep breeding with a 40% improvement.Se evaluaron alternativas ganaderas a la producción de leche con la mejora del pastizal nativo a partir de una asociación de Andropogon gayanus cv. CIAT 621 y Centrosema pubescens, que había mostrado buena adaptación a las condiciones edáficas y climáticas de las sabanas del norte de la provincia de Camagüey, Cuba, donde predominan los suelos Fersialítico Rojo Parduzco Mullido Ferromagnesial, de baja fertilidad. Las alternativas fueron la ceba bovina y la lechería acompañada de la cría ovina. El escenario fue una finca ubicada en la zona con características típicas de ese lugar. Se realizaron los balances de forrajes y alimentarios para obtener la respuesta productiva a la siembra de pasto y suplementación y el análisis de presupuesto parcial para el cambio neto de utilidades de cada variante. Los cálculos se hicieron en USD de acuerdo a los costos y precios vigentes en 2003. Dentro de las variantes de ceba la siembra de la asociación en el 25 y 40 % del área con o sin suplemento lograron los mayores cambios netos de utilidades con respecto a la actividad lechera, mientras que en  el  caso  de  la lechería  diversificada  con la  cría  ovina  las  mayores  ventajas  se obtienen para el 40 % de mejora del pastizal nativo en ambos casos. De acuerdo con los resultados, para la región las mejores opciones de explotación ganadera y mejora del pastizal nativo a partir de la asociación con respecto a la lechería serían la ceba bovina con 25 y 40 % de mejora con y sin suplementación y la lechería diversificada con la cría de ovinos con un 40 % de mejora