Scalar field critical collapse in 2+1 dimensions

We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2+1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the $n=4$ Garfinkle solution, matched at the lightcone to a Vaidya-like solution, and corrected to leading order for the effect of $\Lambda<0$. This approximation is only $C^3$ at the lightcone and has three growing modes. We {\em conjecture} that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of $\gamma=8/7$ and a mass-scaling exponent of $\delta=16/23$, compatible with our numerical experiments.Comment: 27 page

Strong and safe Nash equilibrium in some repeated 3-player games

We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players' payoffs do not exceed the non-deviating player payoff more than a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale's good strategies described in \cite{smale}, where the repeated Prisoner's Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.Comment: 19 page

Natural and Anthropogenic Conditions of the Chemical Composition of Pit Lake Waters (Based on Example Pit Lakes from Central Europe)

The article presents a classification of hydrochemical types of waters in pit lakes. Although natural factors significantly influence the chemical composition of water, the differences between hydrochemical types are also determined by anthropogenic factors. The chemical composition of the water in pit lakes is primarily determined by the kind of rocks mined during the excavation, while secondary anthropogenic impacts can modify the chemical composition of the water. A multidimensional clustering analysis of the water was performed, which allowed three main types of hydrochemical reservoirs to be delimited for the pit lakes assessed in this study: a bicarbonate–magnesium–calcium water type ( HCO3–Mg–Ca), a bicarbonate–calcium water type ( HCO3–Ca), and a sulphate–calcium water type ( SO4–Ca)

Scalar field critical collapse in 2+1 dimensions

We carry out numerical experiments in the critical collapse of a spherically symmetric massless scalar field in 2+1 spacetime dimensions in the presence of a negative cosmological constant and compare them against a new theoretical model. We approximate the true critical solution as the n=4 Garfinkle solution, matched at the light cone to a Vaidya-like solution, and corrected to leading order for the effect of ?&lt;0. This approximation is only C3 at the light cone and has three growing modes. We conjecture that pointwise it is a good approximation to a yet unknown true critical solution that is analytic with only one growing mode (itself approximated by the top mode of our amended Garfinkle solution). With this conjecture, we predict a Ricci-scaling exponent of ?=8/7 and a mass-scaling exponent of ?=16/23, compatible with our numerical experiments

Structured catalytic reactor for VOC combustion

VOC emission has recently become a challenge for environmental protection. Catalytic combustion seems a promising method of VOC removal, however, there are still more specific demands concerning the process. The reactor design has to assure enhanced transfer properties accompanied by low flow resistance to reduce the pumping costs. Neither the packed beds nor the classic ceramic monoliths are able to fulfil the requirements. To solve the problem we propose a wire gauze structure composed of several gauze sheets staked. A number of mass transfer and flow resistance experiments were performed for two gauze types and correlations were derived for the Sherwood number and the friction factor. The results were found to be in a reasonable agreement with the literature available. The studied gauze structures were compared with a classic monolith for the assumed case study. The calculated length of the gauze structured reactor was significantly shorter, up to ten times, when compared with a classic ceramic monolith, but the pressure drop was higher

The fluid flow approximation of the TCP vegas and reno congestion control mechanism

TCP congestion control algorithms have been design to improve Internet transmission performance and stability. In recent years the classic Tahoe/Reno/NewReno TCP congestion control, based on losses as congestion indicators, has been improved and many congestion control algorithms have been proposed. In this paper the performance of standard TCP NewReno algorithm is compared to the performance of TCP Vegas, which tries to avoid congestion by reducing the congestion window (CWND) size before packets are lost. The article uses fluid flow approximation to investigate the influence of the two above-mentioned TCP congestion control mechanisms on CWND evolution, packet loss probability, queue length and its variability. Obtained results show that TCP Vegas is a fair algorithm, however it has problems with the use of available bandwidth

H3 mRNA level as a new proliferative marker in astrocytomas

AbstractReplication-dependent H3.1 and H3.2 histones are encoded by 11 genes. The H3 mRNA levels in brain astrocytomas using real-time RT-PCR assay was examined. The sequence of primers and probe used in amplification was designed basing on the reference sequence GenBank accession no. Z83737. The H3 mRNA levels correlated with tumor grade (R=0.56, P=0.0012), Ki-67 proliferative antigen labeling index (R=0.58, P=0.0008) and patient survival time (R=−0.50, P=0.005), discriminating low-grade and high-grade tumors. Quantification of H3 mRNA with real-time RT-PCR using the proposed pair of primers may supplement classic proliferative tests and predictive factors in brain astrocytomas

Neuropsychological characteristics of encephalopathy in Susac's Syndrome – Case report

Susac's Syndrome (SS) is a rare, autoimmune angiopathy characterized by hearing loss, retinal artery occlusions and encephalopathy, which is usually expressed in multifocal neurological signs and symptoms, confusion state and cognitive impairment. There have been few descriptions of neuropsychological assessment of SS. We present a case study of 29-year-old woman who developed full SS. During the post-acute stage of disease, she was admitted to neurorehabilitation ward to improve her cognitive-behavioral and motor functioning. The initial assessment revealed attention, memory and executive dysfunctions, as well as behavioral changes including impulsivity, affective dysregulation and reduced self-awareness of disease deficits. After five weeks recovery process supported by rehabilitation program, improvement was observed, although some cognitive-behavioral deficits were still present in the follow-up assessment