Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation

We study the local well-posedness of the initial-value problem for the nonlinear "good" Boussinesq equation with data in Sobolev spaces \textit{$H^s$} for negative indices of $s$.Comment: Referee comments incorporate

Complexity and hierarchical game of life

Hierarchical structure is an essential part of complexity, important notion relevant for a wide range of applications ranging from biological population dynamics through robotics to social sciences. In this paper we propose a simple cellular-automata tool for study of hierarchical population dynamics

CESAREAN SECTION WITH PREMATURE FETUS IN BREECH PRESENTATION

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The ethnopharmacological literature: An analysis of the scientific landscape

ETHNOPHARMACOLOGICAL RELEVANCE The research into bioactive natural products originating from medicinal plants, fungi and other organisms has a long history, accumulating abundant and diverse publications. However no quantitative literature analysis has been conducted. AIM OF THE STUDY Here we analyze the bibliometric data of ethnopharmacology literature and relate the semantic content to the publication and citation data so that the major research themes, contributors, and journals of different time periods could be identified and evaluated. MATERIALS AND METHODS Web of Science (WoS) was searched to identify relevant publications. The Analyze function of WoS and bibliometric software (VOSviewer) were utilized to perform the analyses. RESULTS Until the end of November 2018, 59,576 publications -linked to ‘ethnopharmacology’ indexed by WoS, published since 1958 in more than 5,600 journals, and contributed by over 20,600 institutions located in more than 200 countries/regions, were identified. The papers were published under four dominating WoS categories, namely pharmacology/pharmacy (34.4%), plant sciences (28.6%), medicinal chemistry (25.3%), and integrative complementary medicine (20.6%). India (14.6%) and China (13.2%) were dominating the publication space. The United States and Brazil also had more than 8.0% contribution each. The rest of the top ten countries/regions were mainly from Asia. There were around ten-fold more original articles (84.6%) than reviews (8.4%). CONCLUSIONS Ethnopharmacological research has a consistent focus on food and plant sciences, (bio)chemistry, complementary medicine and pharmacology, with a more limited scientific acceptance in the socio-cultural sciences. Dynamic global contributions have been shifting from developed countries to economically and scientifically emerging countries in Asia, South America and the Middle East. Research on recording medicinal plant species used by traditional medicine continues, but the evaluation of specific properties or treatment effects of extracts and compounds has increased enormously. Moreover increasing attention is paid to some widely distributed natural products, such as curcumin, quercetin, and rutin

Global well-posedness for the KP-I equation on the background of a non localized solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in $x$ and $y$ periodic or conversely)

PHARMACOGENETIC STUDY OF THE ACETYLATION PHENOTYPE IN A BULGARIAN POPULATION

N-acetyltransferase, an enzyme involved in the metabolic inactivation of drugs like isoniazide, some sulfonamides and others is well-known to he under polymorphic genetic control. The acetylation phenotype of the patients may serve as an important guide in foretelling the therapeutic efficacy or tolerahility of a particular drug. In the present study we investigated the distribution of the acetylaiion phenotypes in a group of 100 healthy volunteers of both sexes using sulfadimidine as a substrate. The distribution was found to follow a bimodal pattern, as aspected, with a slight predominance of the "slow" acetylators - in 58 % of the cases, a finding similar to literature data from neighbouring and other European countries. In the men's group the distribution was approximately the same as that in the whole group whilst in the women's one the "rapid" inactivators prevailed. This work represents the first modest attempt in Bulgaria for phenotyping the population according to the individual acetylaiion status

Random data wave equations

Nowadays we have many methods allowing to exploit the regularising properties of the linear part of a nonlinear dispersive equation (such as the KdV equation, the nonlinear wave or the nonlinear Schroedinger equations) in order to prove well-posedness in low regularity Sobolev spaces. By well-posedness in low regularity Sobolev spaces we mean that less regularity than the one imposed by the energy methods is required (the energy methods do not exploit the dispersive properties of the linear part of the equation). In many cases these methods to prove well-posedness in low regularity Sobolev spaces lead to optimal results in terms of the regularity of the initial data. By optimal we mean that if one requires slightly less regularity then the corresponding Cauchy problem becomes ill-posed in the Hadamard sense. We call the Sobolev spaces in which these ill-posedness results hold spaces of supercritical regularity. More recently, methods to prove probabilistic well-posedness in Sobolev spaces of supercritical regularity were developed. More precisely, by probabilistic well-posedness we mean that one endows the corresponding Sobolev space of supercritical regularity with a non degenerate probability measure and then one shows that almost surely with respect to this measure one can define a (unique) global flow. However, in most of the cases when the methods to prove probabilistic well-posedness apply, there is no information about the measure transported by the flow. Very recently, a method to prove that the transported measure is absolutely continuous with respect to the initial measure was developed. In such a situation, we have a measure which is quasi-invariant under the corresponding flow. The aim of these lectures is to present all of the above described developments in the context of the nonlinear wave equation.Comment: Lecture notes based on a course given at a CIME summer school in August 201

Invariance of the white noise for KdV

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space \hat{b}^s_{p, \infty}, sp <-1, contains the support of the white noise. Then, we prove local well-posedness in \hat{b}^s_{p, \infty} for p= 2+, s = -{1/2}+ such that sp <-1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko.Comment: 18 pages. To appear in Comm. Math. Phy

Molecular neuroscience at its "high": bibliometric analysis of the most cited papers on endocannabinoid system, cannabis and cannabinoids

Background Cannabis, cannabinoids and endocannabinoids are heavily investigated topics with many articles published every year. We aimed to identify the 100 most cited manuscripts among the vast literature and analyze their contents