Gradedness of the set of rook placements in An−1A_{n-1}

summary:A rook placement is a subset of a root system consisting of positive roots with pairwise non-positive inner products. To each rook placement in a root system one can assign the coadjoint orbit of the Borel subgroup of a reductive algebraic group with this root system. Degenerations of such orbits induce a natural partial order on the set of rook placements. We study combinatorial structure of the set of rook placements in $A_{n-1}$ with respect to a slightly different order and prove that this poset is graded

Rook placements in G2G_2 and F4F_4 and associated coadjoint orbits

Let $\mathfrak{n}$ be a maximal nilpotent subalgebra of a simple complex Lie algebra with root system $\Phi$. A subset $D$ of the set $\Phi^+$ of positive roots is called a rook placement if it consists of roots with pairwise non-positive scalar products. To each rook placement $D$ and each map $\xi$ from $D$ to the set $\mathbb{C}^{\times}$ of nonzero complex numbers one can naturally assign the coadjoint orbit $\Omega_{D,\xi}$ in the dual space $\mathfrak{n}^*$. By definition, $\Omega_{D,\xi}$ is the orbit of $f_{D,\xi}$, where $f_{D,\xi}$ is the sum of root covectors $e_{\alpha}^*$ multiplied by $\xi(\alpha)$, $\alpha\in D$. (In fact, almost all coadjoint orbits studied at the moment have such a form for certain $D$ and $\xi$.) It follows from the results of Andr\`e that if $\xi_1$ and $\xi_2$ are distinct maps from $D$ to $\mathbb{C}^{\times}$ then $\Omega_{D,\xi_1}$ and $\Omega_{D,\xi_2}$ do not coincide for classical root systems $\Phi$. We prove that this is true if $\Phi$ is of type $G_2$, or if $\Phi$ is of type $F_4$ and $D$ is orthogonal.Comment: 16 pages, 4 figure

Challenges in meeting international standards in undertaking social impact assessment in Russia

Implementing good practice social impact assessment (SIA) that meets international standards in countries in transition is problematic. We reflect on the challenges faced when undertaking SIA in the Russian Federation. These challenges restrict meaningful SIA processes from being undertaken and limit public participation and the effective community engagement of project-affected local people. Based on the self-reflexive professional experience of two Russian-based social practitioners, and their discursive interactions with two leading academics in environmental and social impact assessment, as well as on in-depth interviews with prominent Russian and international experts, we identified the key challenges that prevent effective SIA from being implemented in Russia: a lack of understanding of the international standards; discrepancy in the determination of the social area of influence between the national requirements and international standards; difficulties in combining national and international impact assessment processes; and a tendency by companies to restrict stakeholder engagement to the minimum. We hope that by having an awareness of these limitations, improvements to SIA practice in Russia and elsewhere will be made

Qualitative analysis and numerical simulation of equations of the standard cosmological model: Λ /= 0

On the basis of qualitative analysis of the system of differential equations of the standard cosmological model it is shown that in the case of zero cosmological constant this system has a stable center corresponding to zero values of potential and its derivative at infinity. Thus, the cosmological model based on single massive classical scalar field in infinite future would give a flat Universe. The carried out numerical simulation of the dynamic system corresponding to the system of Einstein - Klein - Gordon equations showed that at great times of the evolution the invariant cosmological acceleration has an oscillating character and changes from -2 (braking), to +1 (acceleration). Average value of the cosmological acceleration is negative and is equal to -1/2. Oscillations of the cosmological acceleration happen on the background of rapidly falling Hubble constant. In the case of nonzero value of the cosmological constant depending on its value there are possible three various qualitative behavior types of the dynamic system on 2-dimensional plane (, ), which correspond either to zero attractive focus or to stable attractive knot with zero values of the potential and its derivative. Herewith the system asymptotically enters the secondary inflation. Carried out numerical simulation showed that at cosmological constant (m23?10-8 the macroscopic value of the cosmological acceleration behaves itself similar to the case = 0, i.e. in the course of the cosmological evolution there appears a lasting stage when this value is close to -1/2 which corresponds to non-relativistic equation of state.130-14

Vacuum polarization for compactified QED4+1QED_{4+1} in a magnetic flux background

We evaluate one-loop effects for $QED_{4+1}$ compactified to ${\bf R}^4 \times S^1$, in a non-trivial vacuum for the gauge field, such that a non-vanishing magnetic flux is encircled along the extra dimension. We obtain the vacuum polarization tensor and evaluate the exact parity breaking term, presenting the results from the point of view of the effective 3+1 dimensional theory.Comment: 8 pages no figures Revte

GUT, Neutrinos, and Baryogenesis

It is an exciting time for flavor physics. In this talk, I discuss recent topics in baryogenesis and leptogenesis in light of new data, and implications in B and neutrino physics. I also discuss current situation of grand unified theories concerning coupling unification, proton decay, and indirect consequences in lepton flavor violation and B physics. I explain attempts to understand the origin of flavor based on flavor symmetry, in particular "anarchy" in neutrinos.Comment: Talk presented at 5th KEK Topical Conference: Frontiers In Flavor Physics, 20-22 Nov 2001, Tsukuba, Ibaraki, Japan. Includes comments on SUSY GUT contribution to B->phi K

Monitoring the health status of the population by age groups

A multi-criteria method for selecting informative sets of different features for a quantitative assessment of the population’s health status in 14 age groups is considered. To compare samples from two classes (groups), it is proposed to form a unified description of objects according to two gradations of nominal features. The unified description is used to synthesize latent features and calculate the values of the compactness measure of class objects on the numerical axis. The transformation of quantitative features into nominal gradations is implemented according to the search criterion for the minimum coverage of their values by non-overlapping intervals. The values of the boundaries of the intervals and their number are determined by a recursive algorithm considering the objects belonging to classes. An important property of the transformation is the invariance to measurement scales. A formula is proposed for calculating the membership function of class objects for each feature gradation. Function values are used to unify object descriptions and calculate the stability index of a feature, regardless of its measurement scale. The unification of descriptions by two gradations does not change the stability index but increases the contribution of each gradation to the separation of class objects. The ranking of features about their stability was used both for individual samples and for a set of defined samples. The results of ranking over a set of samples were used to search for patterns in individual features and to form sets from them to calculate the values of latent features of objects. A set of thirteen data samples from representatives of two classes was formed as follows. The first class was represented by objects of the younger age group, and the second class — by objects of different age groups. A set of seven different types of features has been identified. For each of 13 samples, the values of latent features on this set and measures of compactness of class objects on the numerical axis were calculated. A monotonically non-decreasing sequence of values of measures of compactness of data samples that are invariant to the order of precedence of age groups is obtained. The property of monotonicity of sequence values is consistent with empirical estimates of the health state in the process of population aging

Monitoring of water quality with HPLSEC and fluorescence method in the ozonated recirculating aquaculture system

In recirculating aquaculture systems (RAS), it is important to monitor the water quality to keep the fish healthy. Especially in water treatment with oxidizing agents, for example, ozone (O3) or hydrogen peroxide (H2O2), the monitoring of the quality of dissolved organic matter (DOM) in water is advisable to keep track of the treatment’s effect. Previously in wastewater treatment plant (WWTP) studied, HPLSEC and fluorescence method for monitoring and characterization of organic matter was used here to track the effect of oxidative treatments; 5 duplicated treatments (2 × O3, 1 × O3 + H2O2, 1 × H2O2, 1 × control) were performed for four months with weekly samplings. Systems that contained O3 injection reduced fluorescence on average over 90%, except tyrosine-like fluorescence with removal of 80%. Combined O3 + H2O2 treatment did not bring any advantages over pure O3 treatment, and H2O2 had no significant effect on fluorescence. Humic and fulvic compounds were detected to largely be derived from inlet lake water, while large protein-like structures were mostly created in RAS. A peak of benzoic acid-like molecules was also detected in all RAS waters. Treatments did not change the molecular weight profile of DOM systems and inlet water, having most of their fluorescence coming from medium-sized (108–1322 Da) molecules. DOC was lower in O3 treatments, but the linear connection between DOC and fluorescence was not observed, although this was proposed in earlier studies. Most likely, the oxidizing treatments induce change to DOM in a way that such comparison becomes inaccurate, although this must be studied further in the future