Classical Integrable 2-dim Models Inspired by SUSY Quantum Mechanics

A class of integrable 2-dim classical systems with integrals of motion of fourth order in momenta is obtained from the quantum analogues with the help of deformed SUSY algebra. With similar technique a new class of potentials connected with Lax method is found which provides the integrability of corresponding 2-dim hamiltonian systems. In addition, some integrable 2-dim systems with potentials expressed in elliptic functions are explored.Comment: 19 pages, LaTeX, final version to be published in J.Phys.

On the taxonomical status of Aquilegia kansuensis (Ranunculaceae)

Для рода Aquilegia L. (Ranunculaceae) предложена новая номенклатурная комбинация – A. kansuensis (Brühl) Erst.DOI: 10.14258/turczaninowia.17.4.4 A new combination in the genus Aquilegia L. (Ranunculaceae) – A. kansuensis (Brühl) Erst have been proposed.DOI: 10.14258/turczaninowia.17.4.

Chaotic Phenomenon in Nonlinear Gyrotropic Medium

Nonlinear gyrotropic medium is a medium, whose natural optical activity depends on the intensity of the incident light wave. The Kuhn's model is used to study nonlinear gyrotropic medium with great success. The Kuhn's model presents itself a model of nonlinear coupled oscillators. This article is devoted to the study of the Kuhn's nonlinear model. In the first paragraph of the paper we study classical dynamics in case of weak as well as strong nonlinearity. In case of week nonlinearity we have obtained the analytical solutions, which are in good agreement with the numerical solutions. In case of strong nonlinearity we have determined the values of those parameters for which chaos is formed in the system under study. The second paragraph of the paper refers to the question of the Kuhn's model integrability. It is shown, that at the certain values of the interaction potential this model is exactly integrable and under certain conditions it is reduced to so-called universal Hamiltonian. The third paragraph of the paper is devoted to quantum-mechanical consideration. It shows the possibility of stochastic absorption of external field energy by nonlinear gyrotropic medium. The last forth paragraph of the paper is devoted to generalization of the Kuhn's model for infinite chain of interacting oscillators

Spectroscopy with random and displaced random ensembles

Due to the time reversal invariance of the angular momentum operator J^2, the average energies and variances at fixed J for random two-body Hamiltonians exhibit odd-even-J staggering, that may be especially strong for J=0. It is shown that upon ensemble averaging over random runs, this behaviour is reflected in the yrast states. Displaced (attractive) random ensembles lead to rotational spectra with strongly enhanced BE2 transitions for a certain class of model spaces. It is explained how to generalize these results to other forms of collectivity.Comment: 4 pages, 4 figure

Symplectic Structures for the Cubic Schrodinger equation in the periodic and scattering case

We develop a unified approach for construction of symplectic forms for 1D integrable equations with the periodic and rapidly decaying initial data. As an example we consider the cubic nonlinear Schr\"{o}dinger equation.Comment: This is expanded and corrected versio

The Lake Baikal neutrino experiment: selected results

We review the present status of the lake Baikal Neutrino Experiment and present selected physical results gained with the consequetive stages of the stepwise increasing detector: from NT-36 to NT-96. Results cover atmospheric muons, neutrino events, very high energy neutrinos, search for neutrino events from WIMP annihilation, search for magnetic monopoles and environmental studies. We also describe an air Cherenkov array developed for the study of angular resolution of NT-200.Comment: 25 pages, 12 figures. To appear in the Procrrdings of International Conference on Non-Accelerator New Physics, June 28 - July 3, 1999, Dubna, Russi

BAIKAL experiment: status report

We review the present status of the Baikal Neutrino Project and present the results obtained with the deep underwater neutrino telescope NT-200.Comment: 4 pages, 3 figures. Presented at TAUP 2001 (7th international workshop on Topics in Astroparticle and Underground Physics), Sep. 2001, Laboratori Nazionali del Gran Sasso, Assergi, Ital

Increased gene sampling strengthens support for higher-level groups within leaf-mining moths and relatives (Lepidoptera: Gracillariidae)

Background: Researchers conducting molecular phylogenetic studies are frequently faced with the decision of what to do when weak branch support is obtained for key nodes of importance. As one solution, the researcher may choose to sequence additional orthologous genes of appropriate evolutionary rate for the taxa in the study. However, generating large, complete data matrices can become increasingly difficult as the number of characters increases. A few empirical studies have shown that augmenting genes even for a subset of taxa can improve branch support. However, because each study differs in the number of characters and taxa, there is still a need for additional studies that examine whether incomplete sampling designs are likely to aid at increasing deep node resolution. We target Gracillariidae, a Cretaceous-age (similar to 100 Ma) group of leaf-mining moths to test whether the strategy of adding genes for a subset of taxa can improve branch support for deep nodes. We initially sequenced ten genes (8,418 bp) for 57 taxa that represent the major lineages of Gracillariidae plus outgroups. After finding that many deep divergences remained weakly supported, we sequenced eleven additional genes (6,375 bp) for a 27-taxon subset. We then compared results from different data sets to assess whether one sampling design can be favored over another. The concatenated data set comprising all genes and all taxa and three other data sets of different taxon and gene sub-sampling design were analyzed with maximum likelihood. Each data set was subject to five different models and partitioning schemes of non-synonymous and synonymous changes. Statistical significance of non-monophyly was examined with the Approximately Unbiased (AU) test. Results: Partial augmentation of genes led to high support for deep divergences, especially when non-synonymous changes were analyzed alone. Increasing the number of taxa without an increase in number of characters led to lower bootstrap support; increasing the number of characters without increasing the number of taxa generally increased bootstrap support. More than three-quarters of nodes were supported with bootstrap values greater than 80% when all taxa and genes were combined. Gracillariidae, Lithocolletinae + Leucanthiza, and Acrocercops and Parectopa groups were strongly supported in nearly every analysis. Gracillaria group was well supported in some analyses, but less so in others. We find strong evidence for the exclusion of Douglasiidae from Gracillarioidea sensu Davis and Robinson (1998). Our results strongly support the monophyly of a G.B.R.Y. clade, a group comprised of Gracillariidae + Bucculatricidae + Roeslerstammiidae + Yponomeutidae, when analyzed with non-synonymous changes only, but this group was frequently split when synonymous and non-synonymous substitutions were analyzed together. Conclusions: 1) Partially or fully augmenting a data set with more characters increased bootstrap support for particular deep nodes, and this increase was dramatic when non-synonymous changes were analyzed alone. Thus, the addition of sites that have low levels of saturation and compositional heterogeneity can greatly improve results. 2) Gracillarioidea, as defined by Davis and Robinson (1998), clearly do not include Douglasiidae, and changes to current classification will be required. 3) Gracillariidae were monophyletic in all analyses conducted, and nearly all species can be placed into one of six strongly supported clades though relationships among these remain unclear. 4) The difficulty in determining the phylogenetic placement of Bucculatricidae is probably attributable to compositional heterogeneity at the third codon position. From our tests for compositional heterogeneity and strong bootstrap values obtained when synonymous changes are excluded, we tentatively conclude that Bucculatricidae is closely related to Gracillariidae + Roeslerstammiidae + Yponomeutidae

Simultaneous measurements of water optical properties by AC9 transmissometer and ASP-15 Inherent Optical Properties meter in Lake Baikal

Measurements of optical properties in media enclosing Cherenkov neutrino telescopes are important not only at the moment of the selection of an adequate site, but also for the continuous characterization of the medium as a function of time. Over the two last decades, the Baikal collaboration has been measuring the optical properties of the deep water in Lake Baikal (Siberia) where, since April 1998, the neutrino telescope NT-200 is in operation. Measurements have been made with custom devices. The NEMO Collaboration, aiming at the construction of a km3 Cherenkov neutrino detector in the Mediterranean Sea, has developed an experimental setup for the measurement of oceanographic and optical properties of deep sea water. This setup is based on a commercial transmissometer. During a joint campaign of the two collaborations in March and April 2001, light absorption, scattering and attenuation in water have been measured. The results are compatible with previous ones reported by the Baikal Collaboration and show convincing agreement between the two experimental techniques.Comment: 16 pages, submitted to NIM-