All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe

Anomalous far infrared monochromatic transmission through a film of type-II superconductor in magnetic field

Anomalous far infrared monochromatic transmission through a lattice of Abrikosov vortices in a type-II superconducting film is found and reported. The transmitted frequency corresponds to the photonic mode localized by the defects of the Abrokosov lattice. These defects are formed by extra vortices placed out of the nodes of the ideal Abrokosov lattice. The extra vortices can be pinned by crystal lattice defects of a superconductor. The corresponding frequency is studied as a function of magnetic field and temperature in the framework of the Dirac-type two-band model. While our approach is valid for all type-II superconductors, the specific calculations have been performed for the YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO). The control of the transmitted frequency by varying magnetic field and/or temperature is analyzed. It is suggested that found anomalously transmitted localized mode can be utilized in the far infrared monochromatic filters.Comment: 9 pages, 2 figure

The atomic structure of large-angle grain boundaries Σ5\Sigma 5 and Σ13\Sigma 13 in YBa2Cu3O7−δ{\rm YBa_2Cu_3O_{7-\delta}} and their transport properties

We present the results of a computer simulation of the atomic structures of large-angle symmetrical tilt grain boundaries (GBs) $\Sigma 5$ (misorientation angles \q{36.87}{^{\circ}} and \q{53.13}{^{\circ}}), $\Sigma 13$ (misorientation angles \q{22.62}{^{\circ}} and \q{67.38}{^{\circ}}). The critical strain level $\epsilon_{crit}$ criterion (phenomenological criterion) of Chisholm and Pennycook is applied to the computer simulation data to estimate the thickness of the nonsuperconducting layer ${\rm h_n}$ enveloping the grain boundaries. The ${\rm h_n}$ is estimated also by a bond-valence-sum analysis. We propose that the phenomenological criterion is caused by the change of the bond lengths and valence of atoms in the GB structure on the atomic level. The macro- and micro- approaches become consistent if the $\epsilon_{crit}$ is greater than in earlier papers. It is predicted that the symmetrical tilt GB $\Sigma5$ \theta = \q{53.13}{^{\circ}} should demonstrate a largest critical current across the boundary.Comment: 10 pages, 2 figure

Computation of Invariants of Lie Algebras by Means of Moving Frames

A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. The algorithm is applied, in particular, to computation of invariants of real low-dimensional Lie algebras. A number of examples are calculated to illustrate its effectiveness and to make a comparison with the same cases in the literature. Bases of invariants of the real solvable Lie algebras up to dimension five, the real six-dimensional nilpotent Lie algebras and the real six-dimensional solvable Lie algebras with four-dimensional nilradicals are newly calculated and listed in tables.Comment: 17 pages, extended versio

Genetic recombination is targeted towards gene promoter regions in dogs

The identification of the H3K4 trimethylase, PRDM9, as the gene responsible for recombination hotspot localization has provided considerable insight into the mechanisms by which recombination is initiated in mammals. However, uniquely amongst mammals, canids appear to lack a functional version of PRDM9 and may therefore provide a model for understanding recombination that occurs in the absence of PRDM9, and thus how PRDM9 functions to shape the recombination landscape. We have constructed a fine-scale genetic map from patterns of linkage disequilibrium assessed using high-throughput sequence data from 51 free-ranging dogs, Canis lupus familiaris. While broad-scale properties of recombination appear similar to other mammalian species, our fine-scale estimates indicate that canine highly elevated recombination rates are observed in the vicinity of CpG rich regions including gene promoter regions, but show little association with H3K4 trimethylation marks identified in spermatocytes. By comparison to genomic data from the Andean fox, Lycalopex culpaeus, we show that biased gene conversion is a plausible mechanism by which the high CpG content of the dog genome could have occurred.Comment: Updated version, with significant revision

Lie families: theory and applications

We analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study relations of these families, called Lie families, with the theory of Lie and quasi-Lie systems and apply our theory to provide common time-dependent superposition rules for certain Lie families.Comment: 23 pages, revised version to appear in J. Phys. A: Math. Theo

Central obesity as a precursor to the metabolic syndrome in the AusDiab study and Mauritius

Evidence from epidemiologic studies that central obesity precedes future metabolic change and does not occur concurrently with the appearance of the blood pressure, glucose, and lipid abnormalities that characterize the metabolic syndrome (MetS) has been lacking. Longitudinal surveys were conducted in Mauritius in 1987, 1992, and 1998, and in Australia in 2000 and 2005 (AusDiab). This analysis included men and women (aged 25 years) in three cohorts: AusDiab 2000&ndash;2005 (n = 5,039), Mauritius 1987&ndash;1992 (n = 2,849), and Mauritius 1987&ndash;1998 (n = 1,999). MetS components included waist circumference, systolic blood pressure, fasting and 2-h postload plasma glucose, high-density lipoprotein (HDL) cholesterol, triglycerides, and homeostasis model assessment of insulin sensitivity (HOMA-S) (representing insulin sensitivity). Linear regression was used to determine which baseline components predicted deterioration in other MetS components over 5 years in AusDiab and 5 and 11 years in Mauritius, adjusted for age, sex, and ethnic group. Baseline waist circumference predicted deterioration (P &lt; 0.01) in four of the other six MetS variables tested in AusDiab, five of six in Mauritius 1987&ndash;1992, and four of six in Mauritius 1987&ndash;1998. In contrast, an increase in waist circumference between baseline and follow-up was only predicted by insulin sensitivity (HOMA-S) at baseline, and only in one of the three cohorts. These results suggest that central obesity plays a central role in the development of the MetS and appears to precede the appearance of the other MetS components.<br /

Effect of 3d-doping on the electronic structure of BaFe2As2

The electronic structure of BaFe2As2 doped with Co, Ni, and Cu has been studied by a variety of experimental and theoretical methods, but a clear picture of the dopant 3d states has not yet emerged. Herein we provide experimental evidence of the distribution of Co, Ni, and Cu 3d states in the valence band. We conclude that the Co and Ni 3d states provide additional free carriers to the Fermi level, while the Cu 3d states are found at the bottom of the valence band in a localized 3d10 shell. These findings help shed light on why superconductivity can occur in BaFe2As2 doped with Co and Ni but not Cu.Comment: 18 pages, 8 figure

Group Diffie-Hellman Key Exchange Secure against Dictionary Attacks

Group Diffie-Hellman schemes for password-based key exchange are designed to provide a pool of players communicating over a public network, and sharing just a human-memorable password, with a session key (e.g, the key is used for multicast data integrity and confidentiality) . The fundamental security goal to achieve in this scenario is security against dictionary attacks. While solutions have been proposed to solve this problem no formal treatment has ever been suggested. In this paper, we define a security model and then present a protocol with its security proof in both the random oracle model and the ideal-cipher model