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

Invariants of Lie Algebras with Fixed Structure of Nilradicals

An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras, here the effectiveness of the algorithm is demonstrated by its application to computation of invariants of solvable Lie algebras of general dimension $n<\infty$ restricted only by a required structure of the nilradical. Specifically, invariants are calculated here for families of real/complex solvable Lie algebras. These families contain, with only a few exceptions, all the solvable Lie algebras of specific dimensions, for whom the invariants are found in the literature.Comment: LaTeX2e, 19 page

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

Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials

A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative Lagrangian formulations is proved, both Lagrangians being of a non-natural class (neither potential nor kinetic term). These higher-order Abel equations are studied by means of their Darboux polynomials and Jacobi multipliers. In all the cases a family of constants of the motion is explicitly obtained. The general n-dimensional case is also studied

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

Effectiveness of enterosgel usage in the conditions of simultaneous destruction of rats by karbofos and carbon tetrachloride

The aim of our study was to examine the effectiveness of the enterosgel sorbent in the terms of simultaneous destruction of rats by karbofos and carbon tetrachloride. Experiments were carried out on white rats weighing 175–200 g, which were kept on a standard diet. Karbofos was administered intragastrically on daily basis in the aqueous solution at the rate of 20 mg/kg of the body weight, which is 1/10 of the LD50. Carbon tetrachloride was administered intraperitoneally, twice a day in the form of a 50% oil solution at a dose of 1.0 ml/kg of animal. Animals received enterosgel daily by intragastric way at the rate of 120 mg/kg of body weight. The activity of free radical processes in rats was assessed by thiobarbituric acid content – active products (TBA-AP) in serum, liver and heart homogenates. Level of endogenous intoxication was determined by the content of average weight molecules (AWM) in serum and liver homogenate. The degree of cytolysis of hepatocytes was assessed by the activity of alanine and aspartate aminotransferase (AlAT, AsAT), alkaline phosphatase (ALP) in serum, liver and heart homogenates. The degree of damage of the nervous system was studied by the activity of acetylcholinesterase (AChE) in serum and liver homogenate. Content of TBA-AP in serum, liver and myocardium increased throughout the period of study. Reduction of TBA-AP was observed in studied tissues after applying of enterosgel sorbent in the affected body. After the defeat by toxicants we showed significant increase of fraction of AM1 (chain aminoacids dominate) and AM2 (aromatic aminoacids dominate) in serum and liver of experimental rats throughout the experiment. Enterosgel showed a positive effect on this index, reducing the content of MSM molecules. Due to toxic effects of endogenous and exogenous toxins in cells degradation and changing the permeability of plasma membranes of hepatocytes was observed as evidenced by the increased activity of both AlAT and AsAT in serum and decreased in liver and myocardium. Throughout the experiment a positive effect of enterosgel on these indices was observed, which activity decreased in serum and increased in liver and myocardium. Another marker of hepatic cytolysis is alkaline phosphatase, which activity increase in serum shows the development of inflammation in the liver. It is noted that after enterosgel introduction into the body affected by xenobiotics ALP activity decreases. The main pathogenetic mechanism of karbofos action is based on the inhibition of AChE – an enzyme that catalyzes the hydrolysis of acetylcholine and plays an important role in synaptic transmission of nerve impulses. Throughout the experiment, under the action of toxicants, decreasing of the AChE activity took place, and when injecting into the affected body enterosgel we observed increased activity of the enzyme. Thus, the usage of enterosgel resulted in the depressing process of free radical oxidation, reduction of endogenous intoxication and decrease in the inflammation in the rats affected by xenobiotics, allowing to carry out subsequent studies of the efficiency of this sorbent under conditions of chemical poisoning

Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Furthermore, the possible additional equivalence transformations between equations from the class under consideration are investigated. Exact solutions of special forms of these equations are also constructed via classical Lie method and generalized conditional transformations. Local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations.Comment: 23 page

Non-invasive diagnostics of extrahepatic portal hypertension at the proliferative processes in the pancreas

The study of hemodynamics in 199 patients with chronic pancreatitis and pancreatic cancer was performed with use of radiological diagnostics methods: ultrasound research, CT and. portal scintigraphy. Ultrasound examination with color and. power Doppler, CT with 3D-reconstruction give an idea of the local hemodynamic changes in extrahepatic portal hypertension and. can identify preoperative anatomic and. topographic relationship of great vessels in their involvement in mass lesion of the pancreas. Portal scintigraphy with accuracy 83 %, sensitivity 62 % and. specificity 100 % functional condition evaluates collateral flow in extrahepatic portal hypertensio

New results on group classification of nonlinear diffusion-convection equations

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.Comment: LaTeX2e, 19 page

Two-Fermion Production in Electron-Positron Collisions

This report summarizes the results of the two-fermion working group of the LEP2-MC workshop, held at CERN from 1999 to 2000. Recent developments in the theoretical calculations of the two fermion production process in the electron-positron collision at LEP2 center of the mass energies are reported. The Bhabha process and the production of muon, tau, neutrino and quark pairs is covered. On the basis of comparison of various calculations, theoretical uncertainties are estimated and compared with those needed for the final LEP2 data analysis. The subjects for the further studies are identified.Comment: 2-fermion working group report of the LEP2 Monte Carlo Workshop 1999/2000, 113 pages, 24 figures, 35 table