2,285 research outputs found
Explicit Free Parameterization of the Modified Tetrahedron Equation
The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at
N-th root of unity is solved by a rational mapping operator which is obtained
from the solution of a linear problem. We show that the solutions can be
parameterized in terms of eight free parameters and sixteen discrete phase
choices, thus providing a broad starting point for the construction of
3-dimensional integrable lattice models. The Fermat curve points parameterizing
the representation of the mapping operator in terms of cyclic functions are
expressed in terms of the independent parameters. An explicit formula for the
density factor of the MTE is derived. For the example N=2 we write the MTE in
full detail. We also discuss a solution of the MTE in terms of bosonic
continuum functions.Comment: 28 pages, 3 figure
Quantum 2+1 evolution model
A quantum evolution model in 2+1 discrete space - time, connected with 3D
fundamental map R, is investigated. Map R is derived as a map providing a zero
curvature of a two dimensional lattice system called "the current system". In a
special case of the local Weyl algebra for dynamical variables the map appears
to be canonical one and it corresponds to known operator-valued R-matrix. The
current system is a kind of the linear problem for 2+1 evolution model. A
generating function for the integrals of motion for the evolution is derived
with a help of the current system. The subject of the paper is rather new, and
so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page
Generalized Calogero-Moser systems from rational Cherednik algebras
We consider ideals of polynomials vanishing on the W-orbits of the
intersections of mirrors of a finite reflection group W. We determine all such
ideals which are invariant under the action of the corresponding rational
Cherednik algebra hence form submodules in the polynomial module. We show that
a quantum integrable system can be defined for every such ideal for a real
reflection group W. This leads to known and new integrable systems of
Calogero-Moser type which we explicitly specify. In the case of classical
Coxeter groups we also obtain generalized Calogero-Moser systems with added
quadratic potential.Comment: 36 pages; the main change is an improvement of section 7 so that it
now deals with an arbitrary complex reflection group; Selecta Math, 201
β-Polymorph of phenazepam: a powder study
The title compound [systematic name: 7-bromo-5-(2-chlorophenyl)-1H-1,4-benzodiazepin-2(3H)-one] (β-polymorph), C15H10BrClN2O, has been obtained via cryomodification of the known α-polymorph of phenazepam [Karapetyan et al. (1979 ▶). Bioorg. Khim.
5, 1684–1690]. In both polymorphs, the molecules, which differ only in the dihedral angles between the aromatic rings [75.4 (2)° and 86.2 (3)° in the α- and β-polymorphs, respectively], are linked into centrosymmetric dimers via N—H⋯O hydrogen bonds. In the crystal structure of the β-polymorph, weak intermolecular C—H⋯O hydrogen bonds further link these dimers into layers parallel to bc plane
Amplitude-Frequency Characteristic of a Neural Control Based DC Drive
The paper interprets characteristics of a neural-control-based DC servodrive in terms of the classical theory of automatic control. It also touches on the problem of choosing training patterns to synthesize a nonlinear PID-controller with a desired amplitude-frequency characteristic and analyses the efficiency of using for this purpose input signals in form of a step function and a harmonic one. Synthesis of the neurocontroller has been performed within the framework of a three-layer perceptron. To train it, a genetic algorithm has been developed
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