Results 181 to 190 of about 6,368 (219)
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Bogoliubov Transformation and Lobachevsky Planimetry
Physics of Particles and Nuclei Letters, 2006The relation between the Bogoliubov transformation in the theory of superfluidity and the Lobachevsky planimetry in two conformally Euclidean Poincare models is established. The parameter of this transformation, a complex number with the modulus
N A Chernikov
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Poisson Kernel on the Quantum Lobachevsky Spaces
Acta Applicandae Mathematicae, 2004The Poisson transform on the quantum Lobachevsky spaces is defined and the properties of the transform are discussed. The idea of the note is to define an analog of the Poisson transform on the quantum Lobachevsky space based on the classical Lobachevsky space \(L^3\) equipped with the hyperbolic metric.
Olshanetsky, M. A., Rogov, V.-B. K.
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Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes
Functional Analysis and Its Applications, 2004 Congruences generalizing Fermat's little theorem are proved for the traces of powers of integer matrices. Their relations to Lobachevsky geometries over finite fields and combinatorics of the matrix squaring operation as well as to the corresponding ...
V I Arnold
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Plagiarism, salami slicing, and Lobachevsky
Skeletal Radiology, 2008Plagiarism is defined as “using someone else’s words, ideas or results without attribution” [7]. Plagiarism can occur in two forms: (a) self-plagiarism, when authors reuse portions of their own previous writings in a subsequent paper [8], i.e., redundant and duplicate publications; and (b) “salami slicing”—i.e., dividing reports of the outcome of a ...
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Canonical and Boundary Representations on the Lobachevsky Plane
Acta Applicandae Mathematica, 2002The authors study canonical representations of the Lobachevsky plane. The representations are labeled by a complex parameter \(\lambda\). If \(\lambda\in (-3/2,0)\) then they coincide with the Vershik-Gelfand-Graev canonical unitary (with respect to the Berezin form) representations on a Hermitian symmetric space.
Molchanov, V. F., Grosheva, L. I.
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American Journal of Applied Science and Technology
It is known that the Poincaré interpretation of Lobachevsky’s geometry is used in solving many technical problems, in problems related to the theory of complex variable functions.In this article, we show the Poincaré interpretation of the Lobachevsky plane, which is interpreted in a circle in a plane, using one circle of a two-section hyperboloid ...
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It is known that the Poincaré interpretation of Lobachevsky’s geometry is used in solving many technical problems, in problems related to the theory of complex variable functions.In this article, we show the Poincaré interpretation of the Lobachevsky plane, which is interpreted in a circle in a plane, using one circle of a two-section hyperboloid ...
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2010
Lobachevsky wrote his Pangeometry in 1855, the year before his death. This memoir is a résumé of his work on non-Euclidean geometry and its applications, and it can be considered as his clearest account on the subject. It is also the conclusion of his lifework, and the last attempt he made to acquire recognition.
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Lobachevsky wrote his Pangeometry in 1855, the year before his death. This memoir is a résumé of his work on non-Euclidean geometry and its applications, and it can be considered as his clearest account on the subject. It is also the conclusion of his lifework, and the last attempt he made to acquire recognition.
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On infinite polygons of the Lobachevsky plane
Journal of Mathematical Sciences, 2007The author considers a Poincaré model of the Lobachevsky geometry. In this field a equidistant line is a convex curve defined by the property that all its points form a convex curve which are on the same distance from a given line. The infinite polygon is an intersection of closed semi-planes, such that their boundaries are lines without common points.
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An integral transformation in Lobachevsky space
Journal of Mathematical Physics, 1984The integral formulas of the one-to-one correspondence between the one-particle state Fsλ( p) with nonzero mass p2=E2−p̄2, helicity (−s≤λ≤s), and the state Fν(k)(ν=±s,±(s−1),...,0 or ±( 1/2 ) with mass equal to zero (k2=ω2−k̄2=0) is obtained.
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Stark Effect in the Lobachevsky Space
2013A possibility to define an analog of a uniform electric field in the Lobachevsky space is considered. Schrödinger equation for the hydrogen atom in this electric field is separated and Stark shifts of energy levels are evaluated.
Kurochkin, Yu., Otchik, V.
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