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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
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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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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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Geometric Algebra and Lobachevski Geometry
1998Geometric Algebra is used to study Lobachevski geometry and some research results are reported. Not only old results are obtained more easily, but some interesting new results are obtained. It seems that Geometric Algebra is a natural way to study Lobachevski geometry.
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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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Acerca de la Geometrìa de Lobachevski
1978El objetivo de este libro es dar a conocer al lector los fundamentos principales de la geometría no euclidiana de Lobachevski. El célebre científico ruso Nikolai Ivanovich Lobachevski era un pensador notable. A él le pertenece uno de los inventos matemáticos más importantes, la creación de un sistema geométrico original distinto de la geometría de ...
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