We study the properties of submanifolds of the Grassmannian manifold of the four-dimensional pseudoeuclidean space and also the Grassmann image of a surface in this space. The theorem on existence of a surface in the ...
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We study the properties of submanifolds of the Grassmannian manifold of the four-dimensional pseudoeuclidean space and also the Grassmann image of a surface in this space. The theorem on existence of a surface in the pseudo-euclidean space with given Grassmann image is formulated and proved.
We prove that every minimal equivalence relation on a Cantor set arising from the continuous hull of an aperiodic and repetitive euclidean tiling is affable. To cite this article: F Alcalde Cuesta et al., C R. Acad. S...
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We prove that every minimal equivalence relation on a Cantor set arising from the continuous hull of an aperiodic and repetitive euclidean tiling is affable. To cite this article: F Alcalde Cuesta et al., C R. Acad. Sci. Paris, Ser. I 347 (2009). (c) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Black box quantum mechanical scattering on R-d in even dimensions d >= 2 has many characteristics distinct from the odd-dimensional situation. In this article, we study the scattering matrix in even dimensions and ...
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Black box quantum mechanical scattering on R-d in even dimensions d >= 2 has many characteristics distinct from the odd-dimensional situation. In this article, we study the scattering matrix in even dimensions and prove several identities which hold for its meromorphic continuation onto Lambda, the Riemann surface of the logarithm function. We prove a theorem relating the multiplicities of the poles of the continued scattering matrix to the multiplicities of the poles of the continued resolvent. Moreover, we show that the poles of the scattering matrix on the mth sheet of Lambda are determined by the zeros of a scalar function defined on the physical sheet. Although analogs of these results are well known in odd dimension d, we are unaware of a reference for all of Lambda for the even-dimensional case. Our analysis also yields some surprising results about "pure imaginary" resonances. As an example, in contrast with the odd-dimensional case, we show that in even dimensions there are no "pure imaginary" resonances on any sheet of Lambda for Schrodinger operators with potentials 0 <= V is an element of L-0(infinity) (R-d).
We develop by example a type of index theory for non-Fredholm operators. A general framework using cyclic homology for this notion of index was introduced in a separate article (Carev and Kaad, Topological invariance ...
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We develop by example a type of index theory for non-Fredholm operators. A general framework using cyclic homology for this notion of index was introduced in a separate article (Carev and Kaad, Topological invariance of the homological index. arXiv:1402.0475 [***], 2014) where it may be seen to generalise earlier ideas of Carey-Pincus and Gesztesy-Simon on this problem. Motivated by an example in two dimensions in Boll, et al. (J Math Phys 28:1512-1525, 1987) we introduce in this paper a class of examples of Dirac type operators on that provide non-trivial examples of our homological approach. Our examples may be seen as extending old ideas about the notion of anomaly introduced by physicists to handle topological terms in quantum action principles, with an important difference, namely, we are dealing with purely geometric data that can be seen to arise from the continuous spectrum of our Dirac type operators.
Focuses on the compact hypersurfaces of a euclidean space. Absence of Minkowski integrands; Use of the Gauss and Weingarten formulas; Presence of Ricci curvature.
Focuses on the compact hypersurfaces of a euclidean space. Absence of Minkowski integrands; Use of the Gauss and Weingarten formulas; Presence of Ricci curvature.
We show that second-order superintegrable systems in two-dimensional and three-dimensional euclidean space generate both exactly solvable (ES) and quasiexactly solvable (QES) problems in quantum mechanics via separati...
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We show that second-order superintegrable systems in two-dimensional and three-dimensional euclidean space generate both exactly solvable (ES) and quasiexactly solvable (QES) problems in quantum mechanics via separation of variables, and demonstrate the increased insight into the structure of such problems provided by superintegrability. A principal advantage of our analysis using nondegenerate superintegrable systems is that they are multiseparable. Most past separation of variables treatments of QES problems via partial differential equations have only incorporated separability, not multiseparability. Also, we propose another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schrodinger equation can be expressed in terms of hypergeometric functions F-m(n) and is QES if the Schrodinger equation admits polynomial solutions with coefficients necessarily satisfying a three-term or higher order of recurrence relations. In three dimensions we give an example of a system that is QES in one set of separable coordinates, but is not ES in any other separable coordinates. This example encompasses Ushveridze's tenth-order polynomial QES problem in one set of separable coordinates and also leads to a fourth-order polynomial QES problem in another separable coordinate set. (c) 2006 American Institute of Physics.
In this Note, we show that the presence of a unit Killing vector field on an orientable compact hypersurface of a euclidean space with shape operator A and induced metric g such that g(A xi, xi )is a constant, renders...
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In this Note, we show that the presence of a unit Killing vector field on an orientable compact hypersurface of a euclidean space with shape operator A and induced metric g such that g(A xi, xi )is a constant, renders it to be a round sphere and also influences the dimension of the ambient euclidean space. 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
A system of Schwinger-Dyson equations for the model of scalar-field interaction is studied in a deep euclidean region. It is shown that there exists a critical coupling constant that separates the weak-coupling region...
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A system of Schwinger-Dyson equations for the model of scalar-field interaction is studied in a deep euclidean region. It is shown that there exists a critical coupling constant that separates the weak-coupling region characterized by the asymptotically free behavior and the strong-coupling region, where the asymptotic behavior of field propagators becomes ultralocal.
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