相关论文: A Generalization of the Kepler Problem
We present a spectral triple for $\kappa$-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the $\kappa$-Poincar\'e algebra. The…
Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are…
It is known that besides the usual unitary mappings $\Omega = 1/\Omega^\dagger$ between the equivalent representations of the physical Hilbert space of Quantum Mechanics (often, Fourier transformations), the generalized non-unitary maps…
The generalized Cartan-Hadamard conjecture says that if $\Omega$ is a domain with fixed volume in a complete, simply connected Riemannian $n$-manifold $M$ with sectional curvature $K \le \kappa \le 0$, then the boundary of $\Omega$ has the…
The generalized Markoff mod $p$ graph is defined via the equation $x^2+y^2+z^2=xyz+\kappa$ over the finite field $\mathbb{F}_p$ of prime order $p$. In this paper, we investigate the topological properties of the graph such as non-planarity,…
In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi-Maupertuis metric. This characterization works for the $N$-body problem with general masses and any $1/r^{\alpha}$ potential…
Quantum mechanical WKB-method is elaborated for the known quantum Kepler problem in curved 3-space models Euclide, Riemann and Lobachevsky in the framework of the complex variable function theory. Generalized Schr\"{o}dinger, Klein-Fock…
Using a theorem from pcf theory, we show that for any singular cardinal nu, the product of the Cohen forcing notions on kappa, kappa < nu adds a generic for the Cohen forcing notion on nu^+. This solves Problem 5.1 in Miller's list…
Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamental solution to the Laplacian (with delta source at the "sun")…
Assuming $\kappa$ is a supercompact cardinal and $\lambda$ is an inaccessible cardinal above it, we present an idea due to Magidor, to find a generic extension in which $\kappa=\aleph_\omega$ and $\lambda=\aleph_{\omega+1}.$
The notion of commutation of operations in universal algebra leads to the concept of centralizer clone and gives rise to a well-known class of problems that we call centralizer problems, in which one seeks to determine whether a given set…
We obtain a generalization of the Picone inequality which, in combination with the classical Picone inequality, appears to be useful for problems with the $(p,q)$-Laplace type operators. With its help, as well as with the help of several…
We first consider the Klein-Gordon equation in the 6-dimensional space $M_{2,4}$ with signature $+ - - - - +$ and show how it reduces to the Stueckelberg equation in the 4-dimensional spacetime $M_{1,3}$. A field that satisfies the…
We present a systematic methodology for the reformulation of a broad class of three-dimensional (3D) piezoelectric problems into a two-dimensional (2D) mathematical form. The sole underlying hypothesis is that the system geometry and…
In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold. Moreover, we obtain some geometric…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
We present an alternative description of magnetic monopoles by lifting quantum mechanics from 3-dimensional space into a one with 2 complex dimensions. Magnetic monopoles are realized as a generalization of the considered states. Usual…
We investigate a notion called uniqueness in power kappa that is akin to categoricity in power kappa, but is based on the cardinality of the generating sets of models instead of on the cardinality of their universes. The notion is quite…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions…