The fundamental quantum Coulomb problem in the momentum space is considered. A differential equation with SO (4) symmetry has been obtained instead of integral Fock equation. corresponding coordinate sum squares angular and Runge–Lenz operators. This approach unknown where operator not applied. simpler than that allows one to effectively consider space. relation new infinitesimal rotation three...

We present and analyse numerical methods with operator splitting procedures, applied to an epidemic model which takes into account the space-dependence of infection. derive conditions on time step, under preserve non-negativity monotonicity properties exact solution. Our results are illustrated by experiments.

On a discrete group G a length function may implement a spectral triple on the reduced group C*-algebra. Following A. Connes, the Dirac operator of the triple then can induce a metric on the state space of reduced group C*-algebra. Recent studies by M. Rieffel raise several questions with respect to such a metric on the state space. Here it is proven that for a free non Abelian group, the metri...

We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.

We develop a certain piece of functional analysis on general graphs and use it to create what Connes calls a’spectral triple’, i.e. a Hilbert space structure, a representation of a certain (function) algebra and a socalled ’Dirac operator’, encoding part of the geometric/algebraic properties of the graph. We derive in particular an explicit expression for the ’Connesdistance function’ and show ...

The role of the Killing–Yano tensors in the construction of the Dirac-type operators is pointed out. The general results are applied to the case of the four-dimensional Euclidean Taub–Newman–Unti–Tamburino space. Three new Dirac-type operators, equivalent to the standard Dirac operator, are constructed from the covariantly constant Killing–Yano tensors of this space. Finally the Runge–Lenz oper...

This paper studies a model of strategic communication by an informed and upwardly biased sender to one or more receivers. Applications include situations in which (i) it is costly for the sender to misrepresent information, due to legal, technological, or moral constraints, or (ii) receivers may be credulous and blindly believe the sender’s recommendation. In contrast to the predictions obtaine...

One of the key ingredients of A. Connes’ noncommutative geometry is a generalized Dirac operator which induces a metric(Connes’ distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al , whose Connes’ distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being “naturally” defined has the “local eigenvalue property” and i...

During the last fifty years, Clifford analysis has gradually developed to a comprehensive theory offering a direct, elegant, and powerful generalization to higher dimension of the theory of holomorphic functions in the complex plane. In its most simple but still useful setting, flat m-dimensional Euclidean space, Clifford analysis focusses on the so-called monogenic functions, that is, null sol...