Spontaneous spherical symmetry breaking in atomic confinement

The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The reason is that such boundary conditions could yield a large magnitude of electronic wavefunction in some sector of the box boundary, what in turn promotes atomic displacement from the box center towards this part of the boundary, and so the underlying SO(3) symmetry spontaneously breaks. The emerging Goldstone modes, coinciding with rotations around the box center, restore the symmetry by spreading the atom over a spherical shell localized at some distances from the box center. Atomic confinement inside the cavity proceeds dynamically -- due to the boundary condition the deformation of electronic wavefunction near the boundary works as a spring, that returns the atomic nuclei back into the box volume.Comment: 12 pages, 12 figures. arXiv admin note: text overlap with arXiv:1301.3399 . authors note: added reference, changes in introduction, added acknowledgemen

Contextual algorithm for decision of fuzzy estimation problems with network-like structure of criteria on the basis of fuzzy measures Sugeno

In this article the algorithm for the decision of alternatives' estimation problems for following conditions is considered. Values of alternative's characteristics (properties) are fuzzy. They are formalized as fuzzy sets. The estimation criteria structure is network-like and is formalized as the oriented graph with one source and many drains. The alternative's estimation result is calculated in criterion-source. Connections between criteria are formalized by fuzzy measures Sugeno. Upper-level criteria are considered as contexts for lower-level criteria. Fuzzy integrals Sugeno or Choquet are used as aggregation operator. In article also the properties of fuzzy measure and fuzzy integrals (Sugeno and Choquet) are analyzed. Properties of fuzzy measure and integrals are comparing with properties of other mathematical tools. As example the car's estimation problem is presented.fuzzy measure (Sugeno); fuzzy integral (Sugeno and Choquet); alternatives estimation; criteria structure

Modeling risk of international country relations

In this article we consider the modeling principles and model for estimation of tension of international relations of a country with other countries. We use the tension of international relations as partial indicator of international political-economical country-risk. The model bases on estimation of coincidences and contradictions of views of countries concerning decision of political, economic, military, domestic and international problems and projects. The model aggregates detailed estimations of separate problems into composite estimation of relations tension with using of fuzzy measures and integrals. The model allows receiving quantitative estimations of tension of international relations which are necessary for making investment decisions. We use this model for estimation of international political-economical risk of Ukraine.model; international relations; fuzzy measure; political-economical risks

Algorithm of arithmetical operations with fuzzy numerical data

In this article the theoretical generalization for representation of arithmetic operations with fuzzy numbers is considered. Fuzzy numbers are generalized by means of fuzzy measures. On the basis of this generalization the new algorithm of fuzzy arithmetic which uses a principle of entropy maximum is created. As example, the summation of two fuzzy numbers is considered. The algorithm is realized in the software "Fuzzy for Microsoft Excel".fuzzy measure (Sugeno), fuzzy integral (Sugeno), fuzzy numbers; arithmetical operations; principle of entropy maximum