Pieri's Formula for Generalized Schur Polynomials

Young's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young tableaux. We define a generalization of Schur polynomials as expansion coefficients of generalized Schur operators. We show that the commutating relation of generalized Schur operators implies Pieri's formula to generalized Schur polynomials

Photoluminescence of tetrahedral quantum-dot quantum wells

Taking into account the tetrahedral shape of a quantum dot quantum well (QDQW) when describing excitonic states, phonon modes and the exciton-phonon interaction in the structure, we obtain within a non-adiabatic approach a quantitative interpretation of the photoluminescence (PL) spectrum of a single CdS/HgS/CdS QDQW. We find that the exciton ground state in a tetrahedral QDQW is bright, in contrast to the dark ground state for a spherical QDQW.Comment: 4 pages, 2 figure

Foreign trade and marketing processes in the context of sustainable development

Purpose: The article aims to study foreign economic and trade relations between the countries of Central and Eastern Europe, the CIS and the Western European countries. In addition, the study improves forms of foreign economic cooperation between the countries and suggests the stages of its implementation in the integration group. Design/Methodology/Approach: Central and Eastern European countries are experiencing the increase and acceleration of the labour migration to Western European countries, which has a negative impact on their medium-and long-term development. As a theoretical and methodological basis, the article uses historical-logical, dialectical principles and contradictions, the method of the scientific abstraction. The process-system approach, which was used in the study of foreign economic relations between the partner countries, gained special importance in the argument of the need to implement stages. Findings: Authors presented the form of the foreign economic cooperation between the countries as the geostrategic economic block and the stages of its implementation. As the study shows, these stages will help to smooth out the economic inequality between the Central and Eastern regions of Europe and Western European countries. Practical implications: In practice, authors investigate the phased implementation of the geostrategic economic bloc form, which will reduce inequality between the partner countries of the European Union. Originality/Value: The economic inequality between developed and developing countries of the European Union is increasing every year, which can lead to the transformation of the integration group, so it is necessary to develop new forms and mechanisms of foreign economic relations between the partner countries.peer-reviewe

Stable vortex-antivortex molecules in mesoscopic superconducting triangles

A thermodynamically stable vortex-antivortex pattern has been revealed in mesoscopic type I superconducting triangles, contrary to type II superconductors where similar patterns are unstable. The stable vortex-antivortex "molecule" appears due to the interplay between two factors: a repulsive vortex-antivortex interaction in type I superconductors and the vortex confinement in the triangle.Comment: 5 pages, 4 figures, E-mail addresses: [email protected], [email protected], [email protected], [email protected]

Temperature Dependence of the Cyclotron Mass in n-Type CdS

Recent cyclotron resonance experiments in n-type CdS at ultra-high magnetic fields have revealed a pronounced maximum of the electron cyclotron mass as a function of temperature. In order to interpret these data, we calculate the magneto-absorption spectra of polarons in n-CdS using the arbitrary-coupling approach. We show that in high magnetic fields the polaron effects beyond the weak-coupling approximation clearly reveal themselves in the magneto-optical absorption even at relatively small values of the Froehlich coupling constant. In particular, those effects result in a non-monotonous behaviour of the cyclotron mass as a function of temperature. We extend the theory to take into account a combined effect of several scattering mechanisms on the magneto-absorption spectra. The extended theory allows us to interpret quantitatively the experimentally observed behaviour of the cyclotron mass in CdS.Comment: 4 pages, 3 figures, E-mail addresses: [email protected], [email protected]