On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)

In the recent years a generalization of Hermiticity was investigated using a complex deformation H=p^2 +x^2(ix)^\epsilon of the harmonic oscillator Hamiltonian, where \epsilon is a real parameter. These complex Hamiltonians, possessing PT symmetry (the product of parity and time reversal), can have real spectrum. We will consider the most simple case: \epsilon even. In this paper we describe all self-adjoint (Hermitian) and at the same time PT symmetric operators associated to H=p^2 +x^2(ix)^\epsilon. Surprisingly it turns out that there are a large class of self-adjoint operators associated to H=p^2 +x^2(ix)^\epsilon which are not PT symmetric

Operating with UXO Containing White Phosphorus

This article provides a brief account of the unexploded ordnance problem in Azerbaijan and describes the particular hazards of dealing with UXO containing white phosphorus. Drawing from the experience of the Azerbaijan National Agency for Mine Action\u27s work at Saloglu, guidelines for handling WP UXO are discussed

PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics

In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x real. We will give a complete characterization of three different classes of operators associated with the differential expression H: The class of all self-adjoint (Hermitian) operators, the class of all PT symmetric operators and the class of all P-self-adjoint operators. Surprisingly, some of the PT symmetric operators associated to this expression have no resolvent set

The Study of the Experience of Developed East Asian Countries in Customs Audit Methodology and Its Implementation in Uzbekistan

A Customs audit is an evaluation of company practices and records. The audit assists in judging the integrity of information supplied under self-assessment and the level of compliance with legislative requirements. As an importer or exporter, people are legally responsible for the accuracy of information supplied to Customs, even though they must use a Customs Broker to prepare and lodge your declarations. The article reveals the methodology of the organization and conducting of the customs audit, which is effectively used in the practice of developed East Asian countries, as well as the possibility of introducing their experience in Uzbekistan Keywords: Foreign trade, export, import, customs auditing, exporter, importer, Uzbekistan

PT-Symmetric Quantum Theory Defined in a Krein Space

We provide a mathematical framework for PT-symmetric quantum theory, which is applicable irrespective of whether a system is defined on R or a complex contour, whether PT symmetry is unbroken, and so on. The linear space in which PT-symmetric quantum theory is naturally defined is a Krein space constructed by introducing an indefinite metric into a Hilbert space composed of square integrable complex functions in a complex contour. We show that in this Krein space every PT-symmetric operator is P-Hermitian if and only if it has transposition symmetry as well, from which the characteristic properties of the PT-symmetric Hamiltonians found in the literature follow. Some possible ways to construct physical theories are discussed within the restriction to the class K(H).Comment: 8 pages, no figures; Refs. added, minor revisio

THEORETICAL AND PRACTICAL BASIS OF IMPLEMENTING INNOVATIVE TECHNOLOGIES IN TEACHING THE ENGLISH LANGUAGE TO B1 LEVEL LEARNERS

The article considers one of the most important issues of modern foreign languages teaching: the innovative methods of developing language learners’ skills in a target language deeply and systematically. Today specialists of foreign languages, namely teachers are demanded to develop learners’ language skills and competences according to the measures and tasks of the study programs using innovative methods. The theoretical basis and practical results of applying social networking services and messengers as modern means of information and communication technologies and the effective usage of foreign language study materials in teaching the English language to learners in the example of B1 levelled ones on the online platform (using Telegram messenger) are analysed in the article. To illustrate the practical results of our research, we have showed the gradual steps which were used to develop the learners’ main four skills, such as listening, reading, speaking and writing ones with the help of the effective functions of the above-mentioned means in the virtual environment during our research. Besides that, we have highlighted the methods of assessing learners online in the virtual environment in this article