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

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

Design of a chamber dryer for sugar cubes drying

The main aim of the task is to make new design of chamber dryer. New design of chamber dryer for sugar cubes drying was performed by using laboratory dryer and doing measurements. Specification of drying time according to these measurements by dewatering sugar cubes moisture content from 2% to 0,1% was the most important parameter for design. The second important aim was finding out the amount of heat for heating aims and fan. By using Autocad software the basic design of both Belt and Chamber dryers were performed.The main aim of the task is to make new design of chamber dryer. New design of chamber dryer for sugar cubes drying was performed by using laboratory dryer and doing measurements. Specification of drying time according to these measurements by dewatering sugar cubes moisture content from 2% to 0,1% was the most important parameter for design. The second important aim was finding out the amount of heat for heating aims and fan. By using Autocad software the basic design of both Belt and Chamber dryers were performed

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

The species composition and nutrition of dominant species of fish of Absheron Gulfs of the Caspian Sea

The analysis of net catches made in Absheron Gulfs of the Caspian Sea during 2011-2012 is provided. The ichthyofauna of Absheron Gulfs, including 26 species found in the North Gulf, and 33 species and subspecies found in the South Gulf was studied for the first time. A taxonomical and ecological diversity of the fish fauna of North and South Absheron Gulfs is characterized. The peculiarities of distribution and population densities of all species of fishes from different families within the studied territories were analyzed. For each of hydrological seasons, numerous, common, infrequent and rare species were revealed. On migration patterns and catch, the lowest biomass of fishes was observed in the warm season, while the highest was in the winter and spring seasons. The tendency of expansion of ranges of some marine fishes - Gasankuli herring Alosa braschnikowi kisselewitschi, Sara herring A. braschnikowi sarensis, big-eyed herring A. braschnikowi autumnalis, Sara shad A.caspia knipowitschi - to the north was recorded

The features of the feeding of Caspian marine shad, Alosa braschnikowii (Borodin, 1904) in western part of the Caspian Sea

Feeding habits of Caspian marine shad Alosa braschnikowii (Borodin, 1904), inhabiting in the western part of Caspian Sea such as prey spectrum and seasonal dynamics have been studied. As in other parts of Caspian Sea, throughout the year, the main hunt of Caspian marine shad constituted kilkas, gobies and shrimps while other groups of zoobenthos were represented in a lesser extent. Importance of other fishes and zoobenthos in the diet of Caspian marine shad is influenced by their ecological morpho-functional peculiarities. Seasonal changes of species composition and proportions of fodder food items are caused by life cycles of fishes and migrations of fodder entities. The changes of food composition depending length of fishes, the depth and haul region are analyzed. Caspian marine shad most intensively feeds in spring (March – April) before spawning and in summer (July) after spawning