Physical Vacuum Properties and Internal Space Dimension

The paper addresses matrix spaces, whose properties and dynamics are determined by Dirac matrices in Riemannian spaces of different dimension and signature. Among all Dirac matrix systems there are such ones, which nontrivial scalar, vector or other tensors cannot be made up from. These Dirac matrix systems are associated with the vacuum state of the matrix space. The simplest vacuum system realization can be ensured using the orthonormal basis in the internal matrix space. This vacuum system realization is not however unique. The case of 7-dimensional Riemannian space of signature 7(-) is considered in detail. In this case two basically different vacuum system realizations are possible: (1) with using the orthonormal basis; (2) with using the oblique-angled basis, whose base vectors coincide with the simple roots of algebra E_{8}. Considerations are presented, from which it follows that the least-dimension space bearing on physics is the Riemannian 11-dimensional space of signature 1(-)& 10(+). The considerations consist in the condition of maximum vacuum energy density and vacuum fluctuation energy density.Comment: 19 pages, 1figure. Submitted to General Relativity and Gravitatio

On correspondence between tensors and bispinors

It is known that in the four-dimensional Riemannian space the complex bispinor generates a number of tensors: scalar, pseudo-scalar, vector, pseudo-vector, antisymmetric tensor. This paper solves the inverse problem: the above tensors are arbitrarily given, it is necessary to find a bispinor (bispinors) reproducing the tensors. The algorithm for this mapping constitutes construction of Hermitean matrix $M$ from the tensors and finding its eigenvalue spectrum. A solution to the inverse problem exists only when $M$ is nonnegatively definite. Under this condition a matrix $Z$ satisfying equation $M=ZZ^{+}$ can be found. One and the same system of tensor values can be used to construct the matrix $Z$ accurate to an arbitrary factor on the left-hand side, viz. unitary matrix $U$ in polar expansion $Z=HU$. The matrix $Z$ is shown to be expandable to a set of bispinors, for which the unitary matrix $U$ is responsible for the internal (gauge) degrees of freedom. Thus, a group of gauge transformations depends only on the Riemannian space dimension, signature, and the number field used. The constructed algorithm for mapping tensors to bispinors admits extension to Riemannian spaces of a higher dimension.Comment: 14 pages;LaTeX2e;to appear in the 9th Marcel Grossmann Meeting (MG9) Proceedings,Rome, July, 200

QUALITY ASSESSMENT OF SLIGHTLY SALINE MEDIUM LOAM TYPICAL CHERNOZEMS IN CHORNOBAYIV REGION

The theoretical analysis of scientific sources was conducted in Chornobayiv Region to define general characteristics, including soil farmland. The soil fertility in Chornobayiv Region is one of the highest in Ukraine. The soils and environmental conditions of Chornobai zoning district are fully suitable to use agro-industrial qualities of agricultural areas (moisture resources and natural potential of soils), for development and introduction of selective farming systems and technologies adapted to specific natural conditions according to soil monitoring soil data. According to eco-geographical atlas of Ukraine and our results the soil cover characteristics were determined. To control the soil quality the data of agrochemical and eco-certification that allows them to assess the Agroecological state. Studies were carried out on slightly saline medium loam typical chernozems JV "Mayak". The environmental and agrochemical soil indices were studied. On the basis of data from ecological and agrochemical passports of fields soil quality indexes were defined by their suitability for agriculture. About 91% of all agricultural lands belong to the land of average quality. The soils of the first field crop rotation belong to moderate quality soils namely Class VI (fair lands) allowing them to be characterized as moderately supplied by nutrients and productive moisture. The pronounced negative properties of soils and technological properties of land decrease the quality and require additional measures to eliminate the negative effects

Synthesis and catalytic properties of copper(II) 1-aryl-5-benzothiazolylformazanates

New copper(II) benzothiazolylformazane complexes were synthesized and immobilized on AN-18 anion exchanger. The influence of the composition of the coordination core of copper(II) benzthiazolylformazanates and temperature on their catalytic properties in decomposition of H2O2 and oxidation of Na2S in aqueous solution was studied

Synthesis and spectroscopic features of iron(II) 1-aryl-5-benzothiazol-2- ylformazanates

New iron(II) coordination compounds with 1-aryl-5-(benzothiazol-2-yl) formazans were prepared. Their compositions and structures were determined by electronic spectroscopy, mass spectrometry, single crystal X-ray diffraction analysis, and magnetochemical measurements. © 2008 Pleiades Publishing, Ltd.Russian Foundation for Basic Researc

Multimodal Discourse on BRICS Produced by Diverse Stakeholders: Identifying Attitudes, Cultures and Perspectives

The paper explores the conceptual vision of BRICS in the contemporary world. The study focuses on language and images that are used within BRICS-related institutional communication. We argue that the research is important because of the increasing impact of BRICS on the development of the multilateral and multipolar world. The research aims to offer preliminary considerations with regard to key topics, features and tools of multimodal discourse that comes from the BRICS nations and representatives of other international/regional organisations. This area has not been subject to academic analysis so far. This confirms the novelty of the present study. The research material includes 600 image-text correlated items from BRICS official sources of information and from organisation and institutions, which are not affiliated with the BRICS and refer to national or international actors. The research combined theoretical analysis of literature, empirical investigation of materials within qualitative paradigm, through content-based analysis and manual coding on thematic and pragmatic criteria. The findings reveal different approaches to BRICS that are introduced by different actors through specific coordination of verbal and visual tools, in explicit and implicit ways. The findings show that BRICS sources contain   proportioned use of texts and photos of high-ranking official events, socio-cultural features of BRICS countries, and pictures of youth with regard to BRICS mission, values, goals, and policies. This strengthens the concept of equality and human rights provision in the modern world in general and leads to the understanding of the need to include the issues of youth rights and their equality on the BRICS agenda in an explicit way

Uniqueness and Self-Conjugacy of Dirac Hamiltonians in arbitrary Gravitational Fields

Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it is proved that using the Parker weight operator and the subsequent transition to the \eta -representation gives the transformation of the Schroedinger equation for nonstationary metric, when the evolution operator becomes self-conjugate. The scalar products in the \eta -representation are flat, which makes possible the use of a standard apparatus for the Hermitian quantum mechanics. Based on the results of this paper the authors draw a conclusion about solution of the problem of uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary gravitational fields including those dependent on time. The general approach is illustrated by the example of Dirac Hamiltonians for several stationary metrics, as well as for the cosmologically flat and the open Friedmann models.Comment: 23 page

Improved Method of Contrast-enhanced Ultrasound examination of the Kidneys in Patients with Type 2 Diabetes Mellitus

Aim of the research. Тo evaluate the diagnostic efficacy of the contrast-enhanced ultrasound examination of kidneys in patients with type 2 diabetes mellitus with a dose of 0.5 ml of contrast agent administered.Materials and methods. We examined 12 patients with a verified diagnosis of type 2 diabetes. The age of the examined patients was 31–59 years, the mean age was 49 ± 1.3 years. All patients underwent complex diagnostics, including ultrasound examination of the kidneys in B-mode with further renal vessels color Doppler imaging to assess vessels hemodynamics. A contrast-enhanced ultrasound examination of the kidneys was carried out using Sonovue contrast agent at the doses of 2.5 ml (according to the European Good Clinical Practice Recommendations for Contrast-Enhanced Ultrasound) and 0.5 ml (an improved technique of contrast agent intravenous bolus administration).Results. The improved technique (0.5 ml of contrast agent intravenous bolus administration) in comparison with the European Recommendations technique (2.5 ml of contrast agent intravenous bolus administration) used in patients with type 2 diabetes showed no or minor differences in the qualitative and quantitative indicators of contrast-enhanced ultrasound examination which did not affect the interpretation of the results.Conclusion. The improved contrast-enhanced ultrasound examination technique using 0.5 ml of a contrast agent showed its possibilities in diagnosing diabetic nephropathy in patients with type 2 diabetes, and also revealed the potential of an economically beneficial distribution of a contrast agent without losing the quality and information content of the study