Casimir Energy for a Wedge with Three Surfaces and for a Pyramidal Cavity

Casimir energy calculations for the conformally coupled massless scalar field for a wedge defined by three intersecting planes and for a pyramid with four triangular surfaces are presented. The group generated by reflections are employed in the formulation of the required Green functions and the wave functions.Comment: Latex, 9 page

Determination of trigonometric Fourier’s series by the method of four-dimensional mathematics

This paper is devoted to the determination of the trigonometric Fourier series by the method of four-dimensional mathematics. In this paper, a new four-dimensional method for evaluation of the sums containing trigonometric function is proposed. Current work provides a first study and finding towards Fourier's series in four-dimensional space

Quadratic Curvature Gravity with Second Order Trace and Massive Gravity Models in Three Dimensions

The quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In $n>4$ dimensions, pure quadratic curvature lagrangian having second order trace constructed contains three free parameters in the most general case. The fourth order field equations of some of these models, in arbitrary dimensions, are cast in a particular form using the Schouten tensor. As a consequence, the field equations for the New massive gravity theory are related to those of the Topologically massive gravity. In particular, the conditions under which the latter is "square root" of the former are presented.Comment: 24 pages, to appear in GR

Ohm's Law for Plasma in General Relativity and Cowling's Theorem

The general-relativistic Ohm's law for a two-component plasma which includes the gravitomagnetic force terms even in the case of quasi-neutrality has been derived. The equations that describe the electromagnetic processes in a plasma surrounding a neutron star are obtained by using the general relativistic form of Maxwell equations in a geometry of slow rotating gravitational object. In addition to the general-relativistic effect first discussed by Khanna \& Camenzind (1996) we predict a mechanism of the generation of azimuthal current under the general relativistic effect of dragging of inertial frames on radial current in a plasma around neutron star. The azimuthal current being proportional to the angular velocity $\omega$ of the dragging of inertial frames can give valuable contribution on the evolution of the stellar magnetic field if $\omega$ exceeds $2.7\times 10^{17} (n/\sigma) \textrm{s}^{-1}$ ($n$ is the number density of the charged particles, $\sigma$ is the conductivity of plasma). Thus in general relativity a rotating neutron star, embedded in plasma, can in principle generate axial-symmetric magnetic fields even in axisymmetry. However, classical Cowling's antidynamo theorem, according to which a stationary axial-symmetric magnetic field can not be sustained against ohmic diffusion, has to be hold in the general-relativistic case for the typical plasma being responsible for the rotating neutron star.Comment: Accepted for publication in Astrophysics & Space Scienc

Analytical solution of the cauchy problem for a nonstationary three-dimensional model of the filtration theory

This paper is devoted to the study of the Cauchy problem for a system of differential equations describing the unsteady flow of a compressible fluid in a homogeneous and inhomogeneous porous medium with a general nonlinear filtration law in three-dimensional space. In the work using the methods of four-dimensional mathematics, a special four-dimensional space of space and time coordinates was developed, as well as a functional space of regular functions, and analytical conditions were obtained on the general form of the nonlinear filtration law for which the Cauchy problem has a solution

Generalized exclusion and Hopf algebras

We propose a generalized oscillator algebra at the roots of unity with generalized exclusion and we investigate the braided Hopf structure. We find that there are two solutions: these are the generalized exclusions of the bosonic and fermionic types. We also discuss the covariance properties of these oscillatorsComment: 10 pages, to appear in J. Phys.

Валідація алкаліметричної методики кількісного визначення вільних органічних кислот у листі малини

 Organic acids are a large group of biologically active compounds that perform important functions in the plant organism. Moreover, all plants, regardless of the species and family, contain organic acids to a small or large extent as organic acids belong to intermediate metabolites arising from the oxidation of proteins and amino acids, fats and carbohydrates.Aim. To validate the method of alkalimetry proposed with potentiometric detection of the end-point for the quantitative determination of free organic acids in raspberry leaves.Results and discussion. The method proposed was validated according to the International Conference on Harmonization (ICH) guidelines. The linearity was in the concentration range of 40 – 200 % (r2 = 0.9991). The percentage of recovery was found to be in the range of 98.77 – 102.48 %. The repeatability and intermediate precision were 1.58 % and 1.74 %, respectively. The method is accurate and reliable, with the relative standard deviation of less than 2 %.Experimental part. Leaves of raspberry were collected in the Kharkiv region during the period of full ripening. A Hanna 2550 pH-meter with a HI 1131P potentiometric electrode was used for alkalimetric titration of free organic acids. The titration was carried out using a microburette with Class A accuracy.Conclusions. The alkalimetry method for the quantitative determination of free organic acids in raspberry leaves has been proposed and validated according to the following parameters: specifcity, linearity, accuracy, repeatability, intermediate precision, robustness. It has been confrmed that the method is simple, reliable, accurate and cost-effective.Key words: raspberry; leaves; free organic acids; alkalimetry; validationОрганічні кислоти – велика група біологічно активних сполук, які виконують важливі функції в обміні речовин рослин. Усі рослини, незалежно від виду та родини, містять органічні кислоти в невеликій або значній кількості, бо ці речовини належать до проміжних метаболітів, що утворюються в результаті окиснення білків, амінокислот, жирів та вуглеводів.Мета. Валідувати запропоновану алкаліметричну методику з потенціометричним виявленням кінцевої точки титрування для кількісного визначення вільних органічних кислот у листі малини.Результати та їх обговорення. Запропонований метод валідовано згідно з директивою International Conference on Harmonization. Лінійність зберігалася в діапазоні концентрацій 40 – 200 % (r2= 0,9991). Визначено, що відсоток відновлення становить 98,77 – 102,48 %, повторюваність та проміжна точність – 1,58 % та 1,74 % відповідно. Метод характеризується як точний і надійний, має відносне стандартне відхилення менше 2 %.Експериментальна частина. Листя малини в період повного дозрівання збирали в Харківській області. Для алкаліметричного титрування вільних органічних кислот використовували рН-метр Hanna 2550 з потенціометричним електродом HI 1131P. Титрування проводили мікробюреткою з класом точності А.Висновки. Розроблену титриметричну методику кількісного визначення вільних органічних кислоту листі малини валідовано за такими параметрами: специфічність, лінійність, точність, збіжність, внутрішня прецизійність, робасність. Підтверджено, що метод є простим, надійним, точним та економічно вигідним.Ключові слова: малина; листя; вільні органічні кислоти; алкаліметрія; валідаці

Ternary algebras and groups

We construct explicitly groups associated to specific ternary algebras which extend the Lie (super)algebras (called Lie algebras of order three). It turns out that the natural variables which appear in this construction are variables which generate the three-exterior algebra. An explicit matrix representation of a group associated to a peculiar Lie algebra of order three is constructed considering matrices with entry which belong to the three exterior algebra.Comment: 11 pages contribution to the 5th International Symposium on Quantum Theory and Symmetries (QTS5

A Unified Approach to Variational Derivatives of Modified Gravitational Actions

Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann curvature tensor and its contractions. We are able to derive a master equation which expresses the variational derivatives of the generalized gravitational actions in terms of the variational derivatives of its constituent curvature scalars. Using the Lagrange multiplier method relative to an orthonormal coframe, we investigate the variational procedures for modified gravitational Lagrangian densities in spacetime dimensions $n\geqslant 3$. We study well-known gravitational actions such as those involving the Gauss-Bonnet and Ricci-squared, Kretchmann scalar, Weyl-squared terms and their algebraic generalizations similar to generic $f(R)$ theories and the algebraic generalization of sixth order gravitational Lagrangians. We put forth a new model involving the gravitational Chern-Simons term and also give three dimensional New massive gravity equations in a new form in terms of the Cotton 2-form

The role of hematological parameters as predictors of mortality in elderly patients in the hospital period

The development of algorithms for predicting adverse outcomes, including death in elderly and senile patients, is an urgent issue. Potential predictors include hematologic parameters. A clinical blood test is one of the most affordable diagnostic methods in practical medicine, reflecting systemic pathological processes in the human body based on a quantitative assessment of the cellular composition and blood morphology. The aim of this study was to evaluate hematological parameters as predictors of in-hospital mortality in patients of the elderly and senile age with acute coronary syndrome.Material and methods. The study included 277 patients with acute coronary syndrome. The study of hematological parameters was carried out on a CELL-DYN Sapphire hematology analyzer (Abbott Laboratories, USA). The values of neutrophil-lymphocytes ratio and platelet-lymphocytes ratio were also evaluated as predictors of in-hospital mortality.Results. High content of leukocytes (above 10.45 x 109/l) during hospitalization in patients with ACS aged 60-74 years are associated with a higher risk of death at the hospital stage. Among patients with ACS aged 75-89 years, the risk of death is associated with the following changes in peripheral blood upon admission: a decrease in the absolute number of eosinophils below 0.086 x 109/l, an increase in the absolute number of basophils above 0.079 x 109/l and a decrease in platelet-lymphocytes ratio below 31.06