LEFT-INVARIANT ALMOST PARA-COMPLEX EINSTEINIAN STRUCTURES ON SIX-DIMENSIONAL NILPOTENT LIE GROUPS

As is well known, there are 34 classes of isomorphic simply connected six-dimensional nilpotent Lie groups. Of these, only 26 classes admit left-invariant symplectic structures and only 18 admit left-invariant complex structures. There are five six-dimensional nilpotent Lie groups G , which do not admit neither symplectic, nor complex structures and, therefore, can be neither almost pseudo- Kӓhlerian, nor almost Hermitian. In this work, these Lie groups are being studied. The aim of the paper is to define new left-invariant geometric structures on the Lie groups under consideration that compensate, in some sense, the absence of symplectic and complex structures. Weakening the closedness requirement of left-invariant 2-forms ω on the Lie groups, non-degenerated 2-forms ω are obtained, whose exterior differential dω is also non-degenerated in Hitchin sense [6]. Therefore, the Hitchin’s operator K dω is defined for the 3-form dω . It is shown that K dω defines an almost complex or almost para-complex structure for G and the couple ( ω, dω ) defines pseudo-Riemannian metrics of signature (2,4) or (3,3), which is Einsteinian for 4 out of 5 considered Lie groups. It gives new examples of multiparametric families of Einstein metrics of signature (3,3) and almost para-complex structures on six-dimensional nilmanifolds, whose structural group is being reduced to SL (3 , R) SO (3 , 3). On each of the Lie groups under consideration, compatible pairs of left-invariant forms (ω, Ω), where Ω = d ω, are obtained. For them the defining properties of half-flat structures are naturally fulfilled: d Ω = 0 and ωΩ = 0. Therefore, the obtained structures are not only almost Einsteinian para-complex, but also pseudo- Riemannian half-flat.

DEVELOPMENT OF RECOMBINANT PEPTIDE TECHNOLOGY WITH ANTIMICROBIAL PROPERTIES OF A BROAD ACTION SPECTRUM

Bacteriocins are antibacterial, mainly complex, substances of protein nature. The promising strains producing bacteriocins used in the food industry are lactic acid microorganisms. This study examines the development of a technology for the production of a recombinant peptide with broad-spectrum antimicrobial properties. An important step is the isolation and purification of the recombinant peptide. It has been proved that the highest antimicrobial activity is manifested by a recombinant peptide isolated by a method based on salting out with ammonium sulfate. During the purification of the recombinant bacteriocin preparation, three kinds of columns were used. In the purification process, the volume of bacteriocin produced decreases 3-fold, while the RU/mL increases 3-fold, and RU/mg increases 6-fold. Purification allows the use of a smaller amount of recombinant bacteriocin in technologies with greater efficacy. Based on the results of determining the molecular weight and purity of the recombinant bacteriocin, it was found that the molecular weight of the recombinant bacteriocin having the amino acid sequence: KYYGNGVTCCKHSCSVDXGKASSCIINNGAMAXATGGH GGNHCCGMSRYIQGIPDFLRGYLHGISSANKHKKGRL, is 13 kDa. A technology for the preparation of a broad-action antimicrobial spectrum peptide has been developed. The process of production of antimicrobial peptide includes such stages as: cultivation of the recombinant strain of Escherichia coli BL21DE3; separation of biomass from the nutrient medium; precipitation of bacteriocins by ammonium sulfate; centrifugation; washing the precipitate; centrifugation at 4200 rpm and separation of the preparation; purification of bacteriocins by HPLC method; packing in bags of polymeric and combined materials; storage at a temperature of 18±2°C for 12 months.

PRELIMINARY TESTS OF LOCAL HYPERTHERMIA BASED ON INDUCTIVELY HEATED TUMOR BED IMPLANT

Hyperthermia, i.e. tissue heating to a temperature of 39-45°C, is considered to be a very promising technique to increase the sensitivity of tumor cells to ionizing radiation and chemical preparations. At the present time, there are numerous methods for producing hyperthermia with the optimum method dependent on the required volume, depth, and site of heating. This paper presents the results of preliminary theoretical and in vivo confirmation studies of the feasibility of intraoperative local hyperthermia via induction heating of ferromagnetic material within a tumor bed implant that fills a resected tumor cavity. The implant is made during the surgical removal of tumor by mechanically filling the tumor bed with a self-polymerizing silicone paste in which very fine electroconductive ferromagnetic particles are uniformly distributed. Therefore, the implant can accommodate unique characteristics of each patient’s tumor bed. For the laboratory experiments, a prototype induction heating system was used to produce an alternating magnetic field with a frequency of about 100 kHz and a maximum intensity up to 3 kA/m inside an induction coil of inner diameter 35 cm. Experiments were conducted to heat a 2.5 cm diameter spherical implant both in open air and inside the thigh of a living rabbit. The results in both cases are in good agreement with our theoretical estimations. It was established that the temperature gradient near the implant surface decreases with increasing implant size, and for typical size tumor bed implants produces effective hyperthermia to a distance of more than 5 mm from the implant surface. This result provides hope for a decrease in relapse after treatment of malignant tumors using our combination heat plus intraoperative high dose rate local radiotherapy approach. Moreover, the externally coupled implant heating can be combined with local chemotherapy by applying a self-resorbable polymer film containing antineoplastic agents to the surface of the implant.

CO2 LASER-DRIVEN REACTIONS IN PURE ACETYLENE FLOW

We show that multiple-photon absorption of radiation from a 10.56 μm cw CO2 laser by intermediates (ethylene, vinylidene) generated in pure acetylene flow makes them decompose to carbon dimers and excited hydrogen. The latter associates with downstream acetylene to feedback those laser absorbing intermediates thus making the reactions self-sustained in the absence of oxygen. This process is different from acetylene self-decomposition that may occur at higher temperature and pressure. The results of our work may be useful for understanding the generation of various carbon allotropes and interstellar dust from acetylene.

IMPLEMENTATION OF THE METHODS OF IDENTIFICATION OF STATIC CONTROL OBJECTS

One of the main tasks solved in the development of automatic control systems is the identification of the control object, which consists in obtaining its mathematical description. The nature and type of the mathematical model is determined by the goals and tasks for which it will be used. In the present case, the aim of obtaining the model is the synthesis of an automatic control system. Proceeding from the requirements of control problems, the identification problem consists in determining the structure and parameters of the mathematical model that ensure the best similarity of the model and object responses to the same input action. The article considers the experimental method of obtaining a mathematical description of the control object based on the results of measuring its input and output parameters and then processing the obtained results. The control object is the EP10 emulator made by the Oven Company, which is a miniature furnace. The emulator is used in experimental research in the process of commissioning using thermostat controls, and also applicable for educational purposes as part of training and research stands. As a result of structural identification with subsequent adjustment of the coefficients with the help of parametric identification, a model of the control object in the form of a second order aperiodic link is obtained. Parameters and type of the mathematical model allowed to make calculations and determine the parameters of adjustment of the TRM251 PID-controller. The software implementation of the automatic control system in the MatLAB environment made it possible to evaluate transient processes in a closed system. Thus, the calculation and analysis of the automatic control system in the first approximation were made. The final result can be obtained at the stage of commissioning the automatic temperature control system in the EP10 emulator using adaptation algorithms.

ON THE REGULARIZATION OF EQUATIONS OF THE MECHANICS OF MIXTURES OF VISCOUS COMPRESSIBLE FLUIDS

Mathematical models of multi-velocity continua, through which the motion of multicomponent mixtures are described, represent a rather extensive area of modern mechanics and mathematics. Mathematical results (statements of problems, theorems on the existence and uniqueness, properties of solutions, etc.) for such models are rather modest in comparison with the results for classical single-phase media. The present paper aims to fill this gap in some extent and is devoted to investigating the global correctness of the boundary value problem for a nonlinear system of differential equations, which is some regularity of the mathematical model of nonstationary spatial flows of a mixture of viscous compressible fluids. Construction of the solution of the problem considered in this article is a key step for the mathematical analysis of the initial model of the mixture, since it allows to obtain globally defined solutions of the latter by means of a limiting transition and, in addition, the proposed algorithm for constructing solutions to the regularized problem is practical. This algorithm is based on the finite-dimensional approximation procedure for an infinite-dimensional problem, and therefore a mathematically grounded algorithm for the numerical solution of the boundary value problem of the motion of a mixture of viscous compressible fluids in a region bounded by solid walls can be constructed on this basis. The local in time solvability of finite- dimensional problems is proved by applying the principle of contracting mappings and the local solution can be extended to an arbitrary time interval with the help of a priori estimates.

TECHNOLOGY OF BARLEY BREEDING FOR RESISTANCE TO SMUT FUNGI

The technology of creating varieties of barley resistant to the smut diseases has been developed. Their cultivation will help to reduce crop losses, increase the profitability of seed production, improve the quality of seeds, and reduce the environmental risk from the use of chemical plant protection products. This technology was first implemented in the Kemerovo Region in 1988-1999. The wide distribution of species Ustilago nuda (Jens.) Kell. et Sw. (65 %) and U. nigra Tapke (35 %) was revealed. The covered smut ( Ustilago hordei (Pers.) Kell. Et Sw.) was registered in individual collection varieties. The first and tenth races of a loose smut and the sixth race of a black loose smut were identified. The sources of individual and group immunity to the smut fungi from the world gene pool of barley are distinguished: Moskovsky 3/125, Suzdalets, Ramos (Moscow Region); Kazer (Rostov Region); line 3 KM-1192 (Belarus); Kumir Odessky (Ukraine); Guardian (Canada). The donor properties of resistance to a loose smut in the Bagan variety, line 53 HVS 91/76, line 1899 were studied. They are recommended for use in breeding programs. With their participation a new hybrid fund was created. Variability and inheritance of quantitative traits of productivity of hybrids was studied. To select the recombinants immune to the loose smut in combination with high productivity, the most promising combinations of hybrids have been identified: Bagan × Viner; Bagan × KM-16; l. 53 HVS 91/76 × KM-7; KM-7 × l. 1899; l. 1899 × KM-7. Among them, prospective breeding lines have been selected. The results of the implementation of technology elements in the selection of barley for resistance to smut fungi is the creation of immune highly productive varieties of a new generation: Simon and Luka (Kemerovo Region). They are included in the State register of breeding achievements since 2004.

RESEARCH ON THE MECHANISM OF MELANOIDIN ADSORPTION KINETICS FROM AQUEOUS SOLUTIONS BY CARBONIC ADSORBENTS

Melanoidins are widely used in food and pharmaceutical industries. Melanoidins, which get in water bodies with wastewater of plants, pollute them, which subsequently can have a negative impact on the population health. Wastewater treatment of plants is an important condition to preserve the integrity of aquatic ecosystems. Sorption filtration is the most effective way of removing organic substances among the methods, used for wastewater treatment. To study the adsorption kinetics, the carbonic sorbents of the brands ABG and Purolat-Standard were used, which differ with a raw material, a surface chemistry state and a porous structure. The study of the adsorption kinetics allows to determine the mechanism of mass transfer in the system adsorbent-adsorbate and to obtain the parameters, necessary for engineering evaluation of adsorption processes in practice. It is shown that the time of reaching equilibrium in the sorption system varies in the range of 150-250 minutes. The degree of reaching the adsorption equilibrium () and the dimensionless kinetic parameters T have been calculated, which are proportional to the time of the process (t). It is found that the melanoidin adsorption rate is controlled by external mass transfer, necessary for calculation of optimum parameters and modes of the adsorption process. Experimental research allows to determine that the granules of the used carbonic sorbents interact with the dissolved substance in the full volume and throughout the particle is in the reaction zone; such interaction relates to a quasi-homogeneous model. It is shown that at the melanoidin adsorption, the rate of the internal diffusive mass transfer depends on the porous structure of the carbonic adsorbents. A high value of the external mass transfer coefficient for the carbonic sorbent Purolat-Standard suggests a high degree of melanoidin extraction from aqueous solutions.

EXTERIOR DIFFERENTIAL FORMS ON RIEMANNIAN SYMMETRIC SPACES

In the present paper we give a rough classification of exterior differential forms on a Riemannian manifold. We define conformal Killing, closed conformal Killing, coclosed conformal Killing and harmonic forms due to this classification and consider these forms on a Riemannian globally symmetric space and, in particular, on a rank-one Riemannian symmetric space. We prove vanishing theorems for conformal Killing L 2-forms on a Riemannian globally symmetric space of noncompact type. Namely, we prove that every closed or co-closed conformal Killing L 2-form is a parallel form on an arbitrary such manifold. If the volume of it is infinite, then every closed or co-closed conformal Killing L 2-form is identically zero. In addition, we prove vanishing theorems for harmonic forms on some Riemannian globally symmetric spaces of compact type. Namely, we prove that all harmonic one-formsvanish everywhere and every harmonic r -form  r  2 is parallel on an arbitrary such manifold. Our proofs are based on the Bochnertechnique and its generalized version that are most elegant and important analytical methods in differential geometry “in the large”.

LIQUID- SOLID AND LIQUID-VAPOR PHASE EQUILIBRIUM IN SECONDARY ALCOHOL - n-ALKANE SYSTEM

Primary and secondary alcohols, obtained as a product of processing of plant raw materials, can be used as additives in fuel. Mixtures of n-alkanes, cyclic alkanes and aromatic hydrocarbons can act as a model for gasoline and diesel fuel. Therefore, it is necessary to study the characteristics of mixtures of alcohols with normal, cyclic and aromatic hydrocarbons. To simulate liquid-solid and liquid-vapor phase equilibria, a method is used to minimize excess Gibbs energy by the solvation parameter. The authors developed the PCEAS (Phase Charts Eutectic and Azeotropic Systems) software. The input data in the case of constant pressure are the temperature T 0 and the enthalpy of the phase change H 0 of the pure components. Prediction of the thermodynamic parameters of secondary alcohols is used to calculate the eutectic and azeotropic parameters of the secondary alcohol - n-alkane mixture: composition, temperature, melting enthalpy and evaporation. The model makes it possible to determine the average value of the association parameter in the liquid phase k . Experimental data for azeotropic mixtures made it possible to establish the association parameter in the vaporphase  of the systems under study. The results of calculations can be used to select the optimal composition and obtain the requiredcharacteristics of biofuel.