DEVELOPMENT OF A CALCULATION METHODFOR TWO-STAGE NATURAL GAS PURIFICATION PLANTS FROM MECHANICAL IMPURITIES

Statement of the problem. Currently, there is no methodology for calculating the degree of clogging of a multilayer filter cartridge taking into account the prevention of deposition of mechanical impurities in the gap between the coarse and fine filter cylindrical filter cartridges. In this regard, the development of such a technique is an urgent task. Results. In this paper, we propose a calculation method for determining the average integral degree of clogging of multilayer cylindrical filter cartridges with mechanical impurities and pressure loss on them which take into account the prevention of sedimentation of mechanical impurities in the gap between the coarse and fine filter cartridges.Conclusions. The results obtained make it possible to determine the pressure loss and the average integral degree of clogging of the multilayer filter cartridge depending on the decrease in the living cross-section of all filter meshes in the process of clogging and to prevent the deposition of solids in the gap between the coarse and fine filter cartridges.

DEVELOPMENT OF A CALCULATION METHOD FOR TWO-STAGE NATURAL GAS PURIFICATION PLANTS FROM MECHANICAL IMPURITIES

Состояние проблемы. В настоящее время отсутствует методика расчета степени засорения многослойного фильтрующего картриджа, учитывающая недопущение осаждения механических примесей в зазоре между цилиндрическими фильтрующими картриджами грубой и тонкой очистки. В этой связи разработка такой методики является актуальной задачей. Результаты. В данной работе предложена методика расчета по определению среднеинтегральной степени засорения многослойных цилиндрических фильтрующих картриджей механическими примесями и потери давления на них, которые учитывают недопущение осаждения механических примесей в зазоре между цилиндрическими фильтрующими картриджами грубой и тонкой очистки. Выводы. Полученные результаты позволяют определить величины потерь давления и среднеинтегральной степени засорения многослойного фильтрующего картриджа в зависимости от величины уменьшения живого сечения всех фильтрующих сеток в процессе их засорения и предотвратить осаждение механических примесей в зазоре между цилиндрическими фильтрующими картриджами грубой и тонкой очистки. Statement of the problem. Currently, there is no methodology for calculating the degree of clogging of a multilayer filter cartridge taking into account the prevention of deposition of mechanical impurities in the gap between the coarse and fine filter cylindrical filter cartridges. In this regard, the development of such a technique is an urgent task. Results. In this paper, we propose a calculation method for determining the average integral degree of clogging of multilayer cylindrical filter cartridges with mechanical impurities and pressure loss on them which take into account the prevention of sedimentation of mechanical impurities in the gap between the coarse and fine filter cartridges. Conclusions. The results obtained make it possible to determine the pressure loss and the average integral degree of clogging of the multilayer filter cartridge depending on the decrease in the living cross-section of all filter grids in the process of clogging and to prevent the deposition of solids in the gap between the coarse and fine filter cartridges. Statement of the problem. Currently, there is no methodology for calculating the degree of clogging of a multilayer filter cartridge taking into account the prevention of deposition of mechanical impurities in the gap between the coarse and fine filter cylindrical filter cartridges. In this regard, the development of such a technique is an urgent task. Results. In this paper, we propose a calculation method for determining the average integral degree of clogging of multilayer cylindrical filter cartridges with mechanical impurities and pressure loss on them which take into account the prevention of sedimentation of mechanical impurities in the gap between the coarse and fine filter cartridges. Conclusions. The results obtained make it possible to determine the pressure loss and the average integral degree of clogging of the multilayer filter cartridge depending on the decrease in the living cross-section of all filter grids in the process of clogging and to prevent the deposition of solids in the gap between the coarse and fine filter cartridges.

Оценка спектральной оптической толщины пламени в камере сгорания судового дизеля

Использование математических моделей, в основу которых положен зональный метод расчета теплообмена излучением, применительно к камере сгорания судового дизеля, требует предварительного определения ряда энергетических характеристик. Важнейшей из них является спектральная оптическая толщина племени. Целью данной статьи является разработка расчетного метода для оценки спектральной оптической толщины пламени в камере сгорания судового дизеля 6 ЧН 24/36. Показано, что величина спектральной оптической толщины пламени зависит от трех основных параметров: коэффициента ослабления излучения, концентрации частиц сажи и их оптических характеристик (среднего диаметра и параметра дифракции). Представлены распределение частиц сажи по размерам и значения спектральной оптической толщины пламени в функции угла поворота коленчатого вала для судового дизеля 6 ЧН 24/36 при испытании его по нагрузочной характеристике. Приведены основные подходы, позволяющие определить интегральную степень черноты пламени в камере сгорания с использованием полученных расчетных данных по его спектральной оптической толщине.Application of mathematical models in the base of them a zonal method of calculation of radiative transfer is included in additional to marine diesel combustion chamber, it is required first determination the number of power data. Spectral optical thickness of flame is very important. Development of method calculation for the estimation of spectral optical thickness of flame in marine diesel 6 ChN 24/36 combustion chamber is the purpose of this paper. A value of spectral optical thickness of flame depends from three basic data: coefficient of attenuation radiation, concentration of soot particles and its optical data (mean diameter and parameter of diffraction) is given. Distribution of soot particles according to sizes and values of spectral optical thickness of flame in function of crank angle degree for marine diesel 6 ChN 24/36 in its power data is shown. Basic methods per missing to determine integral degree of flame blackness in combustion chamber with application of calculation data on its spectral optical thickness is determined.

Modified signomial geometric programming (MSGP) and its applications

A "signomial" is a mathematical function, contains one or more independent variables. Richard J. Duffin and Elmor L. Peterson introduced the term "signomial". Signomial geometric programming (SGP) optimization technique often provides a much better mathematical result of real-world nonlinear optimization problems. In this research paper, we have proposed unconstrained and constrained signomial geometric programming (SGP) problem with positive or negative integral degree of difficulty. Here a modified form of signomial geometric programming (MSGP) has been developed and some theorems have been derived. Finally, these are illustrated by proper examples and applications.

On the Integral Degree of Integral Ring Extensions

Let A ⊂ B be an integral ring extension of integral domains with fields of fractions K and L, respectively. The integral degree of A ⊂ B, denoted by dA(B), is defined as the supremum of the degrees of minimal integral equations of elements of B over A. It is an invariant that lies in between dK(L) and μA(B), the minimal number of generators of the A-module B. Our purpose is to study this invariant. We prove that it is sub-multiplicative and upper-semicontinuous in the following three cases: if A ⊂ B is simple; if A ⊂ B is projective and finite and K ⊂ L is a simple algebraic field extension; or if A is integrally closed. Furthermore, d is upper-semicontinuous if A is noetherian of dimension 1 and with finite integral closure. In general, however, d is neither sub-multiplicative nor upper-semicontinuous.

APPLICATION OF THE THEORY OF LATENT VARIABLES TO PERSONNEL MANAGEMENT METHODS

One of the main tasks of the human-resources (HR) department is the qualitative management of personnel, which is the basis for effective work of the organization. The paper presents models of personnel management based on the theory of latent variables. Research objective is to use the Rasch model for assessing latent variables to evaluate the competence of employees and their suitability for certain positions and also quality control of their work.Three problems of personnel management are considered.Organization of qualitative selection of candidates for vacancies by objective assessment of the degree of professional suitability of candidates with a view to selecting the best employees. Multilateral monitoring as the quality of performance of duties of each employee on the one hand, and the efficiency of the work of the whole team on the other. A dynamic comparison is made between the quality of performance of their duties in different periods of time. Effective appointments of specific employees to certain positions. Based on the criteria of the employee's suitability for certain positions, the integral degree of the employee's suitability for each vacancy is calculated. In addition, the model makes it possible to assess the degree of influence of the criteria on the evaluation of employees.The models proposed in the paper allow obtaining estimates on a linear interval scale, which can be translated into any other scale, for example, probabilistic. Estimates do not depend on a set of criteria and the set of evaluated employees.

The Analysis of the Associated Legendre Functions with Non-Integral Degree

Spherical cap harmonic (SCH) theory has been widely used to format regional model of fields that can be expressed as the gradient of a scalar potential. The functions of this method consist of trigonometric functions and associated Legendre functions with integral-order but non-integral degree. Evidently, the constructing and computing of Legendre functions are the core content of the spherical cap functions. In this paper,the approximated calculation method of the normalized association Legendre functions with non-integral degree is introduced and an analysis of the entire order of associated non-Legendre function calculation is presented. Besides, we use the Muller method to search out for all intrinsic values. The results showed that the highest order of spherical harmonic function for constructing regional model of fields is limited, thus high-resolution spherical harmonic structure of local gravity field need to be improved.

THE PONTRJAGIN–HOPF INVARIANTS FOR SOBOLEV MAPS

Subtle issues arise when extending homotopy invariants to spaces of functions having little regularity, e.g., Sobolev spaces containing discontinuous functions. Sometimes it is not possible to extend the invariant at all, and sometimes, even when the formulas defining the invariants make sense, they may not have expected properties (e.g., there are maps having non-integral degree).In this paper, we define a complete set of homotopy invariants for maps from three-manifolds to the two-sphere and show that these invariants extend to finite Faddeev energy maps and maps in suitable Sobolev spaces. For smooth maps, our description is proved to be equivalent to Pontrjagin's original homotopy classification from the 1930's. We further show that for the finite energy maps the invariants take on exactly the same values as for smooth maps. We include applications to the Faddeev model.The techniques that we use would also apply to many more problems and/or other functionals. We have tried to make the paper accessible to analysts, geometers and mathematical physicists.