An extremal value of a function is the value of the function at one of its extremum points. Each extremum point of a differentiable function of several variables is described by the system of ...equations expressing the vanishing of all partial derivatives. However, in the general case, one cannot obtain equations for extremal values of the function. The case of polynomials significantly differs from the general case, and in this paper we obtain an equation for extremal values of a given polynomial in several variables.
α-Subharmonic Functions Abdullaev, B. I.; Imomkulov, S. A.; Sharipov, R. A.
Journal of mathematical sciences (New York, N.Y.),
2024/1, Volume:
278, Issue:
3
Journal Article
Peer reviewed
In this paper, we study the class of
α
-subharmonic functions. A number of important properties of
α
-subharmonic functions are proved, and an equivalent, more convenient definition of
α
...-subharmonicity is given. The geometric structure of removable singularities for some classes of
α
-subharmonic functions is also described.
A perfect cuboid is a rectangular parallelepiped in which the lengths of all edges, the lengths of all face diagonals, and also the lengths of spatial diagonals are integers. No such cuboid has yet ...been found, but their nonexistence has also not been proved. The problem of a perfect cuboid is among unsolved mathematical problems. The problem has a natural
S
3
-symmetry connected to permutations of edges of the cuboid and the corresponding permutations of face diagonals. In this paper, we give a survey of author’s results and results of J. R. Ramsden on using the
S
3
symmetry for the reduction and analysis of the Diophantine equations for a perfect cuboid.
Abstract
Micro-water energy is a promising alternative energy source that produces electricity in remote areas, separated from the main electricity grid. In this research work, the method of ...increasing the efficiency of gravity-vortex micro-hydroelectric power station operating in low-pressure water flows through the twist angle of the inlet channel of the basin is presented. Gravity-vortex micro-hydroelectric power station is a new modern green technology as an alternative or renewable energy source. The advantage of this method of electricity production is that it is possible to produce electricity at a low pressure, i.e. starting from a pressure of 0.7 meters. In order to increase the initial speed of the water entering the cylindrical basin, the flow fields of the water flow inside the basin in the range of 0-90 degrees of the inlet channel twist angle were numerically simulated using the ANSYS Fluent software. As a result of the study, the parameters of the influence of the flow velocity vector on the flow field were studied.
The paper presents the history of the development of automatic milking systems and their classification. The objects of study were automatic milking systems that are used in world practice. The ...analysis of automatic milking systems showed that they have technological and design differences. Technological and design features of automatic milking systems such as "Astronaut A4", "VMS", "M2erlin", "MR-S2", "MR-D2", "RDS FutureLine", "Galaxy Starline" and "Mlone" were considered in working out of this classification. The studies have shown that the existing automatic milking systems differ in the number of milking boxes and their location, type of robot arm, drive control of robot arm, robot arm location, decision of cleaning the teats and stimulating milk flow, decision of entry and exit of cows from the milking boxes.
The discovery of the CRISPR/Cas9 gene scissors technology was a breakthrough in the development of gene therapy methods and attracted the attention of the entire scientific community. This technology ...provides prospects for the treatment of many neurodegenerative diseases and cancers that were previously considered almost incurable. To date, the mechanisms of the development and progression of these groups of nosologies are becoming increasingly studied due to discoveries in the field of molecular biology and genetics. However, the application of the CRISPR/Cas9 technology has some limitations and difficulties that should be considered. The development of works on the creation and selection of specific gene carriers, a thorough safety assessment of modern genetic manipulations, and the integrated participation of specialists from different fields of science will be important to solve the problems associated with the use of the CRISPR/Cas9 technology and achieve the desired therapeutic effect.
It was found that the addition of C
60
and C
70
fullerenes to Tb
2
(SO
4
)
3
·8H
2
O crystals led to a decrease in the photo- and triboluminescence intensities of the Tb
3+
ion, without affecting the ...positions of its luminescence maxima. An increase in the intensity of the emission band ascribed to fullerene at 630-850 nm, relative to that without terbium sulphate, was also observed in the photoluminescence spectra. The phosphor luminescence was quenched in a mechanical mixture with the quenchers and luminescence sensitization of the quenchers occurred, indicating that quenching took place in the solid phase by a mechanism similar to that observed in solution; this is due to radiationless energy transfer from the excited Tb
3+
ion to the C
60
and C
70
molecules. The excitation energy is probably transferred through the contacting crystal surfaces of the phosphor and quencher.
It was found that the addition of C
60
and C
70
fullerenes to Tb
2
(SO
4
)
3
·8H
2
O crystals led to a decrease in the photo- and triboluminescence intensities of the Tb
3+
ion, without affecting the positions of its luminescence maxima.
In the framework of the proposed theoretical model crossover and scaling equations of state for near-critical multicomponent hydrocarbon mixture were obtained. To elaborate the equations of state the ...experimental data measured on the serial setup intended for comprehensive pressure-volume-temperature (PVT) research of a natural gas-condensate systems were used. The information concerning the mixture composition was not involved. The obtained equations describe the experimental data with the accuracy not exceeding the measurement inaccuracy. It has been shown that in extended range of thermodynamic parameters the crossover equation of state looks more reliable. The crossover model describes the transition from the scaling behavior to the mean-field behavior, which is typical for cubic and multiparameter equations of state. The model was extended for calculation of the volume fractions of gas and liquid phases needed for practical applications. In addition, the expression for isothermal compressibility has been derived. It was demonstrated that the isothermal compressibility has a cusp-like anomaly in the close vicinity of the critical point.
Display omitted
•Scaling and crossover EOS for near-critical ternary hydrocarbon mixture are elaborated on the basis of measured isotherms.•The information concerning the mixture composition was not used.•The lines with constant ratio of gas and liquid volume fractions are obtained.•The isothermal compressibility for a multicomponent mixture in one- and two-phase region is derived.
Introduction.
Surgical intervention is recognized as an integral part of pulmonary tuberculosis treatment. Optimal routing of pulmonary tuberculosis patients to surgical treatment essentially ...improves the effectiveness of tuberculosis treatment. The paper is aimed at analyzing the routing of pulmonary tuberculosis patients to surgical treatment in the Republic of Bashkortostan.
Materials and methods.
The paper presents the structure of Republican Clinical Tuberculosis Dispensary, describes the routing of patients followed by the TB Service of the Republic of Bashkortostan, indicates a significant role of telehealth technologies in providing specialized medical care for patients with pulmonary tuberculosis. In addition, the paper introduces the quantitative data and structure of surgical interventions performed in the TB Surgery Unit of the Republican Clinical Tuberculosis Dispensary.
Results and discussion.
According to the conducted analysis, the TB Service of the Republic of Bashkortostan complies with the regulatory documents of the Russian Federation, thus ensuring the most complete coverage of pulmonary tuberculosis patients in need of thoracic surgery.
Conclusion.
Timely routing of patients to a TB surgery unit enables effective treatment, differential diagnosis, and abacillation of patients to be provided, thereby reducing the spread of tuberculosis in the region.
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