scholarly journals New and simple mathematical description of epidemics including consecutive waves

2021 ◽  
Author(s):  
Pavel Petkov
Keyword(s):  
Mathematical Description

Study on the Modes of Operation of a Multi-Machine Installations with Mechanical Reduction

2019 ◽  
pp. 12-22
Author(s):  
A. M. Oleynikov ◽  
L. N. Kanov
Keyword(s):  
Mathematical Description ◽  
Reactive Power ◽  
Maximum Efficiency ◽  
Wind Flow ◽  
System Of Equations ◽  
Mechanical Equilibrium ◽  
Synchronous Generators ◽  
Electromagnetic Excitation ◽  
Number Of Generators ◽  
Wide Range

The paper gives the description of the original wind electrical installation with mechanical reduction in which the output of vertical axis wind turbine with rather low rotation speed over multiplicator is distributed to a certain number of generators. The number of acting generators is determined by the output of actual operating wind stream at each moment. According to this constructive scheme, it is possible to provide effective and with maximum efficiency installation work in a wide range of wind speeds and under any schedule issued to the consumer of electricity. As there are no any experience in using such complexes, mathematical description of its main elements is given, namely windwheels, generators with electromagnetic excitation of magnetic electrical type, then their interaction with windwheel, and also the results of mathematical modeling of work system regimes under using the offered system of equations. The basis for the mathematical description of the main elements of the installation – synchronous generators – are the system of equations of electrical and mechanical equilibrium in relative units in rotating coordinates without considering saturation of the magnetic circuit. The equation of mechanical equilibrium systems includes torque and brake windwheel electromagnetic moments of generators with taking into account the reduction coefficients and friction. In addition, we specify the alternator rotor dynamics resulting from continuous torque of windwheel fluctuations under the influence of unsteady wind flow and wind speed serving as the original variable is modeled by a set of sinusoids. Model simplification is achieved by equivalization of similar generators and by disregarding these transitions with a small time constant. Calculation the installation with synchronous generators of two types of small and medium capacity taking into account the operational factors allowed us to demonstrate the logic of interactions in the main elements of the reported complex in the process of converting wind flow into the generated active and reactive power. We have shown the possibility of stable system work under changeable wind stream condition by regulating of the plant blade angle and with simultaneous varying of generator number of different types. All these are in great interest for project organizations and power producers.

Classification and Methods for Mathematical Description of Bank Risks

2009 ◽  
Vol 41 (2) ◽  
pp. 38-52
Author(s):  
Petr I. Bidyuk ◽  
Andrey .B. Basarab ◽  
Aidyn Sardar ogly Gasanov
Keyword(s):  
Mathematical Description ◽  
Bank Risks

Mathematical Description of the Influence of the Bunker Outlet on the Grain Motion in the Microwave Convective Area

2020 ◽  
pp. 73-80
Author(s):  
Aleksey N. Vasil’yev ◽  
Andrey A. Tsymbal ◽  
Aleksey A. Vasil’yev
Keyword(s):  
Mathematical Description ◽  
Microwave Field ◽  
Convective Zone ◽  
Research Purpose ◽  
Field Zone ◽  
Flow Process ◽  
Grain Processing ◽  
Grain Flow ◽  
The Right ◽  
Processing Zone

One of the environmentaly friendly methods of drying and decontamination of grain is its processing in microwave-convective installations. The efficiency of using the microwave field depends on the uniformity of its distribution in the grain processing zone. This is provided by the design features of the microwave core and waveguides. The uniformity of grain movement in the microwave field zone is important. It is important that the grain is moved in the microwave convective zone by hydraulic movement. In this case, the grain passes through zones with different intensity of the microwave field sequentially and the grain processing is uniform. (Research purpose) The research purpose is in making a mathematical dependence of parameters of the hopper outlet on the movement of grain in the microwave convective zone. (Materials and methods) The article presents the parameters of the outlet that ensure the grain flow without forming static arches in accordance with the method of calculating outlet bins. Fluctuations in humidity for different crops of processed grain will not lead to a violation of the grain flow process. The resulting equation for changing the height of the dynamic arch, depending on its location in the height of the hopper, allows to determine the uneven flow of grain from the hopper outlet. (Results and discussion) When unloading grain, there is an uneven flow in the right and left halves of the hopper, relative to the central axis. When only one hopper is unloaded, 0.84 kilograms more wheat is unloaded from its left half than from the right. This difference leads to uneven and reduced efficiency of grain processing in the microwave-convective zone. (Conclusions) To ensure the uniformity of grain processing in the microwave convective zone, it is necessary to improve the mechanism of grain flow from the outlet of the hopper.

Stress and Deformation

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Differential Equations ◽  
Mathematical Description ◽  
Finite Strain ◽  
Stress Strain ◽  
Complex Problems ◽  
Vector Algebra ◽  
Stress And Deformation

Students of geology who may have only a modest background in mathematics need to become familiar with the theories of stress, strain, and other tensor quantities, so that they can follow, and apply to their own research, developments in modern, quantitative geology. This book, based on a course taught by the author at UCLA, can provide the proper introduction. Included throughout the eight chapters are 136 complex problems, advancing from vector algebra in standard and subscript notations, to the mathematical description of finite strain and its compounding and decomposition. Fully worked solutions to the problems make up the largest part of the book. With their help, students can monitor their progress, and geologists will be able to utilize subscript and matrix notations and formulate and solve tensor problems on their own. The book can be successfully used by anyone with some training in calculus and the rudiments of differential equations.

scholarly journals A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions

2021 ◽  
Vol 7 (3) ◽  
pp. 41
Author(s):  
Emre Baspinar ◽  
Luca Calatroni ◽  
Valentina Franceschi ◽  
Dario Prandi
Keyword(s):  
Heat Kernel ◽  
Mathematical Description ◽  
Gradient Descent ◽  
Numerical Results ◽  
Visual Illusions ◽  
Efficient Computation ◽  
Functional Architecture ◽  
Descent Algorithms ◽  
Interaction Term

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches, embedding the sub-Riemannian heat kernel into the neuronal interaction term, in agreement with the intrinsically anisotropic functional architecture of V1 based on both local and lateral connections. For the numerical realisation of both models, we consider standard gradient descent algorithms combined with Fourier-based approaches for the efficient computation of the sub-Laplacian evolution. Our numerical results show that the use of the sub-Riemannian kernel allows us to reproduce numerically visual misperceptions and inpainting-type biases in a stronger way in comparison with the previous approaches.

Mathematical description of the isobaric vaporizing crystallization of sucrose

2021 ◽  
pp. 110614
Author(s):  
V.I. Tuzhilkin ◽  
M.G. Balykhin ◽  
S.M. Petrov ◽  
N.M. Podgornova ◽  
N.D. Lukin ◽  
...  
Keyword(s):  
Mathematical Description

scholarly journals Mathematical description of water flow quantity for microhydroelectric station

2020 ◽  
Vol 614 ◽  
pp. 012032
Author(s):  
D Kodirov ◽  
O Tursunov ◽  
S Khushiev ◽  
O Bozarov ◽  
G Tashkhodjaeva ◽  
...  
Keyword(s):  
Water Flow ◽  
Mathematical Description ◽  
Flow Quantity
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