Higher Dimensions in the Theory of Heredity

2021 ◽  
pp. 84-110
Keyword(s):  
Mathematical Model ◽  
Nucleic Acid ◽  
Hydrogen Bonds ◽  
Plant Development ◽  
Equilibrium Position ◽  
Higher Dimensions ◽  
Multidimensional Space ◽  
Nitrogen Bases ◽  
Wide Range ◽  
The Mathematical Model

On the basis Mendel's experiments, a mathematical model is constructed that describes the results of these experiments in a wide range of parameters. There is shown that in the mathematical model of Mendel's experiments, based on real patterns of plant development, there are equilibrium positions between the dominant and recessive forms. This equilibrium position is stable and located in the multidimensional space of system phenotypes. This newly discovered behavior of the dominant and recessive forms in the vicinity of the equilibrium position (true) differs significantly from the logistic equilibrium position in the Hardy-Weinberg principle, built without taking into account the real patterns in the plant population. The geometry of the neighborhood of the compound of two nucleic acid helices with nitrogen bases was investigated. It is proved that this neighborhood is a cross-polytope of dimension 13 (polytope of hereditary information), in the coordinate planes of which there are complementary hydrogen bonds of nitrogenous bases.

Equilibrium in the Population of the Plants

2019 ◽  
pp. 1-18
Keyword(s):  
Mathematical Model ◽  
Plant Development ◽  
Equilibrium Position ◽  
Logistic Model ◽  
Plant Population ◽  
The Real ◽  
Model Based ◽  
Wide Range ◽  
Living Organisms ◽  
The Mathematical Model

On the basis Mendel's experiments, a mathematical model is constructed that describes the results of these experiments in a wide range of parameters. This model is compared with the Hardy-Weinberg logistic model based only on probabilistic ideas about the presence of dominant and recessive alleles in the chromosomes of living organisms. There is shown that in the mathematical model of Mendel's experiments, based on real patterns of plant development, there are equilibrium positions between the dominant and recessive forms. It consists in the fact that with an increase in the number of generations all dominant and recessive phenotypes of organisms, with any number of sings, quickly equalize and then synchronously (in the absence of death of organisms) increase together, seeking asymptotically to a stable isolated equilibrium position of the type of a multidimensional node. This newly discovered behavior of the dominant and recessive forms in the vicinity of the equilibrium position (true) differs significantly from the logistic equilibrium position in the Hardy-Weinberg principle, built without taking into account the real patterns in the plant population.

Robust sideslip angle observer of commercial vehicles based on cornering stiffness estimation using neural network

2022 ◽  
pp. 095440702110724
Author(s):  
Chenyu Zhou ◽  
Liangyao Yu ◽  
Yong Li ◽  
Jian Song
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Stability Control ◽  
Estimation Accuracy ◽  
Accurate Estimation ◽  
Commercial Vehicles ◽  
Sideslip Angle ◽  
The Neural Network ◽  
Wide Range ◽  
The Mathematical Model

Accurate estimation of sideslip angle is essential for vehicle stability control. For commercial vehicles, the estimation of sideslip angle is challenging due to severe load transfer and tire nonlinearity. This paper presents a robust sideslip angle observer of commercial vehicles based on identification of tire cornering stiffness. Since tire cornering stiffness of commercial vehicles is greatly affected by tire force and road adhesion coefficient, it cannot be treated as a constant. To estimate the cornering stiffness in real time, the neural network model constructed by Levenberg-Marquardt backpropagation (LMBP) algorithm is employed. LMBP is a fast convergent supervised learning algorithm, which combines the steepest descent method and gauss-newton method, and is widely used in system parameter estimation. LMBP does not rely on the mathematical model of the actual system when building the neural network. Therefore, when the mathematical model is difficult to establish, LMBP can play a very good role. Considering the complexity of tire modeling, this study adopted LMBP algorithm to estimate tire cornering stiffness, which have simplified the tire model and improved the estimation accuracy. Combined with neural network, A time-varying Kalman filter (TVKF) is designed to observe the sideslip angle of commercial vehicles. To validate the feasibility of the proposed estimation algorithm, multiple driving maneuvers under different road surface friction have been carried out. The test results show that the proposed method has better accuracy than the existing algorithm, and it’s robust over a wide range of driving conditions.

scholarly journals THE MATHEMATICAL MODEL FOR ESTIMATING THE PROBABILITY OF RISK OF INCOMPETENT SPECIALIST GRADUATION

2020 ◽  
Author(s):  
Ganna Khimicheva ◽  
◽  
Antonina Volivach ◽  
Keyword(s):  
Mathematical Model ◽  
Educational Program ◽  
Pairwise Comparison ◽  
Educational Programs ◽  
Educational Process ◽  
Program Quality ◽  
Statistical Characteristics ◽  
Multidimensional Space ◽  
Standards And Guidelines ◽  
The Mathematical Model

The article presents the results of research for the mathematical model for estimating the probability of risk of incompetent specialist graduation. The mechanisms and tools to determine the probability of risk of incompetent specialist graduation have been developed in the course of the research. The goal tree method has been used as a mechanism to determine the relationship between the structural components of the educational process and the educational program. Using this method, the structuring of 9 criteria by which the educational program quality is evaluated has been carried out. That is, its strengths and weaknesses have been identified. In turn, as a tool for estimating the probability of an educational process (educational program) risks and the graduation of an incompetent specialist, it has been proposed to use a regression mathematical model. To build a mathematical model, an active experiment, a qualimetric approach, a method of regression analysis, and 16 conditional educational programs that met the "Standards and Guidelines for Quality Assurance in the European Higher Education Area" (ESG) have been used. The construction of the model has been carried out according to a specially designed scheme, which included 5 stages. In the first stage, a group of experts was formed and their consistency was determined with the help of the "HEI Experts" software. In the second stage, six groups of indicators were identified, which further estimated the educational process (educational program) quality. For this purpose, the experts used the method of pairwise comparison to select 9 unit indicators, which further estimated the levels of compliance of 16 conditional educational programs. The estimation was conducted according to standardized quality indicators that are inherent in the real educational process (educational program). In the third stage, a robust plan of the experiment was constructed using the method of pseudo-random LP-τ numbers uniformly distributed in multidimensional space. According to the plan, a working matrix of the experiment was formed. Then, the group of experts formed in the first stage carried out the percentage estimation of the probability of risk of incompetent specialist graduation. In the fourth stage, a mathematical model was built using the PRIAM (planning, regression, and model analysis) software. This model allows us to assess nine factors that affect the probability of risk of incompetent specialist graduation. In the fifth stage, the statistical characteristics of the model were tested. According to the test results, it was proved that the model is informative, adequate, and stable, both in terms of structure and calculations. At the same stage, the marginal surfaces were constructed and the forces of influence of regressors (indicators) on the probability of risk of competent/incompetent specialist graduation were determined. According to the results of research, it has been proved that such indicators as compliance of the applicants (bachelors) level with the second Master's level and the level of considering labor market employers (stakeholders) requirements have the strongest impact on the competence of the future specialists. The proposed model allows us to estimate the factors influencing the efficiency (effectiveness) of the educational process and to determine the probability of the risk of competent/incompetent specialist graduation.

scholarly journals Kinetics of filtration consolidation of water-saturated clay soils

2020 ◽  
pp. 86-95 ◽  
Author(s):  
O. V. Ageikina ◽  
V. V. Vorontsov ◽  
R. R. Sufyanov
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Saturated Porous Medium ◽  
Experimental Studies ◽  
Saturated Soils ◽  
Consolidation Process ◽  
Filtration Consolidation ◽  
Wide Range ◽  
Water Saturated ◽  
The Mathematical Model

The relevance of the research processes filtration consolidation due to the place of water-saturated soils in various design solutions related to the exploration, production and transportation of hydrocarbons. It should be noted that the diversity of soils led to the emergence of a wide range of mathematical models, obtained on the basis of generalization of experimental data and various assumptions to simplify engineering calculations. The article presents the results of theoretical and experimental studies of the mathematical model of the consolidation process of a water-saturated porous medium. This model is based on simplifying assumptions that are different from those adopted in well-known solutions. A fundamental approach to the formation of the model was developed on the basis of the kinetic representations of chemical reactions used in solving the environmental problems of epoxidation reactions of olefins. We determined the parameters of the mathematical model of the consolidation process of the saturated porous medium of clayey soil and confirmed its adequacy by the research results. In addition, we established the parameters of the field of non-equilibrium filtration, reducing the nonexistent ability of water-saturated soils.

scholarly journals The Polytope of Hereditary Information the Structure, Location, Signification

2019 ◽  
pp. 56-62 ◽  
Author(s):  
Gennadiy Vladimirovich Zhizhin
Keyword(s):  
Nucleic Acid ◽  
Hydrogen Bonds ◽  
High Intensity ◽  
Information Exchange ◽  
Nitrogen Bases ◽  
Higher Dimensional ◽  
Low Dimensional

The geometry of the neighborhood of the compound of two nucleic acid helices with nitrogen bases was investigated. It is proved that this neighborhood is a cross-polytope of dimension 13 (polytope of hereditary information), in the coordinate planes of which there are complementary hydrogen bonds of nitrogenous bases. The structure of this polytope is defined, its image is given. The total incident flows from the low-dimensional elements to the higher-dimensional elements and vice versa of the hereditary information polytope are calculated equal to each other. High values of these flows indicate a high intensity of information exchange in the polytope of hereditary information that ensures the transfer of this information

The Structure of the Polytope of Hereditary Information

2019 ◽  
Vol 8 (2) ◽  
pp. 7-22
Author(s):  
Gennadiy Vladimirovich Zhizhin
Keyword(s):  
Nucleic Acid ◽  
Hydrogen Bonds ◽  
Phosphoric Acid ◽  
High Intensity ◽  
Information Exchange ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Nitrogen Bases ◽  
Higher Dimensional ◽  
Low Dimensional

The representations of the sugar molecule and the residue of phosphoric acid in the form of polytopes of higher dimension are used. Based on these ideas and their simplified three-dimensional images, a three-dimensional image of nucleic acids is constructed. The geometry of the neighborhood of the compound of two nucleic acid helices with nitrogen bases has been investigated in detail. It is proved that this neighborhood is a cross-polytope of dimension 13 (polytope of hereditary information), in the coordinate planes of which there are complementary hydrogen bonds of nitrogenous bases. The structure of this polytope is defined, and its image is given. The total incident flows from the low-dimensional elements to the higher-dimensional elements and vice versa of the hereditary information polytope are calculated equal to each other. High values of these flows indicate a high intensity of information exchange in the polytope of hereditary information that ensures the transfer of this information.

Design and Modeling of an Experimental ROV with Six Degrees of Freedom

Drones ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 113
Author(s):  
Aleksey Kabanov ◽  
Vadim Kramar ◽  
Igor Ermakov
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Experimental Tests ◽  
Underwater Vehicles ◽  
Six Degrees Of Freedom ◽  
Functional Capabilities ◽  
Classical Design ◽  
Wide Range ◽  
Reduced Costs ◽  
The Mathematical Model

With the development of underwater technology, it is important to develop a wide range of autonomous and remotely operated underwater vehicles for various tasks. Depending on the problem that needs to be solved, vehicles will have different designs and dimensions, while the issues surrounding reduced costs and increasing the functionality of vehicles are relevant. This article discusses the development of inspection class experimental remotely operated vehicles (ROVs) for performing coastal underwater inspection operations, with a smaller number of thrusters, but having the same functional capabilities in terms of controllability (as vehicles with traditionally-shaped layouts). The proposed design provides controllability of the vehicle in six degrees of freedom, using six thrusters. In classical design vehicles, such controllability is usually achieved using eight thrusters. The proposed design of the ROV is described; the mathematical model, the results of modeling, and experimental tests of the developed ROVs are shown.

Mathematical modeling of articulated passenger train spatial vibrations

2021 ◽  
Vol 2021 (2) ◽  
pp. 91-99
Author(s):  
O. Markova ◽  
◽  
H. Kovtun ◽  
V. Maliy ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Ride Quality ◽  
Railway Transport ◽  
Passenger Train ◽  
Wide Range ◽  
Random Track Irregularities ◽  
The Mathematical Model

The problem of high-speed railway transport development is important for Ukraine. In many countries articulated trains are used for this purpose. As the connections between cars in such a train differ from each other, to investigate its dynamic characteristics not a separate car, but a full train vibrations model is necessary. The article is devoted to the development of the mathematical model for articulated passenger train spatial vibrations. The considered train consists of 7 cars: one motor-car, one transitional car, three articulated cars, one more transitional car and again one motor-car. Differential equations of the train motion along the track of arbitrary shape are set in the form of Lagrange’s equations of the second kind. All the necessary design features of the vehicles are taken into account. Articulated cars have common bogies with adjoining cars and a transfer car and the cars are united by the hinge. The operation of the central hinge between two cars is modeled using springs and dampers acting in the horizontal and vertical directions. Four dampers between two adjacent car-bodies act as dampers for pitching and hunting and are represented in the model by viscous damping. The system of 257 differential equations of the second order is set, which describes the articulated train motion along straight, curved, and transitional track segments with taking into account random track irregularities. On the basis of the obtained mathematical model the algorithm and computational software has been developed to simulate a wide range of cases including all possible combinations of parameters for the train elements and track technical state. The study of the train self-exited vibrations has shown the stable motion in all the range of the considered speeds (40 km/h – 180 km/h). The results obtained at the train motion along the track maintained for the speedy motion have shown that all the dynamic characteristics and ride quality index insure train safe motion and comfortable conditions for the travelling passengers.

Residual Stresses due to High Temperature Annealing. Mathematical Model and Calculations

2006 ◽  
Vol 524-525 ◽  
pp. 355-360
Author(s):  
O.R. Hachkevych ◽  
V.S. Mykhailyshyn ◽  
A. Ravska-Skotnichna
Keyword(s):  
Mathematical Model ◽  
High Temperature ◽  
Residual Stresses ◽  
Thermal Sensitivity ◽  
High Temperature Annealing ◽  
The Finite Element Method ◽  
Initial Temperature Distribution ◽  
Wide Range ◽  
Thermomechanical Processes ◽  
The Mathematical Model

The mathematical model is developed for description of thermomechanical processes at cooling during high temperature annealing with the known initial temperature distribution (the temperature of holding) and stresses (acquired stresses at the final of a holding). It is taken into account the thermal sensitivity and material hardening at elasto-plastic solid deforming. The methodology based on the finite element method is proposed for solving thermomechanics problems of wide range. The suitable software is developed. At the final stage of annealing a cylindrical solid it is investigated residual stresses being formed on the cooling stage.

A Model for Determining the Asperity Engagement Height in Relation to Web Traction Over Non-Vented Rollers

2002 ◽  
Vol 124 (3) ◽  
pp. 584-594 ◽  
Author(s):  
Brian S. Rice ◽  
Kevin A. Cole ◽  
Sinan Mu¨ftu¨
Keyword(s):  
Mathematical Model ◽  
Optimization Technique ◽  
Peak Height ◽  
Height Distribution ◽  
Gaussian Peak ◽  
Wide Range ◽  
Non Gaussian ◽  
Wide Speed Range ◽  
Air Film ◽  
The Mathematical Model

The traction developed between a thin flexible web, wrapped around a non-vented, rotating cylindrical roller is studied experimentally and theoretically. A series of eight webs representing a wide range of surface roughness characteristics are traction-tested against the same roller over a wide speed range. A mathematical model that couples air film pressure, web deflection, and asperity deformations is used to model the web/roller interface. An optimization technique is used to estimate the asperity compliance function parameters based on the experimental results and the mathematical model. A new model for determining the asperity engagement height, for surfaces with non-Gaussian peak height distribution, is proposed when the roughness of both surfaces is taken into account. Results are presented that indicate the viability and utility of the new methods.

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