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Journal articles on the topic 'Mathematical induction'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

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1

Klotz, Frederick S. "Turtle Graphics and Mathematical Induction." Mathematics Teacher 80, no. 8 (November 1987): 636–54. http://dx.doi.org/10.5951/mt.80.8.0636.

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Although induction is widely used in mathematics, it is a difficult concept to explain in the classroom. For students who have had little experience with inductive thinking, inductive proofs can appear somewhat arbitrary and unconvincing.

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2

BOUHOULA, ADEL, EMMANUEL KOUNALIS, and MICHAËL RUSINOWITCH. "Automated Mathematical Induction." Journal of Logic and Computation 5, no. 5 (1995): 631–68. http://dx.doi.org/10.1093/logcom/5.5.631.

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3

Baker, A. "Mathematical induction and explanation." Analysis 70, no. 4 (August 30, 2010): 681–89. http://dx.doi.org/10.1093/analys/anq074.

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4

Dubeau, Francois. "Cauchy and mathematical induction." International Journal of Mathematical Education in Science and Technology 22, no. 6 (November 1991): 965–69. http://dx.doi.org/10.1080/0020739910220614.

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5

LI, JIANXIN, and ARUN LAKHOTIA. "USING MATHEMATICAL INDUCTION IN SYSTEMATIC PROGRAM DEVELOPMENT." International Journal of Software Engineering and Knowledge Engineering 04, no. 04 (December 1994): 561–74. http://dx.doi.org/10.1142/s0218194094000271.

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This paper makes a contribution to the calculational paradigm of program development, a paradigm in which programs are calculated from their specifications by applying meaning preserving transformations. It introduces program induction, a technique analogous to mathematical induction, and iteration folding, a refinement rule. Using program induction, a specification is decomposed into a base case and an inductive case and their solutions are sequentially composed to derive the final program. The iteration folding rule is applied to transform potentially infinite nested if statements into a while statement. Our technique and rule augment the existing repertoire of techniques and rules in the calculus of program refinement.

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6

Barglik, Jerzy. "Mathematical modeling of induction surface hardening." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 35, no. 4 (July 4, 2016): 1403–17. http://dx.doi.org/10.1108/compel-09-2015-0323.

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Purpose – As far as the author knows the modeling of induction surface hardening is still a challenge. The purpose of this paper is to present both mathematical models of continuous and simultaneous hardening processes and exemplary results of computations and measurements. The upper critical temperature Ac3 is determined from the Time Temperature Austenization diagram for investigated steel. Design/methodology/approach – Computation of coupled electromagnetic, thermal and hardness fields is based on the finite element methods, while the hardness distribution is determined by means of experimental dependence derived from the continuous cooling temperature diagram for investigated steel. Findings – The presented results may be used as a theoretical background for design of inductor-sprayer systems in continual and simultaneous arrangements and a proper selection of their electromagnetic and thermal parameters. Research limitations/implications – The both models reached a quite good accuracy validated by the experiments. Next work in the field should be aimed at further improvement of numerical models in order to shorten the computation time. Practical implications – The results may be used for designing induction hardening systems and proper selection of field current and cooling parameters. Originality/value – Complete mathematical and numerical models for continuous and simultaneous surface induction hardening including dual frequency induction heating of gear wheels. Experimental validation of achieved results. Taking into account dependence of the upper critical temperature Ac3 on speed of heating.

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7

Martin ‎, Andreas. "Mathematical-Physical Approach to Prove that the Navier-‎Stokes Equations Provide a Correct Description of Fluid ‎Dynamics." Hyperscience International Journals 2, no. 3 (September 2022): 97–102. http://dx.doi.org/10.55672/hij2022pp97-102.

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This publication takes a mathematical approach to a general solution to the Navier-Stokes equations. The basic idea is a ‎mathematical analysis of the unipolar induction according to Faraday with the help of the vector analysis. The vector analysis ‎enables the unipolar induction and the Navier-Stokes equations to be related physically and mathematically since both ‎formulations are mathematically equivalent. Since the unipolar induction has proven itself in practice, it can be used as a ‎reference for describing the Navier-Stokes equations‎.

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8

Dogan, Hamide. "Mathematical induction: deductive logic perspective." European Journal of Science and Mathematics Education 4, no. 3 (July 15, 2016): 315–30. http://dx.doi.org/10.30935/scimath/9473.

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9

Urso, Pascal, and Emmanuel Kounalis. "Sound generalizations in mathematical induction." Theoretical Computer Science 323, no. 1-3 (September 2004): 443–71. http://dx.doi.org/10.1016/j.tcs.2004.05.022.

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10

Beeson, Michael. "Mathematical Induction in Otter-Lambda." Journal of Automated Reasoning 36, no. 4 (October 7, 2006): 311–44. http://dx.doi.org/10.1007/s10817-006-9036-z.

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11

Lutfullin, M. "THE PROBLEM OF CORRELATION OF INDUCTION AND DEDUCTION IN THE HISTORY OF MATHEMATICS AND MATHEMATICAL EDUCATION." Pedagogical Sciences, no. 72 (August 16, 2019): 103–8. http://dx.doi.org/10.33989/2524-2474.2018.72.176129.

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The analysis of the scientists’ views on the role of induction and deduction in the development of mathematics is carried out. There are no substantial difference in the estimation of the importance of deductive substantiation of mathematical concepts, theorems and theories in these views. But we had to establish the big differences and even absolutely opposite views on the role of induction in the process of generation, extension and integration of mathematical knowledge. The most conclusive are the opinions of the thing that an induction is a match for a deduction (L. Euler, F. Klein, G. Polya and others). The importance of inductive method of research in the scientific development, especially in mathematics, was even greater emphasized by L. de Broglie. Absolutely opposite are the views of those scientists who consider the mathematics to be an absolutely deductive science (T. Huxley, J. Murray, B. Pierce and others). The most categorical point of such view was expressed by J. Murray.In the mathematical education the false opinion of the thing that this science is supposedly to be absolutely deductive inevitably lead to pedagogical mistakes. The threat of these mistakes concerns mainly the geometrical training. The deductive character of statement of proving the geometrical theorems in the manuals and at the lessons leads to the pupils’ material difficulties in the process of digestion of knowledge. Inductive method of education may lighten the process of digestion of geometry. Not of less importance this method is at the lessons of algebra.If the importance of role of the deduction in the mathematical development is old-confirmed by the perfection of deductive proofs of Euclid, the consciousness of the importance of induction in the mathematical researches is set just in the first quarter of the XVII century with the publication of “Novum Organum” by Francis Bacon. The first thinker who consciously combined deduction with induction in his researches was R. Descartes. Indissoluble correlation of induction and deduction is brilliantly shown in many researches of L. Euler.In the second half of the XVIII century the induction comes to gaining practical application in the mathematical education. For the first time the inductive method was realized in the “Universal arithmetic” manual the author of which was an outstanding educator N. G. Kurganov. This manual was notable for the simplicity of teaching materialexposition.The increasing of attention to the mathematical education by inductive method is founded in the manuals, methodical works and educational activity of F. I. Busse, P. S. Hurjev, O. M. Strannoliubskiy,S. I. Shohor-Trotskiy. The valuable contribution to this problem development is issued to K. F. Lebedintsev, the author of specific inductive method of mathematical education. In the second half of the XX century the many lines of the application of induction in the secondary and higher mathematical education became a subject of long-term fundamental investigation by G. Polya.Hence, it is established that the requisite condition of the improving of mathematical education is following the principle of indissoluble correlation of induction and deduction in the educational process. This principle claims active energies of the manuals authors and teachers of mathematics at general secondary schools and higher educational establishments which provide practical realization of the unique methodical heritage of K. F. Lebedintsev and G. Polya.

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12

Li, Zhong Hua, Qian Tang, Di Yan, and Jie Wu. "Design of the Conjugate Cam Induction Hardening Mechanism and Establishment of the Motion Controlling Mathematical Model." Applied Mechanics and Materials 155-156 (February 2012): 726–30. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.726.

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The common methods of cam induction hardening are discussed at present. By analyzing the basic motion law of conjugate cam, a new induction hardening mechanism is designed. The motion controlling mathematical model is built on the basis of the kinematic relationship of the transmission of the induction hardening mechanism. Through the mathematical model calculation, we can get angular velocity of the workbench, then realize that single axis on NC machine controls the inductor to make isometric uniform motion relative to the cam surface, so that the cam hardening depth distribution is uniform.

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13

Schurz, Gerhard. "Meta-Induction and Social Epistemology: Computer Simulations of Prediction Games." Episteme 6, no. 2 (June 2009): 200–220. http://dx.doi.org/10.3366/e1742360009000641.

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ABSTRACTThe justification of induction is of central significance for cross-cultural social epistemology. Different ‘epistemological cultures’ do not only differ in their beliefs, but also in their belief-forming methods and evaluation standards. For an objective comparison of different methods and standards, one needs (meta-)induction over past successes. A notorious obstacle to the problem of justifying induction lies in the fact that the success of object-inductive prediction methods (i.e., methods applied at the level of events) can neither be shown to be universally reliable (Hume's insight) nor to be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. The meta-inductivist applies the principle of induction to all competing prediction methods that are accessible to her. By means of mathematical analysis and computer simulations of prediction games I show that there exist meta-inductive prediction strategies whose success is universally optimal among all accessible prediction strategies, modulo a small short-run loss. The proposed justification of meta-induction is mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. In the final section I draw conclusions about the significance of meta-induction for the social spread of knowledge and the cultural evolution of cognition, and I relate my results to other simulation results which utilize meta-inductive learning mechanisms.

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14

Emeira, G., Hapizah, and Scristia. "Mathematical proof analysis using mathematical induction of grade XI students." Journal of Physics: Conference Series 1480 (March 2020): 012044. http://dx.doi.org/10.1088/1742-6596/1480/1/012044.

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15

Selke, David. "From Mathematical Induction to Discrete Time." Applied Physics Research 8, no. 3 (April 26, 2016): 75. http://dx.doi.org/10.5539/apr.v8n3p75.

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Proof by induction involves a chain of implications in which the stages are well ordered. A chain of cause and effect in nature also involves a chain of implications. For this chain to “imply” or bring about its effects in a logical sense, it also has to be organized into a well ordering of stages (which are the points or quanta of time). This means that time must be quantized rather than continuous. An argument from relativity implies that space is quantized as a consequence.

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16

Dickman, Benjamin, and Erik Nauman. "Innovative Induction and Mathematical Code Switching." Journal of Humanistic Mathematics 10, no. 2 (July 2020): 258–90. http://dx.doi.org/10.5642/jhummath.202002.13.

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17

McAndrew, Alasdair. "Mathematical induction, difference equations and divisibility." International Journal of Mathematical Education in Science and Technology 40, no. 8 (December 15, 2009): 1013–25. http://dx.doi.org/10.1080/00207390903121743.

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18

Shah, Nagendra Prasad. "Theorem & Problems by Mathematical Induction." BIBECHANA 2 (February 18, 2018): 21–23. http://dx.doi.org/10.3126/bibechana.v2i0.19231.

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19

Marty, Roger H. "Natural numbers, order and mathematical induction." International Journal of Mathematical Education in Science and Technology 21, no. 4 (July 1990): 623–27. http://dx.doi.org/10.1080/0020739900210417.

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20

Blubaugh, William L. "Computer Assisted Introduction to Mathematical Induction." School Science and Mathematics 93, no. 1 (January 1993): 31–34. http://dx.doi.org/10.1111/j.1949-8594.1993.tb12188.x.

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21

Doornbos, Henk, Roland Backhouse, and Jaap van der Woude. "A calculational approach to mathematical induction." Theoretical Computer Science 179, no. 1-2 (June 1997): 103–35. http://dx.doi.org/10.1016/s0304-3975(96)00154-5.

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22

Sherry, David. "Mathematical reasoning: induction, deduction and beyond." Studies in History and Philosophy of Science Part A 37, no. 3 (September 2006): 489–504. http://dx.doi.org/10.1016/j.shpsa.2005.06.012.

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23

Cohen, Daniel H. "Conditionals, quantification, and strong mathematical induction." Journal of Philosophical Logic 20, no. 3 (August 1991): 315–26. http://dx.doi.org/10.1007/bf00250543.

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24

Mackie, Randall. "Mathematical Methods for Geo-Electromagnetic Induction." Physics of the Earth and Planetary Interiors 97, no. 1-4 (October 1996): 279–80. http://dx.doi.org/10.1016/0031-9201(95)03114-6.

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25

Xie, Danyang. "Mathematical induction applied of Leontief systems." Economics Letters 39, no. 4 (August 1992): 405–8. http://dx.doi.org/10.1016/0165-1765(92)90176-y.

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26

Allen, Lucas G. "Teaching Mathematical Induction: An Alternative Approach." Mathematics Teacher 94, no. 6 (September 2001): 500–504. http://dx.doi.org/10.5951/mt.94.6.0500.

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27

Cuoco, Albert A., and E. Paul Goldenberg. "Mathematical Induction in a Visual Context." Interactive Learning Environments 2, no. 3 (September 1992): 181–204. http://dx.doi.org/10.1080/1049482920020304.

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28

Raju, M. Naga, and M. Sandhya Rani. "Mathematical Modelling of Linear Induction Motor." International Journal of Engineering & Technology 7, no. 4.24 (November 27, 2018): 111. http://dx.doi.org/10.14419/ijet.v7i4.24.21868.

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The Linear Induction Motor is a special purpose electrical machines it produces rectilinear motion in place of rotational motion. By using D-Q axes equivalent circuit the mathematical modelling is done because to distinguish dynamic behavior of LIM, because of the time varying parameters like end effect, saturation of core, and half filled slot the dynamic modelling of LIM is difficult. For simplification hear we are using the two axes modelling because to evade inductances time varying nature it becomes complex in modelling, this also reduces number of variables in the dynamic equation. Modelling is done using MATLAB/SIMULINK. LIM can be controlled by using sliding model control, vector control, and position control.

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29

Kiaer, Lynn. "FOSTERING AN APPRECIATION OF MATHEMATICAL INDUCTION." PRIMUS 5, no. 3 (January 1995): 218–28. http://dx.doi.org/10.1080/10511979508965788.

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30

Correia, António. "Mathematical methods for geo-electromagnetic induction." Tectonophysics 244, no. 4 (April 1995): 286–87. http://dx.doi.org/10.1016/0040-1951(95)90040-3.

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31

Alfano, L. "Mathematical methods for geo-electromagnetic induction." Earth-Science Reviews 38, no. 1 (March 1995): 84–85. http://dx.doi.org/10.1016/0012-8252(95)90057-8.

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32

Livelybrooks, D. "Mathematical methods for geo-electromagnetic induction." Journal of Atmospheric and Terrestrial Physics 57, no. 10 (August 1995): 1186–87. http://dx.doi.org/10.1016/0021-9169(95)90101-9.

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33

Walidah, Natasya Ziana, and Elly Susanti. "Senior high school students’ argumentation in proving mathematical induction based on mathematical abilities." International Journal on Teaching and Learning Mathematics 4, no. 1 (June 23, 2021): 36–44. http://dx.doi.org/10.18860/ijtlm.v4i1.14315.

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Argumentation and proof are two interrelated elements in mathematics, which is one of the important goals in mathematics education. Furthermore, these also need to be supported by students' mathematical abilities, so that it has implications for proving they did. This qualitative research will be explained descriptively which aims to find out senior high school students' argumentation in proving mathematical induction. This research subjects consisted of six senior high school students in Surabaya who had low, medium, and high mathematical abilities. Research data were collected through a written test about proving mathematical induction. Then, the data analysis will be carried out, including: sorting the data, presenting the data, and making conclusions. The results shows that senior high school students who have medium and high mathematical abilities can proving mathematical induction which bring up claims, evidence, and reasoning in their argumentation. Meanwhile, senior high school students who have low mathematical abilities can proving mathematical induction which only bring up claims and evidence in their argumentation.

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34

Okhrimenko, Viacheslav, and Maiia Zbіtnieva. "Mathematical Model of Tubular Linear Induction Motor." Mathematical Modelling of Engineering Problems 8, no. 1 (February 28, 2021): 103–9. http://dx.doi.org/10.18280/mmep.080113.

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Problem of calculation of distribution of magnetic field induction in clearance of tubular linear induction motor (TLIM) is considered. Mathematical model is represented by Fredholm integral equations of second kind for complexes of electric field strength and density of coupled magnetization currents at interface of environments. Algorithm of calculation of distribution of magnetic field induction in TLIM clearance has been developed. Dependence of magnetic field induction in motor clearance on value of pole division is investigated. There is area of optimum pole pitch. Reliability of results of calculations on mathematical model is confirmed by their comparison with results obtained on physical model. Calculated dependence of induction on thickness of runner's iron circuit also has extreme character. Given model can be used at design stage of TLIM. Model allows calculating its optimal geometric dimensions based on criterion of maximum induction in motor clearance, taking into account physical properties of applied materials.

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35

Atmaja, I. Made Dharma. "Prinsip Induksi Matematika dalam Pengambilan Keputusan Organisasi." CENDEKIA : Jurnal Penelitian dan Pengkajian Ilmiah 1, no. 4 (April 14, 2024): 115–31. http://dx.doi.org/10.62335/v1519165.

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The principle of mathematical induction can be an effective tool in organizational decision making. Although these principles have the potential to increase efficiency, reduce uncertainty, and increase accuracy in organizational decision making, their application is limited and has not been fully exploited. Studies need to be conducted to bridge this gap by strengthening the understanding and application of the principles of mathematical induction in the context of organizational decision making. By considering the gaps that occur, it is necessary to conduct research on "The Principle of Mathematical Induction in Organizational Decision Making". This research provides an overview of how the principles of mathematical induction can bridge this gap and improve the quality of decision making in an organizational context. The research method used in this research is a qualitative approach and literature study which involves analysis of relevant literature related to the principles of mathematical induction in the context of organizational decision making. The conclusions from this research are: 1) Applying the principles of mathematical induction in organizational decision making can strengthen efficiency, reduce uncertainty, and increase accuracy in decision making; 2) In applying the principles of mathematical induction in organizational decision making, there are obstacles and challenges that need to be overcome; and 3) Utilizing the principles of mathematical induction involves the use of structured methods, in-depth analysis, and a more objective approach.

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36

UYGUN-ERYURT, Tugba. "Conception and development of inductive reasoning and mathematical induction in the context of written argumentations." Acta Didactica Napocensia 13, no. 2 (December 30, 2020): 65–79. http://dx.doi.org/10.24193/adn.13.2.5.

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Abstract: Nowadays, mathematical reasoning and making proof have taken importance for all students from the grade level of elementary education to university. More specifically, mathematical induction (MI) is a kind of proof and reasoning strategy taking place nearly all grade levels. Moreover, teachers are important factors affecting student learning and they can acquire necessary knowledge and skills developmentally in their teacher education programs. This paper makes contributions to domain of research by investigating the development of PMT’s conception of MI in the context of written argumentations encouraging MI. In other words, the purpose of this multiple case study is to explore how PMT’s conception of mathematical induction develop through their written argumentations. These cases show that there exist improvements in PMT’s written argumentations, conception of MI and proof construction activities related to MI. In other words, the more organized and structured they produced written argumentation, the more successfully they use and make mathematical induction.

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37

Lutso, V. V., and Anton M. Silvestrov. "Mathematical model of a two-machine induction motor with rotating inductor." System research and information technologies, no. 1 (March 25, 2019): 66–74. http://dx.doi.org/10.20535/srit.2308-8893.2019.1.05.

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38

Do, Quoc Am. "A Mathematical Model for a Hybrid Ignition System." Journal of Technical Education Science, no. 79 (October 28, 2023): 16–22. http://dx.doi.org/10.54644/jte.79.2023.1420.

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In the operation of a car's ignition system, the primary ignition coil is responsible for generating a high voltage that typically ranges from around 100V to 300V. However, this self-induced electromotive force (emf) can lead to certain negative effects such as switch breakdown, inductive noise, and secondary voltage drop. This article introduces a novel hybrid ignition system designed for a 4-cylinder engine. This innovative system is a combination of capacitive discharge ignition system (CDI) and induction discharge ignition (IDI) system. The excess electromagnetic force energy (emf) generated during the induction ignition stage will be used in the capacitive ignition. Thereby contributing to limiting the negative effects as mentioned. Forming and solving the mathematical model for the hybrid ignition system mentioned above enables us to analyze the transient responses of the primary current (i1) and primary voltage (V1). These instantaneous responses are crucial in understanding the behavior of the composite ignition circuit and calculating key parameters such as ignition energy during the inductive and capacitive ignition stages, as well as the magnitude of the maximum secondary voltage (V2m). Furthermore, the article also presents experimental results from the hybrid ignition system to complement the theoretical analysis.

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39

Murashov, Iurii, Vyacheslav Shestakov, Vladimir Skornyakov, and Irina Savelieva. "Simulation of induction heating technology for the production of seamless large diameter tees." MATEC Web of Conferences 245 (2018): 04002. http://dx.doi.org/10.1051/matecconf/201824504002.

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The article is dedicated to nonstationary simulation of induction heating technology for the production of seamless large diameter tees. A mathematical model of induction heating process representing a multi-physical (heat transfer and electromagnetism) task for technology of tees production is developed. Numerical simulation was carried out for a flat spiral inductor. The developed model was verified according to the results of experimental studies. The hydrodynamic 3D mathematical model is developed for the design of the inductor cooling system. Optimal operating modes are determined by simulation results and confirmed by experimental data. The calculation results are presented for pipes with wall thicknesses: 15 mm, 40 mm, 60 mm, 70 mm.

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40

Surovtsev, Valeriy A. "Yablo's Paradox, Self-Reference and Mathematical Induction." Vestnik Tomskogo gosudarstvennogo universiteta. Filosofiya, sotsiologiya, politologiya, no. 50 (August 1, 2019): 262–68. http://dx.doi.org/10.17223/1998863x/50/24.

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41

Donskoi, N. V. "Three-phase mathematical model of induction motor." Russian Electrical Engineering 82, no. 1 (January 2011): 38–43. http://dx.doi.org/10.3103/s1068371211010032.

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42

Banerjee, Sandeep, Dheeraj Joshi, and Madhusudan Singh. "Mathematical modelling of doubly-fed induction generator." Journal of Interdisciplinary Mathematics 23, no. 5 (April 14, 2020): 927–34. http://dx.doi.org/10.1080/09720502.2020.1723922.

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43

Argyros, Ioannis K. "On Newton's method and nondiscrete mathematical induction." Bulletin of the Australian Mathematical Society 38, no. 1 (August 1988): 131–40. http://dx.doi.org/10.1017/s0004972700027349.

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The method of nondiscrete mathematical induction is used to find sharp error bounds for Newton's method. We assume only that the operator has Hölder continuous derivatives. In the case when the Fréchet-derivative of the operator satisfies a Lipschitz condition, our results reduce to the ones obtained by Ptak and Potra in 1972.

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44

Smith, Leslie. "Mathematical induction and its formation during childhood." Behavioral and Brain Sciences 31, no. 6 (December 2008): 669–70. http://dx.doi.org/10.1017/s0140525x08005864.

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AbstractI support Rips et al.'s critique of psychology through (1) a complementary argument about the normative, modal, constitutive nature of mathematical principles. I add two reservations about their analysis of mathematical induction, arguing (2) for constructivism against their logicism as to its interpretation and formation in childhood (Smith 2002), and (3) for Piaget's account of reasons in rule learning.

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45

Dyke, Frances Van. "Activities: A Concrete Approach to Mathematical Induction." Mathematics Teacher 88, no. 4 (April 1995): 302–18. http://dx.doi.org/10.5951/mt.88.4.0302.

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46

Sury, B. "Mathematical induction — An impresario of the infinite." Resonance 3, no. 2 (February 1998): 69–76. http://dx.doi.org/10.1007/bf02838987.

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47

Gunawan, Ridwan, Feri Yusivar, and Budiyanto Budiyanto. "The Self Exitated Induction Generator with Observation Magnetizing Characteristic in The Air Gap." International Journal of Power Electronics and Drive Systems (IJPEDS) 5, no. 3 (February 1, 2015): 355. http://dx.doi.org/10.11591/ijpeds.v5.i3.pp355-365.

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This paper discusses the Self Exitated induction Generator (SEIG) by approaching the induction machine, physically and mathematically which then transformed from three-phase frame abc to-axis frame, direct axis and quadratur-axis. Based on the reactive power demand of induction machine, capacitor mounted on the stator of the induction machine then do the physical and mathematical approach of the system to obtain a state space model. Underknown relationships, magnetization reactance and magnetizing current is not linear, so do mathematical approach to the magnetization reactance equation used in the calculation. Obtained state space model and the magnetic reactance equation is simulated by Runge kutta method of fourth order. The equation of reactance, is simulated by first using the polynomial equation and second using the exponent equation. The load voltage at d axis and q axis using the polynomial laggs 640µs to the exponent equation. The polynomial voltage magnetitude is less than 0.6068 volt from the exponent voltage magnitude

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48

Tyapin, Aleksey, Vasiliy Panteleev, and Evgeny Kinev. "Mathematical models of non-sinusoidal power supply of a three-phase transverse field MHD inductor." E3S Web of Conferences 270 (2021): 01024. http://dx.doi.org/10.1051/e3sconf/202127001024.

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The article presents an approach to the development of mathematical models of non-sinusoidal and dual-frequency power supply for a linear induction MHD machine for metallurgical purposes. The issues of construction and numerical modeling of the modes of a three-phase inductor for a liquid aluminum stirrer are considered. Reduction of losses is ensured by the use of a toothless design of the MHD inductor. The absence of steel teeth reduces saturation of the magnetic circuit and current distortion. It is proposed to use the parametric model of the inductor under the furnace in the ANSYS environment to clarify the modes of the complex. To take into account mutual induction, using controlled sources, a circuit model was built, and a numerical calculation of the modes was carried out. The characteristics of instantaneous currents and voltages are obtained when powered from a three-phase source with close frequencies, with pronounced beats. It is shown that the presence of mutual inductance redistributes currents in the delta windings, which must be taken into account when developing the design of linear induction machines. It is proposed to use sources with non-sinusoidal periodic currents in the modeling system. The analysis is carried out and the main types of modulated voltage characteristics in the power supply system of the induction MHD stirrer are shown.

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Liu, Defu, Guowu Yang, Yong Huang, and Jinzhao Wu. "Inductive Method for Evaluating RFID Security Protocols." Wireless Communications and Mobile Computing 2019 (April 11, 2019): 1–8. http://dx.doi.org/10.1155/2019/2138468.

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Authentication protocol verification is a difficult problem. The problem of “state space explosion” has always been inevitable in the field of verification. Using inductive characteristics, we combine mathematical induction and model detection technology to solve the problem of “state space explosion” in verifying the OSK protocol and VOSK protocol of RFID system. In this paper, the security and privacy of protocols in RFID systems are studied and analysed to verify the effectiveness of the combination of mathematical induction and model detection. We design a (r,s,t)-security experiment on the basis of privacy experiments in the RFID system according to the IND-CPA security standard in cryptography, using mathematical induction to validate the OSK protocol and VOSK protocol. Finally, the following conclusions are presented. The OSK protocol cannot resist denial of service attacks or replay attacks. The VOSK protocol cannot resist denial of service attacks but can resist replay attacks. When there is no limit on communication, the OSK protocol and VOSK protocol possess (r,s,t)-privacy; that is to say they can resist denial of service attacks.

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Biryukova, V. I., and A. A. Kartashevich. "Modeling of production indicators of mining companies to improve the efficiency of the management system." Interexpo GEO-Siberia 2, no. 4 (May 18, 2022): 205–10. http://dx.doi.org/10.33764/2618-981x-2022-2-4-205-210.

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In the context of the special relevance of the oil and gas complex for Russia, many new oil and gas fields are being developed and exploited every year. The state, in an effort to stimulate economic growth, implements large-scale projects related to the extraction of hydrocarbons. Such projects require geological and economic assessment, which can take place both at different stages of development and by different methods. In this paper, a general method of forecasting total production volumes, drive through mathematical induction, is presented. The methods of forecasting production volumes by the average debit, as well as by the initial and current debit are mathematically described. And also a proof of the hypothesis using mathematical induction is presented. This work can be useful for modeling forecasting by mathematical and economic methods of production indicators of an oil field.

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