Relevant bibliographies by topics / Mathematical induction

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Mathematical induction'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 July 2024

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Journal articles on the topic "Mathematical induction"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Mathematical induction"

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Wedin, Hanna. "Mathematical Induction." Thesis, Uppsala universitet, Algebra och geometri, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414099.

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Gruver, John David. "Growth in Students' Conceptions of Mathematical Induction." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2166.

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While proof and reasoning lie at the core of mathematical practice, how students learn to reason formally and build convincing proofs continues to invite reflection and discussion. To add to this discussion I investigated how three students grew in their conceptions of mathematical induction. While each of the students in the study had different experiences and grew in different ways, the grounded axes (triggering events, personal questions about mathematics, and personal questions about a particular solution) highlighted patterns in the narratives and from these patterns a theoretical perspective emerged. Reflection, both on mathematics in general and about specific problems, was central to students' growth. The personal reflections of students and triggering events influenced each other in the following way. The questions students wondered about impacted which trigger stimulated growth, while triggers caused students to rethink assumptions and reflect on mathematics or specific problems. The reflections that allowed triggers to stimulate growth along with the reflections that were results of triggering events constitute an "investigative orientation." Each narrative reflects a different investigative orientation motivated by different personal needs. These investigative orientations affected what type of knowledge was constructed.
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Leung, Yee-ho Genthew. "An evaluation of a teaching approach to improve students' understanding of mathematical induction." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B35516124.

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Williams, J. P. "Mathematical modelling of the dynamic characteristics of induction heating systems." Thesis, Swansea University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636635.

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Induction furnaces provide a cost effective, easily controlled means of heating any electrically conductive load by the process of electromagnetic induction. Such furnaces can be more efficient than their fossil fuel equivalents but rising electricity costs have led both the equipment manufacturers and users to demand even higher efficiencies. The research described in this thesis has therefore been undertaken to improve the mathematical analysis with the ultimate aim of developing more rigorous design methodologies. Studies of the mathematical equations describing the energy transfer within the furnace concluded that, due to the complexities involved in predicting magnetic flux distributions, a numerical technique must be used for their solution. The finite element method was identified as the most suitable technique but no package suitable for induction furnaces is commercially available. It was also concluded that full three dimensional analysis would not be viable for most design offices. An existing finite element code (PE2D) used for the analysis of two dimensinal electromagnetic fields was extended to cover the aspects peculiar to induction furnace design. The main development was to enable the solutions of both the magnetic field and the corresponding induced thermal field during transient heating to be obtained. Other developments included such characteristics as non-linear magneto-thermal properties, surface energy losses and optimisation of time step and excitation frequency. The developed models can be applied to two dimensional analysis in a plane normal to conductor coils and also, in some cases, in the plane of a conductor coil. A post-processor was also developed to provide concise graphical output of such information as temperature profiles, magnetic flux distributions and power densities. The models were validated by comparison with analytical examples and by comparison with experimental data obtained with the aid of a fully automated rig capable of three dimensional flux measurements. A future research program has been identified aimed at, firstly, developing the mathematical model to provide a desk top computer design package, and, secondly, extending the experimental work to provide more validation of the code, better material information and supplementary design rules.
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Brown, Stacy A. "The evolution of students' understanding of mathematical induction : a teaching experiment /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC IP addresses, 2003. http://wwwlib.umi.com/cr/ucsd/fullcit?p3090458.

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Leung, Yee-ho Genthew, and 梁以豪. "An evaluation of a teaching approach to improve students' understanding of mathematical induction." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35516124.

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Santhanam, Ramya. "LOCALIZED WOUND HEALING: A MATHEMATICAL MODEL FOR ELECTROMAGNETIC INDUCTION ON COATED NANOFIBER WOUND DRESSINGS." Akron, OH : University of Akron, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=akron1147883471.

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Thesis (M.S.)--University of Akron, Dept. of Biomedical Engineering, 2006.
"May, 2006." Title from electronic thesis title page (viewed 12/03/2007) Advisor, S.I. Hariharan; Committee members, Daniel B. Sheffer, Narender P. Reddy; Department Chair, Daniel B. Sheffer; Dean of the College, George K. Haritos; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.
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Gokhale, S. A. "Mathematical modeling of gene expression system in Eukaryotes: form gene induction to protein synthesis." Thesis(Ph.D.), CSIR-National Chemical Laboratory, Pune, 2013. http://dspace.ncl.res.in:8080/xmlui/handle/20.500.12252/1923.

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VELOZO, NETO Raimundo do Nascimento. "Aplicações do método de indução matemática à geometria." Universidade Federal do Maranhão, 2017. http://tedebc.ufma.br:8080/jspui/handle/tede/1925.

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Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-09-12T20:44:07Z No. of bitstreams: 1 RaimundoVelozoNeto.pdf: 872870 bytes, checksum: ccaffc749ed9ed23b543712ba5273285 (MD5)
Made available in DSpace on 2017-09-12T20:44:07Z (GMT). No. of bitstreams: 1 RaimundoVelozoNeto.pdf: 872870 bytes, checksum: ccaffc749ed9ed23b543712ba5273285 (MD5) Previous issue date: 2017-06-01
This work deals with the Method of Mathematical Induction, in particular, its use with a view to the solution of geometric problems. It initially some considerations are made about the expression "inductive reasoning" whose it meaning, as appropriately must be explained in the text, that differs from that of "mathematical induction". We prove the proposition that guarantees the use of the method based on its foundation, namely the axiom of mathematical induction (one of the postulates that characterize the natural numbers). It exhibited some examples of its use of Algebra and the Theory of Numbers. And then, some applications of the method of mathematical induction to the problems of Geometry are explored to obtain a geometric measure in terms of another(s), either for the demonstration of a proposition that insinuates itself true, or for the stages of construction of a figure given
Este trabalho trata do Método de Indução Matemática, em especial, de seu uso com vistas à solução de problemas geométricos. Inicialmente, são feitas algumas considerações acerca da expressão "raciocínio indutivo", cujo sentido, conforme apropriadamente explicado no texto, difere do de "indução matemática". É provada a proposição que garante o uso do método com base em seu fundamento, a saber, o axioma de indução matemática (um dos postulados que caracterizam os números naturais) e exibidos alguns exemplos de sua utilização em Álgebra e Teoria dos Números. Em seguida, são exploradas algumas aplicações do método de indução matemática à problemas de Geometria, seja para a obtenção de uma medida geométrica em termos de outra(s), para a demonstração de uma proposição que se insinua verdadeira, ou para a exibição das etapas de construção de uma dada figura.
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FÃlix, Hudson de Souza. "PrincÃpio da induÃÃo matemÃtica: fundamentaÃÃo teÃrica e aplicaÃÃes." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=14010.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
O presente trabalho apresenta propriedades e problemas do ensino da matemÃtica que de alguma forma se demonstram ou podem ser resolvidas usando o princÃpio da induÃÃo matemÃtica. Com isso, buscamos despertar o aluno para a importÃncia da demonstraÃÃo em matemÃtica, saindo do conformismo de aceitar a qualquer fÃrmula de formataÃÃo intuitiva indexada ao nÃmeros naturais e partir para uma anÃlise matemÃtica mais refinada dos conceitos, propriedades e problemas que se apresentam na matemÃtica.
This paper presents properties and mathematics teaching issues that somehow show or can be resolved using the principle of mathematics induction. with this, we seek to awaken students to the importance of demonstration in mathematics , leaving the conformity to accept any intuitive formatting formula indexed to natural numbers and go for a more refined mathematical analysis of the concepts , properties and problems that arise in mathematics.
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Books on the topic "Mathematical induction"

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Zhang, Hantao, ed. Automated Mathematical Induction. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-1675-3.

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H, Zhang, ed. Automated mathematical induction. Dordrecht: Kluwer Academic, 1996.

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Zhang, H. Automated Mathematical Induction. Dordrecht: Springer Netherlands, 1996.

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Martin, Glatfeld, Glatfeld Martin, Schröder Erich Christian, and Spalt Detlef D, eds. Überlegungen zum Induktionsbegriff, unter fachdidaktischer Hinsicht. Frankfurt am Main: P. Lang, 1987.

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Samueli, Jean-Jacques. Histoire des probabilités: Des origines à 1900. Paris: Ellipses, 2009.

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Fejer, Peter A. Mathematical Foundations of Computer Science: Sets, Relations, and Induction. New York, NY: Springer New York, 1991.

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A, Dashevsky Yu, ed. Principles of induction logging. Amsterdam: Elsevier, 2003.

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A, Farret Felix, ed. Modeling and analysis with induction generators. Boca Raton: CRC Press, Taylor & Francis Group, 2015.

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Huppunen, Jussi. High-speed solid-rotor induction machine: Electromagnetic calculation and design. Lappeenranta: Lappeenranta University of Technology, 2004.

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Caron, Jean-Pierre. Modélisation et commande de la machine asynchrone. Paris: Editions Technip, 1995.

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Book chapters on the topic "Mathematical induction"

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Ben-Ari, Mordechai. "Induction." In Mathematical Surprises, 61–72. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13566-8_6.

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AbstractThe axiom of mathematical induction is used extensively as a method of proof in mathematics. This chapter presents inductive proofs of results that may not be known to the reader. We begin with a short review of mathematical induction (Sect. 6.1). Section 6.2 proves results about the familiar Fibonacci numbers while Sect. 6.3 proves results about Fermat numbers. Section 6.4 presents the 91-function discovered by John McCarthy; the proof is by induction on an unusual sequence: integers in an inverse ordering. The proof of the formula for the Josephus problem (Sect. 6.5) is also unusual because of the double induction on two different parts of an expression.
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Rosenthal, Daniel, David Rosenthal, and Peter Rosenthal. "Mathematical Induction." In Undergraduate Texts in Mathematics, 9–22. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05654-8_2.

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Eriksson, Kenneth, Donald Estep, and Claes Johnson. "Mathematical Induction." In Applied Mathematics: Body and Soul, 63–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05796-4_6.

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Baxter, Nancy, Ed Dubinsky, and Gary Levin. "Mathematical Induction." In Learning Discrete Mathematics with ISETL, 319–62. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3592-7_7.

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Fenton, William E., and Ed Dubinsky. "Mathematical Induction." In Introduction to Discrete Mathematics with ISETL, 145–61. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-4052-5_7.

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Liu, Andrew Chiang-Fung. "Mathematical Induction." In S.M.A.R.T. Circle Projects, 85–101. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56811-9_5.

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Gries, David, and Fred B. Schneider. "Mathematical Induction." In A Logical Approach to Discrete Math, 217–50. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-3837-7_13.

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Martin, George E. "Mathematical Induction." In Undergraduate Texts in Mathematics, 137–51. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-4878-9_7.

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Weik, Martin H. "mathematical induction." In Computer Science and Communications Dictionary, 985. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_11174.

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Izadkhah, Habib. "Mathematical Induction." In Problems on Algorithms, 1–28. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-17043-0_1.

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Conference papers on the topic "Mathematical induction"

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Rak, Josef. "Mathematical model of induction heating." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992729.

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Drysdale, Robert L. Scot. "Mathematical induction is a recursive technique." In the 42nd ACM technical symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1953163.1953246.

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Marus, Viktor, and Aleksandr Pugachev. "MATHEMATICAL SIMULATION OF INDUCTION MOTOR SCALAR CONTROL SYSTEM." In CAD/EDA/SIMULATION IN MODERN ELECTRONICS 2021. Bryansk State Technical University, 2021. http://dx.doi.org/10.30987/conferencearticle_61c997ef15ba52.23468627.

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The simulation results of 4 kW induction motor electric drive with scalar control system and different control topologies are presented. The perspective directions of further investigations on improving energy efficiency of electric drives with scalar control systems are highlighted.
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Пугачев, А. А., С. В. Морозов, and А. С. Морозов. "MATHEMATICAL SIMULATION OF THERMAL PROCCESSES IN INDUCTION MOTOR." In САПР и моделирование в современной электронике. Брянский государственный технический университет, 2020. http://dx.doi.org/10.51932/9785907271739_177.

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Djagarov, Nikolay. "Mathematical models of brushless doubly-fed induction machines." In 2020 International Conference Automatics and Informatics (ICAI). IEEE, 2020. http://dx.doi.org/10.1109/icai50593.2020.9311381.

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Rajan, Reshma, Lekshmi A, Raji Krishna, and Sreeja S. "Mathematical Modelling and Analysis of Linear Induction Motor." In 2022 IEEE International Power and Renewable Energy Conference (IPRECON). IEEE, 2022. http://dx.doi.org/10.1109/iprecon55716.2022.10059569.

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Teriaiev, Vitalii, Anton Dovbyk, Vladislav Kornienko, Mykola Pechenik, and Sergey Buryan. "Generalized Mathematical Model of a Linear Induction Motor." In 2022 IEEE 41st International Conference on Electronics and Nanotechnology (ELNANO). IEEE, 2022. http://dx.doi.org/10.1109/elnano54667.2022.9927095.

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Neacsu, Dorin O. "Mathematical Model for Induction Machine Drives with Modified PWM." In 2007 International Symposium on Signals, Circuits and Systems. IEEE, 2007. http://dx.doi.org/10.1109/isscs.2007.4292750.

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Nos, O. V. "Matrix transformations in mathematical Models of an induction motor." In 2008 9th International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE). IEEE, 2008. http://dx.doi.org/10.1109/apeie.2008.4897073.

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Nos, O. V. "Induction Motor Mathematical Model for Stator Voltages Vector Control." In 2006 8th International Conference on Actual Problems of Electronic Instrument Engineering. IEEE, 2006. http://dx.doi.org/10.1109/apeie.2006.4292592.

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