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Добірка наукової літератури з теми "Linear mathematical model"

Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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Статті в журналах з теми "Linear mathematical model"

Komogortsev, Oleg, Corey Holland, Sampath Jayarathna, and Alex Karpov. "2D Linear oculomotor plant mathematical model." ACM Transactions on Applied Perception 10, no. 4 (October 2013): 1–18. http://dx.doi.org/10.1145/2536764.2536774.

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Neamah, Kawther Abood. "Mathematical Model for Handling Unstable Time Series by Using a Linear Approximation Technique." Webology 19, no. 1 (January 20, 2022): 2835–52. http://dx.doi.org/10.14704/web/v19i1/web19189.

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Time series are typically built on basic assumptions that include stationarity, linearity and normality. The three characteristics are crucial for estimating and building time series models. Studies on time series include these assumptions. To deal with unstable time series that are based on its basis, mathematical models that are suitable for such series are adopted in this study. A nonlinear self-regression model, called the rational model, is proposed. This model is a fraction in which the numerator is the complete sine function and the denominator is an exponential self-regression model. The fixed point and limit cycle of the model are simulated and determined, and its stability is studied using a linear approximation technique.

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Osipov, S. P., E. Yu Usachev, S. V. Chakhlov, S. A. Schetinkin, A. A. Manushkin, O. S. Osipov, and N. A. Sergeeva. "A Mathematical Model of Digital Linear Tomography." Russian Journal of Nondestructive Testing 55, no. 5 (May 2019): 407–17. http://dx.doi.org/10.1134/s1061830919050085.

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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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Parovik, Roman. "Mathematical Modeling of Linear Fractional Oscillators." Mathematics 8, no. 11 (October 29, 2020): 1879. http://dx.doi.org/10.3390/math8111879.

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In this work, based on Newton’s second law, taking into account heredity, an equation is derived for a linear hereditary oscillator (LHO). Then, by choosing a power-law memory function, the transition to a model equation with Gerasimov–Caputo fractional derivatives is carried out. For the resulting model equation, local initial conditions are set (the Cauchy problem). Numerical methods for solving the Cauchy problem using an explicit non-local finite-difference scheme (ENFDS) and the Adams–Bashforth–Moulton (ABM) method are considered. An analysis of the errors of the methods is carried out on specific test examples. It is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method. Forced oscillations of linear fractional oscillators (LFO) are investigated. Using the ABM method, the amplitude–frequency characteristics (AFC) were constructed, which were compared with the AFC obtained by the analytical formula. The Q-factor of the LFO is investigated. It is shown that the orders of fractional derivatives are responsible for the intensity of energy dissipation in fractional vibrational systems. Specific mathematical models of LFOs are considered: a fractional analogue of the harmonic oscillator, fractional oscillators of Mathieu and Airy. Oscillograms and phase trajectories were constructed using the ABM method for various values of the parameters included in the model equation. The interpretation of the simulation results is carried out.

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KANEKO, Satoshi, Ryuta SATO, and Masaomi TSUTSUMI. "Mathematical Model of Linear Motor Stage with Non-linear Friction Characteristics." Proceedings of International Conference on Leading Edge Manufacturing in 21st century : LEM21 2007.4 (2007): 8D414. http://dx.doi.org/10.1299/jsmelem.2007.4.8d414.

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KANEKO, Satoshi, Ryuta SATO, and Masaomi TSUTSUMI. "Mathematical Model of Linear Motor Stage with Non-Linear Friction Characteristics." Journal of Advanced Mechanical Design, Systems, and Manufacturing 2, no. 4 (2008): 675–84. http://dx.doi.org/10.1299/jamdsm.2.675.

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M. "Mathematical Analysis of the Non Linear Epidemic Model." Journal of Mathematics and Statistics 8, no. 2 (February 1, 2012): 258–63. http://dx.doi.org/10.3844/jmssp.2012.258.263.

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KARLBERG, J., I. ENGSTRÖM, P. KARLBERG, and J. G. FRYER. "Analysis of Linear Growth Using a Mathematical Model." Acta Paediatrica 76, no. 3 (May 1987): 478–88. http://dx.doi.org/10.1111/j.1651-2227.1987.tb10503.x.

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Zhuzhgov, Nikita, and Anatoly Klyuchnikov. "Mathematical Model for Studying a Linear Synchronous Motor." Известия высших учебных заведений. Электромеханика 64, no. 6 (2021): 22–28. http://dx.doi.org/10.17213/0136-3360-2021-6-22-28.

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In the presented article, synchronous electric motors of reciprocating motion of a linear structure and a typical rotational motion are considered. As a rule, such electric motors are two-phase, one winding is supplied with constant voltage, and the other with alternating voltage. To study transient processes in linear synchronous motors (SM), the equations of Park-Gorev SD of rotary action were taken as a basis, but they were transformed taking into account the necessary additions. As a result of the work, a mathematical model of linear SD is shown, which allows one to study the reciprocating motion of linear SD. With the help of the developed mathematical model, the study of the asynchronous start of the linear SD in the coordinates α-β and d-q was carried out. As a result of comparing the results in different coordinates, an acceptable accuracy of the calculated data was obtained.

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Дисертації з теми "Linear mathematical model"

Tonner, Jaromír. "Overcomplete Mathematical Models with Applications." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-233893.

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Chen, Donoho a Saunders (1998) studují problematiku hledání řídké reprezentace vektorů (signálů) s použitím speciálních přeurčených systémů vektorů vyplňujících prostor signálu. Takovéto systémy (někdy jsou také nazývány frejmy) jsou typicky vytvořeny buď rozšířením existující báze, nebo sloučením různých bazí. Narozdíl od vektorů, které tvoří konečně rozměrné prostory, může být problém formulován i obecněji v rámci nekonečně rozměrných separabilních Hilbertových prostorů (Veselý, 2002b; Christensen, 2003). Tento funkcionální přístup nám umožňuje nacházet v těchto prostorech přesnější reprezentace objektů, které, na rozdíl od vektorů, nejsou diskrétní. V této disertační práci se zabývám hledáním řídkých representací v přeurčených modelech časových řad náhodných veličin s konečnými druhými momenty. Numerická studie zachycuje výhody a omezení tohoto přístupu aplikovaného na zobecněné lineární modely a na vícerozměrné ARMA modely. Analýzou mnoha numerických simulací i modelů reálných procesů můžeme říci, že tyto metody spolehlivě identifikují parametry blízké nule, a tak nám umožňují redukovat původně špatně podmíněný přeparametrizovaný model. Tímto významně redukují počet odhadovaných parametrů. V konečném důsledku se tak nemusíme starat o řády modelů, jejichž zjišťování je většinou předběžným krokem standardních technik. Pro kratší časové řady (100 a méně vzorků) řídké odhady dávají lepší predikce v porovnání s těmi, které jsou založené na standardních metodách (např. maximální věrohodnosti v MATLABu - MATLAB System Identification Toolbox (IDENT)). Pro delší časové řady (500 a více) obě techniky dávají v podstatě stejně přesné predikce. Na druhou stranu řešení těchto problémů je náročnější, a to i časově, nicméně výpočetní doba je stále přijatelná.

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Goldin, Graham Mark. "A linear eddy model for steady-state turbulent combustion." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/12547.

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Mi, Wen. "System identification and model reduction with adaptive rational orthogonal basis." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2581511.

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Chen, Fei, and 陳飛. "Linear programming techniques for algorithms with applications in economics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206329.

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We study algorithms and models for several economics-related problems from the perspective of linear programming. In network bargaining games, stable and balanced outcomes have been investigated in previous work. However, existence of such outcomes requires that the linear program relaxation of a certain maximum matching problem has integral optimal solution. We propose an alternative model for network bargaining games in which each edge acts as a player, who proposes how to split the weight of the edge among the two incident nodes. We show that the distributed protocol by Kanoria et. al can be modified to be run by the edge players such that the configuration of proposals will converge to a pure Nash Equilibrium, without the linear program integrality gap assumption. Moreover, ambiguous choices can be resolved in a way such that there exists a Nash Equilibrium that will not hurt the social welfare too much. In the oblivious matching problem, an algorithm aims to find a maximum matching while it can only makes (random) decisions that are essentially oblivious to the input graph. Any greedy algorithm can achieve performance ratio 0:5, which is the expected number of matched nodes to the number of nodes in a maximum matching. We revisit the Ranking algorithm using the linear programming framework, where the constraints of the linear program are given by the structural properties of Ranking. We use continuous linear program relaxation to analyze the limiting behavior as the finite linear program grows. Of particular interest are new duality and complementary slackness characterizations that can handle monotone constraints and mixed evolving and boundary constraints in continuous linear program, which enable us to achieve a theoretical ratio of 0:523 on arbitrary graphs. The J-choice K-best secretary problem, also known as the (J;K)-secretary problem, is a generalization of the classical secretary problem. An algorithm for the (J;K)-secretary problem is allowed to make J choices and the payoff to be maximized is the expected number of items chosen among the K best items. We use primal-dual continuous linear program techniques to analyze a class of infinite algorithms, which are general enough to capture the asymptotic behavior of the finite model with large number of items. Our techniques allow us to prove that the optimal solution can be achieved by a (J;K)-threshold algorithm, which has a nice \rational description" for the case K = 1.
published_or_final_version
Computer Science
Doctoral
Doctor of Philosophy

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Omari, Mohamed. "Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamics." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/17793.

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Thesis (MSc)--Stellenbosch University, 2011.
ENGLISH ABSTRACT: An integro-differential equation describing the dynamical behaviour of phytoplankton cells is considered in which the effects of cell division and aggregation are incorporated by coupling the coagulation-fragmentation equation with growth, and the McKendrick-von Foerster renewal model of an age-structured population. Under appropriate conditions on the model parameters, the associated initial-boundary value problem is shown to be well posed in a physically relevant Banach space using the theory of strongly continuous semigroups of operators, the theory of perturbation of positive semigroups and the semilinear abstract Cauchy problems theory. In particular, we provide sufficient conditions for honesty of the model. Finally, the results on the effects of the growth-fragmentation-coagulation on the overall evolution of the phytoplankton population are summarised.
AFRIKAANSE OPSOMMING: ’n Integro-differensiaalvergelyking wat die dinamiese ontwikkeling van fitoplanktonselle beskryf, word beskou. Die uitwerking van seldeling en -aggregasie is geïnkorporeer deur die vergelyking van koagulasie en fragmentasie met groeiaan die McKendrick-von Foerster hernuwingsmodel van ’n ouderdomsgestruktureerde populasie te koppel. Die teorie van sterk kontinue semigroepe van operatore, steuringsteorie van positiewe semigroepe en die teorie van semilineêre abstrakte Cauchy probleme word aangewend om, onder gepaste voorwaardes met betrekking tot die model se parameters, te bewys dat die geassosieerde beginwaarde-probleem met randvoorwaardes ‘goed gestel’ is in ’n fisies relevante Banach-ruimte. In die besonder word voldoende voorwaardes vir eerlikheid van die model verskaf. Ten slotte word ’n opsomming van die resultate met betrekking tot die gekombineerde uitwerking van groei-fragmentasie- koagulasie op die gesamentlike ontwikkeling van die fitoplanktonpopulasie verskaf.

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Abeykoon, Mahinda. "Stepwise application of unconstrained linear mixture model for classification of urban land cover." Virtual Press, 2004. http://liblink.bsu.edu/uhtbin/catkey/1306381.

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This study involves stepwise application of Unconstrained Linear Mixer Model (ULMM) for sub-pixel classification of residential areas using Land sat 7 TM image. The image was geometrically and radiometrically corrected and spectral enhancement and classifications were done to determine the possible number of target classes. In the first step, five end-members were used as inputs and the pixels which were considered as well fit to ULMM were identified as outputs. The unidentified pixels were separated and taken to the second step with new end members. This method identified 52% of the mixed pixels were identified in the first phase and 6% in the second phase. 42% of the pixels were left as unidentified after the two steps. The pixels identified by ULMM were grouped into high and low density residential subclasses. The resulting image indicated very low RMS errors. However the percentages of pixels unidentified were high. The independent accuracy test carried out using census population density and the resulting image indicated a low relationship. A hyper-spectral imagery with finer spatial resolution may provide a better sub pixel classification.
Department of Geography

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Loik, V. B., V. Havrysh, and L. Kolyasa. "Non-linear mathematical 3D model of determination of temperature field in elements of microelectronic devices (Scopus)." Thesis, XIІI International Scientific and Technical Conference “Computer Sciences and Information Technologies” CSIT 2018, 2018. http://hdl.handle.net/123456789/5324.

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Wang, Qing, and 王卿. "Model reduction for dynamic systems with time delays: a linear matrix inequality approach." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B38645439.

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Marx, Brian D. "Ill-conditioned information matrices and the generalized linear model: an asymptotically biased estimation approach." Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/53584.

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In the regression framework of the generalized linear model (Nelder and Wedderburn (1972)), interative maximum likelihood parameter estimation is employed via the method of scoring. This iterative procedure involves a key matrix, the information matrix. Ill-conditioning of the information matrix can be responsible for making many desirable properties of the parameter estimates unattainable. Some asymptotically biased alternatives to maximum likelihood estimation are put forth which alleviate the detrimental effects of near singular information. Notions of ridge estimation (Hoerl and Kennard (1970a) and Schaefer (1979)), principal component estimation (Webster et al. (1974) and Schaefer (1986)), and Stein estimation (Stein (1960)) are extended into a regression setting utilizing any one of an entire class of response distributions.
Ph. D.

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Carman, Benjamin Andrew. "Repairing Redistricting: Using an Integer Linear Programming Model to Optimize Fairness in Congressional Districts." Ohio University Honors Tutorial College / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ouhonors1619177994406176.

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Книги з теми "Linear mathematical model"

Williams, H. P. Model building in mathematical programming. 5th ed. Chichester, West Sussex: Wiley, 2013.

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Duke, Eugene L. Derivation and definition of a linear aircraft model. Washington, D.C: National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

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Dipak, Dey, ed. A first course in linear model theory. Boca Raton: Chapman & Hall/CRC, 2002.

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Extending the linear model with R: Generalized linear, mixed effects and nonparametric regression models. Boca Raton: Taylor & Francis, 2016.

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Enderle, John D. Models of horizontal eye movements: A 3rd order linear saccade model. San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA): Morgan & Claypool, 2010.

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Driscoll, M. J. The linear reactivity model for nuclear fuel management. La Grange Park, Ill., USA: American Nuclear Society, 1990.

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Bunke, Helga, and Olaf Bunke, eds. Statistical Methods of Model Building: V1. Statistical Inference in Linear Models. Chichester, New York, USA: John Wiley & Sons Ltd, 1986.

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Kallio, Markku. A model for the forest sector. Laxenburg, Austria: International Institute for Applied Systems Analysis, 1985.

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Lindstadt, Gregory L. Comparison of linear and non-linear hydrologic flood routing models on four California rivers and relationship of model parameters to channel physical characteristics. Berkeley, Calif: Hydraulic Engineering Laboratory and Water Resources Center Archives, University of California, 1986.

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Benigno, Pierpaolo. Optimal taxation in an RBC model: A linear-quadratic approach. Cambridge, Mass: National Bureau of Economic Research, 2005.

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Частини книг з теми "Linear mathematical model"

Williams, H. P. "Model Building in Linear and Integer Programming." In Computational Mathematical Programming, 25–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82450-0_2.

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Bucalem, Miguel Luiz, and Klaus-Jürgen Bathe. "The linear 3-D elasticity mathematical model." In Computational Fluid and Solid Mechanics, 83–177. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-540-26400-2_3.

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Tanizaki, Hisashi. "State-Space Model in Linear Case." In Lecture Notes in Economics and Mathematical Systems, 14–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-22237-9_2.

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Dhaene, Geert. "Encompassing tests for the linear model." In Lecture Notes in Economics and Mathematical Systems, 105–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-46832-2_5.

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Murray, Walter. "Methods for Large-Scale Linear Programming." In Algorithms and Model Formulations in Mathematical Programming, 115–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83724-1_5.

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van de Panne, Cornelis. "Decentralized Optimization for Structured Linear Programming Models." In Algorithms and Model Formulations in Mathematical Programming, 174–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83724-1_26.

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Wolkowicz, Henry, and Adi Ben-Israel. "Computational Geometry and Low Dimensional Linear Programs." In Algorithms and Model Formulations in Mathematical Programming, 185–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83724-1_33.

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Gassmann, Gus. "Multiperiod Linear Stochastic Programming and a Forestry Application." In Algorithms and Model Formulations in Mathematical Programming, 152–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83724-1_13.

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Shevchenko, R. I. "Stabilization of the Two Degree of Freedom Linear Milling Model." In Mathematical Analysis With Applications, 151–59. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42176-2_15.

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Hansen, Mark H., and Bin Yu. "Minimum description length model selection criteria for generalized linear models." In Institute of Mathematical Statistics Lecture Notes - Monograph Series, 145–63. Beachwood, OH: Institute of Mathematical Statistics, 2003. http://dx.doi.org/10.1214/lnms/1215091140.

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Тези доповідей конференцій з теми "Linear mathematical model"

Alexander, Shmelev, and Yasoveev Vasih. "Mathematical model of magnetostrictive linear displacement transducer." In 2019 International Conference on Electrotechnical Complexes and Systems (ICOECS). IEEE, 2019. http://dx.doi.org/10.1109/icoecs46375.2019.8949885.

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Rotaru, Constantin, Simona Roateşi, and Ionică Cîrciu. "Aircraft engine mathematical model – linear system approach." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952084.

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Henzel, M., K. Falkowski, and P. Mazurek. "Mathematical model of linear electric nacelle actuation system." In 2013 International Symposium on Electrodynamic and Mechatronic Systems (SELM). IEEE, 2013. http://dx.doi.org/10.1109/selm.2013.6562958.

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Schieber, Jay D., Renat N. Khaliullin, Albert Co, Gary L. Leal, Ralph H. Colby, and A. Jeffrey Giacomin. "Unified Mathematical Model for Linear Viscoelastic Predictions of Linear and Branched Polymers." In THE XV INTERNATIONAL CONGRESS ON RHEOLOGY: The Society of Rheology 80th Annual Meeting. AIP, 2008. http://dx.doi.org/10.1063/1.2964683.

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Vestenicky, Peter, and Martin Vestenicky. "Mathematical model of non-linear RFID reader — Transponder system." In 2018 ELEKTRO. IEEE, 2018. http://dx.doi.org/10.1109/elektro.2018.8398313.

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Jian, Mao, Cao Yanlong, Yang Jiangxin, and Xu Xusong. "Mathematical model for linear symmetry based on tolerancing principle." In 2006 7th International Conference on Computer-Aided Industrial Design and Conceptual Design. IEEE, 2006. http://dx.doi.org/10.1109/caidcd.2006.329490.

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Polyuschenkov, Igor. "Identification Method of Mathematical Model for Linear Dynamic System." In 2021 28th International Workshop on Electric Drives: Improving Reliability of Electric Drives (IWED). IEEE, 2021. http://dx.doi.org/10.1109/iwed52055.2021.9376355.

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Marzocchi, Alfredo, and Elena Vuk. "Asymptotic behavior for a model of transverse vibration of a bar with linear memory." In Mathematical Models and Methods for Smart Materials. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776273_0022.

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Buchfink, Patrick. "Structure-Preserving Model Reduction of Hamiltonian Systems for Linear Elasticity." In 9th Vienna Conference on Mathematical Modelling. ARGESIM Publisher Vienna, 2018. http://dx.doi.org/10.11128/arep.55.a55228.

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Jacob, V. C., T. R. Natesan, V. Rhymend Uthariaraj, and P. Narayanasamy. "AN ANALYSIS OF CONJUNCTIVE MODEL REDUCTION ALGORITHMS FOR SOLVING LINEAR PROGRAMMING PROBLEMS." In Third Asian Mathematical Conference 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777461_0025.

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Звіти організацій з теми "Linear mathematical model"

Lovianova, Iryna V., Dmytro Ye Bobyliev, and Aleksandr D. Uchitel. Cloud calculations within the optional course Optimization Problems for 10th-11th graders. [б. в.], September 2019. http://dx.doi.org/10.31812/123456789/3267.

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The article deals with the problem of introducing cloud calculations into 10th-11th graders’ training to solve optimization problems in the context of the STEM-education concept. After analyzing existing programmes of optional courses on optimization problems, the programme of the optional course Optimization Problems has been developed and substantiated implying solution of problems by the cloud environment CoCalc. It is a routine calculating operation and not a mathematical model that is accentuated in the programme. It allows considering more problems which are close to reality without adapting the material while training 10th-11th graders. Besides, the mathematical apparatus of the course which is partially known to students as the knowledge acquired from such mathematics sections as the theory of probability, mathematical statistics, mathematical analysis and linear algebra is enough to master the suggested course. The developed course deals with a whole class of problems of conventional optimization which vary greatly. They can be associated with designing devices and technological processes, distributing limited resources and planning business functioning as well as with everyday problems of people. Devices, processes and situations to which a model of optimization problem is applied are called optimization problems. Optimization methods enable optimal solutions for mathematical models. The developed course is noted for building mathematical models and defining a method to be applied to finding an efficient solution.

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Semerikov, Serhiy O., Illia O. Teplytskyi, Yuliia V. Yechkalo, and Arnold E. Kiv. Computer Simulation of Neural Networks Using Spreadsheets: The Dawn of the Age of Camelot. [б. в.], November 2018. http://dx.doi.org/10.31812/123456789/2648.

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The article substantiates the necessity to develop training methods of computer simulation of neural networks in the spreadsheet environment. The systematic review of their application to simulating artificial neural networks is performed. The authors distinguish basic approaches to solving the problem of network computer simulation training in the spreadsheet environment, joint application of spreadsheets and tools of neural network simulation, application of third-party add-ins to spreadsheets, development of macros using the embedded languages of spreadsheets; use of standard spreadsheet add-ins for non-linear optimization, creation of neural networks in the spreadsheet environment without add-ins and macros. After analyzing a collection of writings of 1890-1950, the research determines the role of the scientific journal “Bulletin of Mathematical Biophysics”, its founder Nicolas Rashevsky and the scientific community around the journal in creating and developing models and methods of computational neuroscience. There are identified psychophysical basics of creating neural networks, mathematical foundations of neural computing and methods of neuroengineering (image recognition, in particular). The role of Walter Pitts in combining the descriptive and quantitative theories of training is discussed. It is shown that to acquire neural simulation competences in the spreadsheet environment, one should master the models based on the historical and genetic approach. It is indicated that there are three groups of models, which are promising in terms of developing corresponding methods – the continuous two-factor model of Rashevsky, the discrete model of McCulloch and Pitts, and the discrete-continuous models of Householder and Landahl.

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Levi, Mark. Mathematical Models of Non-Linear Mechanical and Electrical Systems and Their Qualitative Behavior. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada248847.

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Trefethen, L. N. Linear non-modal phenomena in numerical analysis and applied mathematics. First annual performance report, February 15, 1994--November 15, 1994. Office of Scientific and Technical Information (OSTI), November 1994. http://dx.doi.org/10.2172/10114048.

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