Relevant bibliographies by topics / Linearization of the mathematical model

Contents

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

Academic literature on the topic 'Linearization of the mathematical model'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 July 2025

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Journal articles on the topic "Linearization of the mathematical model"

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Miková, Lubica. "LINEARIZATION OF A NONLINEAR VEHICLE MODEL." TECHNICAL SCIENCES AND TECHNOLOGIES, no. 2(24) (2021): 33–37. http://dx.doi.org/10.25140/2411-5363-2021-2(24)-33-37.

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The purpose of this article is to create a mathematical model of a vehicle using dynamic equations of motion and simulation of perturbations acting on a vehicle. It is assumed that the tire in the car model behaves linearly. Because the vehicle model is nonlinear, the model will need to be linearized in order to find the transfer function between the angle of rotation of the front wheel and the lateral position of the vehicle. For this purpose, simple dynamic models of the car were created, which reflect its lateral and longitudinal dynamics. These types of models are usually used with a linea
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Zhang, Shuhua, and Ronghu Chi. "Model-free adaptive PID control for nonlinear discrete-time systems." Transactions of the Institute of Measurement and Control 42, no. 10 (2020): 1797–807. http://dx.doi.org/10.1177/0142331219896649.

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This work explores a model-free adaptive PID (MFA-PID) control for nonlinear discrete-time systems with rigorous mathematical analysis under a data-driven framework. An improved compact form dynamic linearization (iCFDL) is proposed to transfer the original nonlinear system into an affined linear data model including a nonlinear residual term. Both a time-difference estimator and a gradient parameter estimator are designed to estimate the nonlinear residual uncertainties and the unknown parameters in the iCFDL model. Subsequently, a novel improved CFDL based MFA-PID (iCFDL-MFA-PID) control is
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Zhang, Bin, and Yung C. Shin. "A Data-Driven Approach of Takagi-Sugeno Fuzzy Control of Unknown Nonlinear Systems." Applied Sciences 11, no. 1 (2020): 62. http://dx.doi.org/10.3390/app11010062.

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A novel approach to build a Takagi-Sugeno (T-S) fuzzy model of an unknown nonlinear system from experimental data is presented in the paper. The neuro-fuzzy models or, more specifically, fuzzy basis function networks (FBFNs) are trained from input–output data to approximate the nonlinear systems for which analytical mathematical models are not available. Then, the T-S fuzzy models are derived from the direct linearization of the neuro-fuzzy models. The operating points for linearization are chosen using the evolutionary strategy to minimize the global approximation error so that the T-S fuzzy
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Jose, Julia Tholath, and Adhir Baran Chattopadhyay. "Mathematical Formulation of Feedback Linearizing Control of Doubly Fed Induction Generator Including Magnetic Saturation Effects." Mathematical Problems in Engineering 2020 (February 1, 2020): 1–10. http://dx.doi.org/10.1155/2020/3012406.

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This paper proposes a control methodology based on feedback linearization for a doubly fed induction generator (DFIG) incorporating the magnetic saturation. The feedback linearization algebraically converts a nonlinear system model into a linear model, allowing the use of linear control techniques. Feedback linearization control depends on the model of the system and is therefore sensitive to parameter variations. The doubly fed induction generator (DFIG) operating under the magnetic saturation conditions results in the nonlinear variation of magnetizing inductance, which affects the performan
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Wang, He Hua, Xiao He Liu, Ming Jie Ma, and Cheng Yang. "Feedback Linearization Control of Pmssm Based on Svpwm." Advanced Materials Research 591-593 (November 2012): 1655–58. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.1655.

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In this paper, according to the AC permanent magnet synchronous servo motor of the laboratory, using appropriate method to deal with servo motor makes its physical model be established. The nonlinear dynamic mathematical model of permanent magnet synchronous servo motor is established on the basis of the physical model. Based on nonlinear dynamic mathematical model of the permanent magnet synchronous servo motor, and through the coordinate transformation and state feedback, the input-output linearization is realized and the system decoupling is achieved. According to the system's linear model,
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Liu, Xuan, Xiang Shi, Zhe Xu, and Ka Tian. "Mathematical Modelling for Wheeled Inverted Pendulum." Applied Mechanics and Materials 543-547 (March 2014): 1365–68. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1365.

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To control wheeled inverted pendulum is a good way to test all kinds of theories of control, On the basis of Newtonian mechanics and dynamic characteristics, the dynamical equation of DC motor, cart and pendulum is studied. Then the approximate linear model of wheeled inverted pendulum is concluded, which is based on the way of linearization of small Angle.
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Gavrus, Cristina, Nicolae-Valentin Ivan, and Gheorghe Oancea. "Machining Parameters Optimization Based on Objective Function Linearization." Mathematics 10, no. 5 (2022): 803. http://dx.doi.org/10.3390/math10050803.

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Manufacturing process optimization is an ever-actual goal. Within this goal, machining parameters optimization is a very important task. Machining parameters strongly influence the manufacturing costs, process productivity and piece quality. Literature presents a series of optimization methods. The results supplied by these methods are comparable and it is difficult to establish which method is the best. For machining parameters optimization, this paper proposes a novel, simple and efficient method, without additional costs related to new software packages. This approach is based on linear mat
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Xian, Yang Jin, Li Zhi Peng, and Chen Chao. "Study of a Four Rotor Aircraft Modeling." Applied Mechanics and Materials 494-495 (February 2014): 293–96. http://dx.doi.org/10.4028/www.scientific.net/amm.494-495.293.

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In order to design the four rotor aircraft attitude control system, take the hover state or low speed flight state as a benchmark, firstly, divide the aircraft model into linear motion model and the angular motion model and model it separately, the nonlinear mathematical model of aircraft can be obtained. And then use the small disturbance linearization principle to linear mathematical model for a simplified model. After substituting into the previous experimental data, the mathematical model which controller design needs is got.
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Guo, Qian, Tianhong Pan, Jinfeng Liu, and Shan Chen. "Explicit model predictive control of permanent magnet synchronous motors based on multi-point linearization." Transactions of the Institute of Measurement and Control 43, no. 12 (2021): 2872–81. http://dx.doi.org/10.1177/01423312211015120.

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Permanent magnet synchronous motors (PMSMs) have been broadly applied in servo-drive applications. It is necessary to improve the performance of PMSM. An explicit controller designed for PMSM based on multi-point linearization is proposed to reduce the linearized model error caused by different running status of PMSM. The mathematical model of PMSM system in the synchronous rotating frame and the problem formulation are introduced at first. Then, the preliminaries about explicit model predictive control (MPC) algorithm are presented in this article. Based on this, the multi-point linearization
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Zeng, Run Zhang, та Huang Qiu Zhu. "Mathematical Model and Control of Axial Hybrid Magnetic Bearings Based on α-th Order Inverse System Theory". Applied Mechanics and Materials 529 (червень 2014): 539–43. http://dx.doi.org/10.4028/www.scientific.net/amm.529.539.

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A linearization control research based on α-th order inverse system method has been developed for an axial hybrid magnetic bearing, which is a nonlinear system. The configuration of the axial hybrid magnetic bearing is briefly introduced, the working principle of the hybrid magnetic bearing is analyzed, and then the suction equations are set up. Based on expounding of α-th order inverse system method, and aiming at dynamics model of the axial hybrid magnetic bearing, the feasibility of linearization control is discussed in detail, the linearization control arithmetic based on α-th order invers
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Dissertations / Theses on the topic "Linearization of the mathematical model"

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Friedbaum, Jesse Robert. "Model Predictive Linear Control with Successive Linearization." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/7063.

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Robots have been a revolutionizing force in manufacturing in the 20th and 21st century but have proven too dangerous around humans to be used in many other fields including medicine. We describe a new control algorithm for robots developed by the Brigham Young University Robotics and Dynamics and Robotics Laboratory that has shown potential to make robots less dangerous to humans and suitable to work in more applications. We analyze the computational complexity of this algorithm and find that it could be a feasible control for even the most complicated robots. We also show conditions for a sys
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Banach, Antoni StanisŁaw. "Feedback design for nonlinear distributed-parameter systems by extended linearization." Diss., Virginia Tech, 1992. http://hdl.handle.net/10919/39429.

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A feedback design procedure known as extended linearization consists in replacing a mathematical model of a nonlinear dynamical system with its family of linearizations, parametrized by the operating point, and then combining feedback gains designed for representatives of the family into a single nonlinear feedback law. The principles of the procedure, applicable both to lumped-parameter and distributed-parameter systems, are discussed at the outset. The development shows limits on feedback laws that can be designed, as well as nonuniqueness of solutions, inherent in the method.<br>Ph. D.
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Chrobok, Viktor. "Harvesting in the Predator - Prey Model." Master's thesis, Vysoká škola ekonomická v Praze, 2009. http://www.nusl.cz/ntk/nusl-10510.

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The paper is focused on the Predator-Prey model modified in the case of harvesting one or both populations. Firstly there is given a short description of the basic model and the sensitivity analysis. The first essential modification is percentage harvesting. This model could be easily converted to the basic one using a substitution. The next modification is constant harvesting. Solving this system requires linearization, which was properly done and brought valuable results applicable even for the basic or the percentage harvesting model. The next chapter describes regulation models, which coul
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Chrobok, Viktor. "Optimization of Harvesting Natural Resources." Doctoral thesis, Vysoká škola ekonomická v Praze, 2008. http://www.nusl.cz/ntk/nusl-196942.

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The thesis describes various modifications of the predator-prey model. The modifications are considering several harvesting methods. At the beginning a solution and a sensitivity analysis of the basic model are provided. The first modification is the percentage harvesting model, which could be easily converted to the basic model. Secondly a constant harvesting including a linearization is derived. A significant part is devoted to regulation models with special a focus on environmental applications and the stability of the system. Optimization algorithms for one and both species harvesting are
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Дмитриенко, Валерий Дмитриевич, Сергей Юрьевич Леонов, Александр Юрьевич Заковоротный та Дмитрий Максимович Главчев. "Проблемы преобразования нелинейных систем управления технологическими процессами к эквивалентным линейным в форме Бруновского". Thesis, ВМВ, 2018. http://repository.kpi.kharkov.ua/handle/KhPI-Press/45506.

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Рассматривается задача линеаризации математических моделей, описывающих технологические процессы, с целью получения удобного инструмента для управления ими. Задача линеаризации решается с помощью геометрической теории управления (ГТУ). Привлекательность ГТУ связана с получением эквивалентных нелинейным моделям линейных моделей, которые удобно использовать для решения задач управления, получая структуры регуляторов или законы управления. После чего осуществляется обратный переход из пространства линейных систем в пространство исходной нелинейной системы. При этом основные аналитические преобраз
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Mahama, Abdul-Salim. "Switched-model Linearization Technique for RF Power Amplifiers." Thesis, Högskolan i Gävle, Avdelningen för elektronik, matematik och naturvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-25495.

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Coskun, Arslan Hakan. "Stochastic Characterization And Mathematical Analysis Of Feedforward Linearizers." Phd thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/626721/index.pdf.

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Feedforward is known to be one of the best methods for power amplifier linearization due to its superior linearization performance and broadband stable operation. However feedforward systems have relatively poor power efficiency and are complicated due to the presence of two nonlinear amplifiers and the requirements of amplitude, phase and delay matching within two different loops. In this thesis stochastic characterization of a simple feedforward system with autocorrelation analysis has been presented for Code Division Multiple Access (CDMA) applications taking the amplitude and delay mismatc
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Главчев, Дмитро Максимович. "Моделі, методи та програмні компоненти комп'ютерної системи тягового рухомого складу". Thesis, Національний технічний університет "Харківський політехнічний інститут", 2020. http://repository.kpi.kharkov.ua/handle/KhPI-Press/48901.

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Дисертація на здобуття наукового ступеня доктора філософії (PhD) за спеціальністю 123 – Комп’ютерна інженерія – Національний технічний університет “Харківський політехнічний інститут”, Харків, 2020. Об’єктом дослідження є процеси управління тяговим рухомим складом за допомогою бортової комп’ютерної системи, що використовується у дизель-потягах серії ДЕЛ-02. Предметом дослідження є моделі, методи та відповідні програмні компоненти, які використовуються в комп’ютерній системі тягового рухомого складу, та розширюють область застосування геометричної теорії управління при синтезі оптимальних керу
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Chung, Gi Yun. "An analytical approach to real-time linearization of a gas turbine engine model." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50702.

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A recent development in the design of control system for a jet engine is to use a suitable, fast and accurate model running on board. Development of linear models is particularly important as most engine control designs are based on linear control theory. Engine control performance can be significantly improved by increasing the accuracy of the developed model. Current state-of-the-art is to use piecewise linear models at selected equilibrium conditions for the development of set point controllers, followed by scheduling of resulting controller gains as a function of one or more of the system
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Lindahl, Karl-Olof. "On the linearization of non-Archimedean holomorphic functions near an indifferent fixed point." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1713.

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Books on the topic "Linearization of the mathematical model"

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Antoniewicz, Robert F. User's manual for interactive LINEAR, a FORTRAN program to derive linear aircraft models. Ames Research Center, 1988.

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L, Duke Eugene, Patterson Brian P, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., eds. User's manual for interactive LINEAR, a FORTRAN program to derive linear aircraft models. National Aeronautics and Space Administration, Scientific and Technical Information Division, 1989.

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A, Muravyov Alexander, and Langley Research Center, eds. Equivalent linearization analysis of geometrically nonlinear random vibrations using commercial finite element codes. National Aeronautics and Space Administration, Langley Research Center, 2002.

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Pshenichnyj, Boris N. The Linearization Method for Constrained Optimization. Springer Berlin Heidelberg, 1994.

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1964-, Hartley T. T., and United States. National Aeronautics and Space Administration., eds. A method for generating reduced order linear models of supersonic inlets: Under grant NAG3-1450. National Aeronautics and Space Administration, 1997.

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W, Zucchini, ed. Model selection. Wiley, 1986.

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Prestel, Alexander, and Charles N. Delzell. Mathematical Logic and Model Theory. Springer London, 2011. http://dx.doi.org/10.1007/978-1-4471-2176-3.

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Bateman, J. E. Surface exafs: A mathematical model. Rutherford Appleton Laboratory, 2000.

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Williams, H. P. Model building in mathematical programming. 3rd ed. Wiley, 1990.

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Williams, H. P. Model building in mathematical programming. 5th ed. Wiley, 2013.

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Book chapters on the topic "Linearization of the mathematical model"

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MirHassani, S. A., and F. Hooshmand. "Linearization of Nonlinear Functions." In Methods and Models in Mathematical Programming. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27045-2_4.

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Nochetto, Ricardo H. "Linearization of Parabolic Free Boundary Problems." In Mathematical Models for Phase Change Problems. Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-9148-6_14.

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Krener, A. J. "Feedback Linearization." In Mathematical Control Theory. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1416-8_3.

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Socha, Leslaw. "Mathematical Preliminaries." In Linearization Methods for Stochastic Dynamic Systems. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-72997-6_2.

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Malley, James D. "Linearization of the Basic Model." In Optimal Unbiased Estimation of Variance Components. Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4615-7554-2_3.

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Kiwiel, Krzysztof C. "A linearization method for minimizing certain quasidifferentiable functions." In Mathematical Programming Studies. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0121139.

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Mozyrska, Dorota, and Zbigniew Bartosiewicz. "Carleman Linearization of Linearly Observable Polynomial Systems." In Mathematical Control Theory and Finance. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-69532-5_17.

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Spong, Mark W. "On Feedback Linearization of Robot Manipulators and Riemannian Curvature." In Essays on Mathematical Robotics. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1710-7_8.

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Gaivoronski, A. "Linearization methods for optimization of functionals which depend on probability measures." In Mathematical Programming Studies. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0121130.

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Antipin, Anatoly. "Linearization Method for Solving Equilibrium Programming Problems." In Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57014-8_1.

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Conference papers on the topic "Linearization of the mathematical model"

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Saetti, Umberto, Ashish Manjhi, Batin Bugday, Alessandro Cocco, and Joseph Horn. "Implementation and Linearization of a State-Space Free Wake Model with a Near-Wake Vortex Lattice Model." In Vertical Flight Society 80th Annual Forum & Technology Display. The Vertical Flight Society, 2024. http://dx.doi.org/10.4050/f-0080-2024-1144.

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This paper describes the implementation and linearization of a state-space free-vortex wake model with a near-wake vortex lattice model as applied to a helicopter rotor. Following a detailed mathematical description, the wake model is implemented for a blade element model of a utility helicopter rotor and tested in multiple flight conditions including hover, forward flight, and vortex ring state (VRS), and for simple control inputs. The model is qualitatively verified against a Vortex Particle Method (VPM). Periodic solutions to the wake model are found by time marching the coupled rotor and v
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Krasinskiy, Aleksandr Ya, and Anastasia N. Ilyina. "Nonlinear Mathematical Model of the Systems Dynamics with Geometric Constraints and its Simplification Due to the Justified Linearization of Constraints." In 2024 6th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA). IEEE, 2024. https://doi.org/10.1109/summa64428.2024.10803756.

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Cedro, Leszek. "Linearization and identification a mathematical model of an excavator." In 2014 15th International Carpathian Control Conference (ICCC). IEEE, 2014. http://dx.doi.org/10.1109/carpathiancc.2014.6843572.

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Borrás Pinilla, Carlos, José Luis Sarmiento, and Juan Felipe Ortiz. "Dynamic Model and Control Design for a Nonlinear Hydraulic Actuator." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-88320.

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Industrial hydraulic systems are complex, and show nonlinear dynamic behavior because of their nature. When it is not easy to deal with the nonlinear models, hydraulic systems are usually described by linear or linearized models around operating points. In this work a nonlinear dynamic and mathematic model for the position control of a double rod hydraulic actuator was developed. Three control strategies were implemented: PID control, optimal control (LQR) and control by Feedback Linearization. For the PID control and optimal control (LQR) strategies a linearized model of the hydraulic actuato
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Dongjie Mu and Changchun Li. "A new mathematical model of twin flapper-nozzle servo valve based on input-output linearization approach." In 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC). IEEE, 2011. http://dx.doi.org/10.1109/aimsec.2011.6009893.

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Saetti, Umberto, and Joseph Horn. "Implementation and Linearization of a Rotor Simulation with a State-Space Free-Vortex Wake Model." In Vertical Flight Society 78th Annual Forum & Technology Display. The Vertical Flight Society, 2022. http://dx.doi.org/10.4050/f-0078-2022-17577.

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This paper describes the implementation and linearization of a free-vortex wake model in state-variable form as applied to a helicopter rotor. Following a detailed mathematical description, the wake model is implemented for a UH-60 rotor and tested in forward flight and for simple control inputs. A periodic solution to the wake model is found by time marching the coupled rotor and vortex wake dynamics. Next, linearized harmonic decomposition models are obtained and validated against nonlinear simulations. Order reduction methods are explored to guide the development of linearized wake models t
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Saetti, Umberto, and Joseph Horn. "Implementation and Linearization of a State-Space Free-Vortex Wake Model for Flapping-Wing Flight." In Vertical Flight Society 78th Annual Forum & Technology Display. The Vertical Flight Society, 2022. http://dx.doi.org/10.4050/f-0078-2022-17578.

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This paper describes the extension of a free-vortex wake method in state-variable form originally developed for rotary-wing applications to flapping-wing flight. Following a detailed mathematical description, the wake model is implemented for a hovering insect representative of a hawk moth. A periodic solution to the wake model is found at hover using a modified harmonic balance algorithm. Next, linearized harmonic decomposition models are obtained and validated against the nonlinear dynamics using simulations. Order reduction methods are explored to guide the development of linearized wake mo
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Shi, Zhanqun, Yibo Fan, Fengshou Gu, Abdul-Hannan Ali, and Andrew Ball. "Neural Network Modelling Applied for Model-Based Fault Detection." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58197.

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This paper aims to combine neural network modelling with model-based fault detection. An accurate and robust model is critical in model-based fault detection. However, the development of such a model is the most difficult task especially when a non-linear system is involved. The problem comes not only from the lack of concerned information about model parameters, but also from the inevitable linearization. In order to solve this problem, neural networks are introduced in this paper. Instead of using conventional neural network modelling, the neural network is only used to approximate the non-l
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Rashid, Muzamil, Sina Shojaei, Fabio Toriumi, et al. "Feedback Linearization-based Thermal Control Strategy for Electrified Vehicles." In WCX SAE World Congress Experience. SAE International, 2023. http://dx.doi.org/10.4271/2023-01-0144.

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&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Modern electric vehicles (EVs) have complex thermal systems due to stringent energy efficiency requirements. The thermal systems of such vehicles have highly nonlinear and strongly coupled dynamics as they operate under various thermal modes. Extracting the maximum performance benefits from such complex systems requires elaborate and modern control strategies since classic and rule-based strategies cannot effectively control them. This is becoming a challenge for electric vehicles. Feedback linearization is a control app
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Sun, Jian, and Ali R. Shahin. "Optimal H∞ Control of Structural Vibrations Using Shape Memory Alloy Actuators." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0540.

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Abstract This paper investigates robust control problem of structural vibrations using shape memory alloy (SMA) wires as actuators. The mathematical model for these SMA actuators is derived with emphasis in model uncertainty. The linearization of the relation between stress and temperature dynamics of SMA actuators is analyzed for active control. To handle the uncertainties caused by the linearization and the neglected high frequency dynamics, optimal H∞ control was employed to design a controller. An example is used to demonstrate the design procedures and the control system is tested in a no
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Reports on the topic "Linearization of the mathematical model"

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Pokorny, Richard, and Pavel R. Hrma. Mathematical Model of Cold Cap?Preliminary One-Dimensional Model Development. Office of Scientific and Technical Information (OSTI), 2011. http://dx.doi.org/10.2172/1012879.

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Buchanan, C. R., and M. H. Sherman. A mathematical model for infiltration heat recovery. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/767547.

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Preto, F. A mathematical model for fluidized bed coal combustion. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1985. http://dx.doi.org/10.4095/302616.

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McWilliams, Jennifer, and Melanie Jung. Development of a Mathematical Air-Leakage Model from MeasuredData. Office of Scientific and Technical Information (OSTI), 2006. http://dx.doi.org/10.2172/883786.

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Schneider, Michael L., and Richard E. Price. Temperature Analysis: Howard A. Hanson Reservoir, Washington. Mathematical Model Investigation. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada200228.

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Smith, F. G. III. Mathematical model of the Savannah River Site waste tank farm. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/5788555.

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Smith, F. G. III. Mathematical model of the Savannah River Site waste tank farm. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/10131180.

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De Silva, K. N. A mathematical model for optimization of sample geometry for radiation measurements. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1988. http://dx.doi.org/10.4095/122732.

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Embid, P., and M. Baer. Mathematical analysis of a two-phase model for reactive granular material. Office of Scientific and Technical Information (OSTI), 1989. http://dx.doi.org/10.2172/5233068.

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Christian Suharlim, Christian Suharlim. Mathematical model to reduce maternal and infant mortality in Southeast Asia. Experiment, 2014. http://dx.doi.org/10.18258/4103.

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