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Published: 30 May 2022
Last updated: 31 May 2022

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1

Bahamonde, Rafael E. "POWER PREDICTION EQUATIONS." Medicine & Science in Sports & Exercise 37, no. 3 (March 2005): 521. http://dx.doi.org/10.1249/01.mss.0000155701.90438.09.

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2

Canavan, Paul K., and Jason D. Vescovi. "POWER PREDICTION EQUATIONS." Medicine & Science in Sports & Exercise 37, no. 3 (March 2005): 522. http://dx.doi.org/10.1249/01.mss.0000155702.99287.37.

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3

TARASOV, VASILY E. "TRANSPORT EQUATIONS FROM LIOUVILLE EQUATIONS FOR FRACTIONAL SYSTEMS." International Journal of Modern Physics B 20, no. 03 (January 30, 2006): 341–53. http://dx.doi.org/10.1142/s0217979206033267.

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We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Gasdynamic equations for fractional systems are derived from the generalized transport equation.
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4

Beauregard, Raymond A., and Vladimir A. Dobrushkin. "Differential equations v. power series." Mathematical Gazette 99, no. 546 (November 2015): 499–503. http://dx.doi.org/10.1017/mag.2015.87.

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5

Karwowski, Jacek, and Henryk A. Witek. "Schrödinger equations with power potentials." Molecular Physics 114, no. 7-8 (December 16, 2015): 932–40. http://dx.doi.org/10.1080/00268976.2015.1115565.

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6

Ingen Schenau, G. J. van, and P. R. Cavanagh. "Power equations in endurance sports." Journal of Biomechanics 23, no. 9 (January 1990): 865–81. http://dx.doi.org/10.1016/0021-9290(90)90352-4.

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7

Bognár, Gabriella, and Ondřej Došlý. "A remark on power comparison theorem for half-linear differential equations." Mathematica Bohemica 133, no. 2 (2008): 187–95. http://dx.doi.org/10.21136/mb.2008.134060.

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8

Costin, Rodica D. "Power and exponential-power series solutions of evolution equations." Annales de la faculté des sciences de Toulouse Mathématiques 13, no. 4 (2004): 551–73. http://dx.doi.org/10.5802/afst.1082.

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9

Győry, K., and Á. Pintér. "Binomial Thue equations, ternary equations and power values of polynomials." Journal of Mathematical Sciences 180, no. 5 (January 10, 2012): 569–80. http://dx.doi.org/10.1007/s10958-012-0656-z.

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10

Okhotin, Alexander, and Oksana Yakimova. "Language equations with complementation: Expressive power." Theoretical Computer Science 416 (January 2012): 71–86. http://dx.doi.org/10.1016/j.tcs.2011.10.003.

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11

Wu, Yingquan, and Christoforos N. Hadjicostis. "On solving composite power polynomial equations." Mathematics of Computation 74, no. 250 (August 20, 2004): 853–69. http://dx.doi.org/10.1090/s0025-5718-04-01710-7.

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12

CHEON, J. H. "Quadratic Equations from APN Power Functions." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A, no. 1 (January 1, 2006): 19–27. http://dx.doi.org/10.1093/ietfec/e89-a.1.19.

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13

Xu, Fei, Yixian Gao, Xue Yang, and He Zhang. "Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method." Mathematical Problems in Engineering 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/5492535.

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This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems inRn. Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2nth-order time-space fractional Boussinesq equations inRand fourth-order time-space fractional Boussinesq equations inR2andRn. Finally, by numerical experiments, it is shown that RPSM is a simple, effective, and powerful method for seeking approximate analytic solutions of fractional differential equations.
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14

Osaji, A., and H. Farrokhfal. "Extraction and Solution of the Gyroplane Trim Equations." Open Aerospace Engineering Journal 2, no. 1 (August 13, 2009): 10–18. http://dx.doi.org/10.2174/1874146000902010010.

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Extraction and solution of the gyroplane trim equations are the goal of this paper. At first according to forces and moments acting on gyroplane and the different parts of gyroplane, the six equations of the rigid body will be extracted. Because of the trim conditions, angular velocity and linear acceleration are considered to be zero. Then the energy balance equation will be derived by modeling forces and velocities. The energy balance equation shows the advancing efficient power, which is derived from the engine, is equal to all depleted powers (induced power, profile power, main rotor power, parasite power, climb power) by the gyroplane. Then by modeling non-dimensional velocities in the parallel and perpendicular directions of the main rotor reference plane, the main rotor momentum equation will be extracted. The forces of each different parts of the gyroplane will be derived according to the trim control parameters in the body axes. They will be assigned into the rigid body equations of motion. By solving the rigid body, energy balance and main rotor momentum equations, for several flight scenarios, the pilot trim control parameters (containing thrust, angle of attack for reference plane, pilot blade pitch angle and Rudder angle) will be obtained.
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15

Grigor'ev, A. A., and V. I. Gromak. "THE POWER EXPANSIONS OF THE SOLUTIONS OF THE FIRST PAINLEVÉ HIERARCHY." Mathematical Modelling and Analysis 11, no. 4 (December 31, 2006): 389–98. http://dx.doi.org/10.3846/13926292.2006.9637326.

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In this paper we consider a hierarchy of the first Painlevé equation's higher order analogues. For these equations three types of power expansions, i.e. holomorphic, polar and asymptotic are found. As an example the equation of the fourth order is considered.
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16

Wang, Zhihua, Xiuming Dong, Themistocles M. Rassias, and Soon-Mo Jung. "STABILITY OF ZEROS OF POWER SERIES EQUATIONS." Bulletin of the Korean Mathematical Society 51, no. 1 (January 31, 2014): 77–82. http://dx.doi.org/10.4134/bkms.2014.51.1.077.

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17

Zhao, L. "Power Concavity for Doubly Nonlinear Parabolic Equations." Journal of Mathematical Study 50, no. 2 (June 2017): 190–98. http://dx.doi.org/10.4208/jms.v50n2.17.05.

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18

Withers, Christopher S., and Saralees Nadarajah. "Power series solutions to Volterra integral equations." Applied Mathematics and Computation 218, no. 5 (November 2011): 2353–63. http://dx.doi.org/10.1016/j.amc.2011.07.046.

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19

Mistry, Ravi, Sudhaker Upadhyay, Ahmed Farag Ali, and Mir Faizal. "Hawking radiation power equations for black holes." Nuclear Physics B 923 (October 2017): 378–93. http://dx.doi.org/10.1016/j.nuclphysb.2017.08.010.

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20

León, Jorge A., David Nualart, and Samy Tindel. "Young differential equations with power type nonlinearities." Stochastic Processes and their Applications 127, no. 9 (September 2017): 3042–67. http://dx.doi.org/10.1016/j.spa.2017.01.007.

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21

Chakraborty, Prakash, and Samy Tindel. "Rough differential equations with power type nonlinearities." Stochastic Processes and their Applications 129, no. 5 (May 2019): 1533–55. http://dx.doi.org/10.1016/j.spa.2018.05.010.

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22

Bajc, Drago. "97.01 Power solutions of some Diophantine equations." Mathematical Gazette 97, no. 538 (March 2013): 107–10. http://dx.doi.org/10.1017/s0025557200005489.

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23

Bidkham, M., H. A. Soleiman Mezerji, and M. Eshaghi Gordji. "Hyers-Ulam Stability of Power Series Equations." Abstract and Applied Analysis 2011 (2011): 1–6. http://dx.doi.org/10.1155/2011/194948.

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24

Fok, Yu‐Si, and Shan‐hsin Chiang. "Upward Infiltration Equations in Power‐Law Form." Journal of Irrigation and Drainage Engineering 113, no. 4 (November 1987): 595–601. http://dx.doi.org/10.1061/(asce)0733-9437(1987)113:4(595).

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25

Roxburgh, I. W., and L. M. Stockman. "Power series solutions of the polytrope equations." Monthly Notices of the Royal Astronomical Society 303, no. 3 (March 1, 1999): 466–70. http://dx.doi.org/10.1046/j.1365-8711.1999.02219.x.

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26

Merle, F. "nonlinear Schr�dinger equations with critical power." Duke Mathematical Journal 69, no. 2 (February 1993): 427–54. http://dx.doi.org/10.1215/s0012-7094-93-06919-0.

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27

Gella, Otto, and Günter Lettl. "Power series and zeroes of trinomial equations." Aequationes Mathematicae 42, no. 1 (August 1991): 297. http://dx.doi.org/10.1007/bf01818498.

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28

Wu, Yingquan. "More on solving systems of power equations." Mathematics of Computation 79, no. 272 (2010): 2317. http://dx.doi.org/10.1090/s0025-5718-10-02363-x.

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29

Berry, T. "Parallel processing of sparse power system equations." IEE Proceedings - Generation, Transmission and Distribution 141, no. 1 (1994): 68. http://dx.doi.org/10.1049/ip-gtd:19949756.

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30

Bykov, V. I., A. M. Kytmanov, and S. G. Myslivets. "Power sums of nonlinear systems of equations." Doklady Mathematics 76, no. 2 (October 2007): 641–44. http://dx.doi.org/10.1134/s1064562407050018.

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31

SAYERS, STEPHEN P., DAVID V. HARACKIEWICZ, EVERETT A. HARMAN, PETER N. FRYKMAN, and MICHAEL T. ROSENSTEIN. "Cross-validation of three jump power equations." Medicine & Science in Sports & Exercise 31, no. 4 (April 1999): 572–77. http://dx.doi.org/10.1097/00005768-199904000-00013.

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32

Cella, Otto, and Günter Lettl. "Power series and zeroes of trinomial equations." Aequationes Mathematicae 43, no. 1 (February 1992): 94–102. http://dx.doi.org/10.1007/bf01840478.

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33

De la Peña, Luis, Ana María Cetto, and Andrea Valdés-Hernández. "Power and beauty of the Lagrange equations." Revista Mexicana de Física E 17, no. 1 Jan-Jun (January 28, 2020): 47. http://dx.doi.org/10.31349/revmexfise.17.47.

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The Lagrangian formulation of the equations of motion for point particles isusually presented in classical mechanics as the outcome of a series ofinsightful algebraic transformations or, in more advanced treatments, as theresult of applying a variational principle. In this paper we stress two mainreasons for considering the Lagrange equations as a fundamental descriptionof the dynamics of classical particles. Firstly, their structure can benaturally disclosed from the existence of integrals of motion, in a waythat, though elementary and easy to prove, seems to be less popular--or less frequently made explicit-- than others insupport of the Lagrange formulation. The second reason is that the Lagrangeequations preserve their form in \emph{any} coordinate system --even in moving ones, if required. Their covariant nature makes themparticularly suited to deal with dynamical problems in curved spaces orinvolving (holonomic) constraints. We develop the above and related ideas inclear and simple terms, keeping them throughout at the level of intermediatecourses in classical mechanics. This has the advantage of introducing sometools and concepts that are useful at this stage, while they may also serveas a bridge to more advanced courses.
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34

Leonidopoulos, Georgios. "Linear power system equations and security assessment." International Journal of Electrical Power & Energy Systems 13, no. 2 (April 1991): 100–102. http://dx.doi.org/10.1016/0142-0615(91)90032-q.

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35

Ferrero, Alberto, Hans-Christoph Grunau, and Paschalis Karageorgis. "Supercritical biharmonic equations with power-type nonlinearity." Annali di Matematica Pura ed Applicata 188, no. 1 (March 26, 2008): 171–85. http://dx.doi.org/10.1007/s10231-008-0070-9.

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36

Dubský, P. "Simple computer solution of coupled power equations." Optical and Quantum Electronics 21, no. 6 (November 1989): 511–15. http://dx.doi.org/10.1007/bf02189132.

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37

Jesus, C. M. S. C., and L. A. F. M. Ferreira. "Complete adjoint-based incremental power flow equations." Electric Power Systems Research 79, no. 7 (July 2009): 1136–44. http://dx.doi.org/10.1016/j.epsr.2009.02.002.

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38

Omuraliev, Asan S., and Élla D. Abylaeva. "Ordinary differential equations with power boundary layers." Journal of Mathematical Sciences 242, no. 3 (August 29, 2019): 427–31. http://dx.doi.org/10.1007/s10958-019-04487-4.

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39

Adomian, G., and R. Rach. "Nonlinear differential equations with negative power nonlinearities." Journal of Mathematical Analysis and Applications 112, no. 2 (December 1985): 497–501. http://dx.doi.org/10.1016/0022-247x(85)90258-6.

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40

Lara-Sánchez, Amador J., María L. Zagalaz, Daniel Berdejo-del-Fresno, and Emilio J. Martínez-López. "Jump Peak Power Assessment Through Power Prediction Equations in Different Samples." Journal of Strength and Conditioning Research 25, no. 7 (July 2011): 1957–62. http://dx.doi.org/10.1519/jsc.0b013e3181e06ef8.

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41

CANAVAN, PAUL K., and JASON D. VESCOVI. "Evaluation of Power Prediction Equations: Peak Vertical Jumping Power in Women." Medicine & Science in Sports & Exercise 36, no. 9 (September 2004): 1589–93. http://dx.doi.org/10.1249/01.mss.0000139802.96395.ac.

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42

Yousefi, Mousa, Ziaadin Daie Koozehkanani, Jafar Sobhi, Hamid Jangi, and Nasser Nasirezadeh. "Efficiency Analysis of Low Power Class-E Power Amplifier." Modern Applied Science 8, no. 5 (August 5, 2014): 19. http://dx.doi.org/10.5539/mas.v8n5p19.

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This paper presents an analysis of effect of inductor and switch losses on output power and efficiency of low power class-E power amplifier. This structure is suitable for integrated circuit implementation. Since on chip inductors have large losses than the other elements, the effect of their losses on efficiency has been investigated. Equations for the efficiency have been derived and plotted versus the value of inductors and switch losses. Derived equations are evaluated using MATLAB. Also, Cadence Spectre has been used for schematic simulation. Results show a fair matching between simulated power loss and efficiency and MATLAB evaluations. Considering the analysis, the proposed power amplifier shows about 13 % improvement in power effiency at 400 MHz and -2 dBm output power. It is simulated in 0.18 ?m CMOS technology.
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43

Kwon, Y. S., and K. T. Kim. "Densification Forming of Alumina Powder—Effects of Power Law Creep and Friction." Journal of Engineering Materials and Technology 118, no. 4 (October 1, 1996): 471–77. http://dx.doi.org/10.1115/1.2805944.

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High temperature forming processes of alumina powder compacts were analyzed by using constitutive equations which are capable of predicting densification and grain growth under diffusional creep and power law creep. Experimental results for alumina powder compacts were compared with finite element calculations by using the constitutive equations. The effects of friction between alumina powder compact and punches during sinter forging of alumina powder compacts were also investigated. Densification mechanism maps of alumina powder, which can be used for the optimization of various process variables, were constructed under hot pressing and general states of stresses.
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44

Atangana, Abdon, and Kolade M. Owolabi. "New numerical approach for fractional differential equations." Mathematical Modelling of Natural Phenomena 13, no. 1 (2018): 3. http://dx.doi.org/10.1051/mmnp/2018010.

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In the present case, we propose the correct version of the fractional Adams-Bashforth methods which take into account the nonlinearity of the kernels including the power law for the Riemann-Liouville type, the exponential decay law for the Caputo-Fabrizio case and the Mittag-Leffler law for the Atangana-Baleanu scenario.The Adams-Bashforth method for fractional differentiation suggested and are commonly use in the literature nowadays is not mathematically correct and the method was derived without taking into account the nonlinearity of the power law kernel. Unlike the proposed version found in the literature, our approximation, in all the cases, we are able to recover the standard case whenever the fractional powerα= 1. Numerical results are finally given to justify the effectiveness of the proposed schemes.
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45

Shepstone, N. M. "Teaching Electrical Power Systems Using Computer Simulations." International Journal of Electrical Engineering & Education 40, no. 1 (January 2003): 72–78. http://dx.doi.org/10.7227/ijeee.40.1.8.

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A computer program has been developed at the Manukau Institute of Technology that can be used for teaching and researching short, medium and long overhead power lines. The program makes use of interconnected icons rather than differential equations written in computer code (text). By using programs consisting of graphical icons it is far easier for students to visualise the power line that they are studying and in addition it makes it simple for them to modify and update the program. Until recently it has been difficult to teach overhead power lines in a meaningful way because the equations modelling the transient behaviour of lines are systems of differential equations and the equations modelling the steady-state behaviour are a set of hyperbolic (or exponential) equations. Both these sets of equations are difficult for students to visualise and interpret. Furthermore, overhead line laboratory exercises that produce realistic results for students are very difficult to arrange in most university laboratories. The program developed at Manukau Institute of Technology overcomes these problems.
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46

Yang, Zhifang, Haiwang Zhong, Qing Xia, Anjan Bose, and Chongqing Kang. "Optimal power flow based on successive linear approximation of power flow equations." IET Generation, Transmission & Distribution 10, no. 14 (November 4, 2016): 3654–62. http://dx.doi.org/10.1049/iet-gtd.2016.0547.

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47

Ghadimi, Noradin. "Two new methods for power flow tracing using bus power balance equations." Journal of Central South University 21, no. 7 (July 2014): 2712–18. http://dx.doi.org/10.1007/s11771-014-2233-8.

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48

Ayuev, B., V. Davydov, P. Erokhin, V. Neuymin, and A. Pazderin. "The Geometry of Power Systems Steady-State Equations– Part I: Power Surface." Energy Systems Research, no. 3(11) (December 27, 2020): 37–46. http://dx.doi.org/10.38028/esr.2020.03.0005.

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Steady-state equations play a fundamental role in the theory of power systems and computation practice. These equations are directly or mediately used almost in all areas of the power system state theory, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I considers steady states of the power system as a surface in the power space. A power flow feasibility region is shown to be widely used in power system theories. This region is a projection of this surface along the axis of a slack bus active power onto a subspace of other buses power. The findings have revealed that the obtained power flow feasibility regions, as well as marginal states of the power system, depend on a slack bus location. Part II is devoted to an analytical study of the power surface of power system steady states.
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49

Olson, Alton T. "Difference Equations." Mathematics Teacher 81, no. 7 (October 1988): 540–44. http://dx.doi.org/10.5951/mt.81.7.0540.

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Much talk is heard these days about the importance of including topics from discrete mathematics in our secondary mathematics curriculum. They are characterized by their treatment of discrete quantities rather than continuous quantities and limit processes. The mathematics of continuity and limit processes leading into calculus will continue to be a major part of our mathematics curriculum. At the same time topics from discrete mathematics will take on more importance because of the presence of inexpensive computing power that is fundamentally finite and discrete.
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50

Li, Shenghu. "Configuration of Jacobian Matrix in Steady-State Voltage Stability Analysis Based on Rotor Flux Dynamics of Rotating Machines." International Journal of Emerging Electric Power Systems 14, no. 3 (June 19, 2013): 239–44. http://dx.doi.org/10.1515/ijeeps-2012-0013.

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Abstract In the existing literatures, modal analysis for steady-state voltage stability is based on the reduced Jacobian matrix, i.e. active power equations are eliminated, and reactive power equations of the constant power/voltage buses (PV buses) are ignored in the polar coordinate expression, which is actually designed for voltage controllability, but questionable for voltage stability.In this article, power outputs of the rotating machines are newly decomposed to the steady-state and dynamic components, with the latter proportional to derivative of the rotor flux. Therefore, neither the active nor the reactive power equations of the rotating machines may be eliminated or ignored in the Jacobian matrix. Only the static buses with constant load impedance should be eliminated. Numerical results show that elimination of active power equations or ignorance of reactive power equations of the rotating machines will yield optimistic stability margins, while including power equations of static load buses yields pessimistic stability margin. It is also find that more static load component yields larger stability margin.
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