Relevant bibliographies by topics / Equation

Academic literature on the topic 'Equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2024

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Journal articles on the topic "Equation"

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Karakostas, George L. "Asymptotic behavior of a certain functional equation via limiting equations." Czechoslovak Mathematical Journal 36, no. 2 (1986): 259–67. http://dx.doi.org/10.21136/cmj.1986.102089.

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Parkala, Naresh, and Upender Reddy Gujjula. "Mohand Transform for Solution of Integral Equations and Abel's Equation." International Journal of Science and Research (IJSR) 13, no. 5 (May 5, 2024): 1188–91. http://dx.doi.org/10.21275/sr24512145111.

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Domoshnitsky, Alexander, and Roman Koplatadze. "On Asymptotic Behavior of Solutions of Generalized Emden-Fowler Differential Equations with Delay Argument." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/168425.

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The following differential equationu(n)(t)+p(t)|u(σ(t))|μ(t) sign u(σ(t))=0is considered. Herep∈Lloc(R+;R+), μ∈C(R+;(0,+∞)), σ∈C(R+;R+), σ(t)≤t, andlimt→+∞⁡σ(t)=+∞. We say that the equation is almost linear if the conditionlimt→+∞⁡μ(t)=1is fulfilled, while iflim⁡supt→+∞⁡μ(t)≠1orlim⁡inft→+∞⁡μ(t)≠1, then the equation is an essentially nonlinear differential equation. In the case of almost linear and essentially nonlinear differential equations with advanced argument, oscillatory properties have been extensively studied, but there are no results on delay equations of this sort. In this paper, new sufficient conditions implying PropertyAfor delay Emden-Fowler equations are obtained.
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Becker, Leigh, Theodore Burton, and Ioannis Purnaras. "Complementary equations: a fractional differential equation and a Volterra integral equation." Electronic Journal of Qualitative Theory of Differential Equations, no. 12 (2015): 1–24. http://dx.doi.org/10.14232/ejqtde.2015.1.12.

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N O, Onuoha. "Transformation of Parabolic Partial Differential Equations into Heat Equation Using Hopf Cole Transform." International Journal of Science and Research (IJSR) 12, no. 6 (June 5, 2023): 1741–43. http://dx.doi.org/10.21275/sr23612082710.

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Zhao, Wenling, Hongkui Li, Xueting Liu, and Fuyi Xu. "Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations." Mathematical Problems in Engineering 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/672695.

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We study the Hermitian positive definite solutions of the nonlinear matrix equationX+A∗X−2A=I, whereAis ann×nnonsingular matrix. Some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation are given. However, based on the necessary and sufficient conditions, some properties and the equivalent equations ofX+A∗X−2A=Iare presented while the matrix equation has a Hermitian positive definite solution.
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Yan, Zhenya. "Complex PT -symmetric nonlinear Schrödinger equation and Burgers equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (April 28, 2013): 20120059. http://dx.doi.org/10.1098/rsta.2012.0059.

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The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg–de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross–Pitaevskii equation in Bose–Einstein condensates) with several complex -symmetric potentials. Finally, some complex -symmetric extension principles are used to generate some complex -symmetric nonlinear wave equations starting from both -symmetric (e.g. the KdV equation) and non- -symmetric (e.g. the Burgers equation) nonlinear wave equations. In particular, we discuss exact solutions of some representative ones of the complex -symmetric Burgers equation in detail.
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Prokhorova, M. F. "Factorization of the reaction-diffusion equation, the wave equation, and other equations." Proceedings of the Steklov Institute of Mathematics 287, S1 (November 27, 2014): 156–66. http://dx.doi.org/10.1134/s0081543814090156.

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Shi, Yong-Guo, and Xiao-Bing Gong. "Linear functional equations involving Babbage’s equation." Elemente der Mathematik 69, no. 4 (2014): 195–204. http://dx.doi.org/10.4171/em/263.

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Mickens, Ronald E. "Difference equation models of differential equations." Mathematical and Computer Modelling 11 (1988): 528–30. http://dx.doi.org/10.1016/0895-7177(88)90549-3.

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Dissertations / Theses on the topic "Equation"

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Thompson, Jeremy R. (Jeremy Ray). "Physical Motivation and Methods of Solution of Classical Partial Differential Equations." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc277898/.

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We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.
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Howard, Tamani M. "Hyperbolic Monge-Ampère Equation." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5322/.

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In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses, and explore the effect of some imposed boundary conditions on the solutions. Next, we prove convergence of the continuous Sobolev steepest descent to show local existence of solutions to the hyperbolic Monge-Ampère equation. Finally, we prove some results on the Sobolev gradients that mainly arise from general nonlinear differential equations.
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Vong, Seak Weng. "Two problems on the Navier-Stokes equations and the Boltzmann equation /." access full-text access abstract and table of contents, 2005. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b19885805a.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2005.
"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy" Includes bibliographical references (leaves 72-77)
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Guan, Meijiao. "Global questions for evolution equations Landau-Lifshitz flow and Dirac equation." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/22491.

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This thesis concerns the stationary solutions and their stability for some evolution equations from physics. For these equations, the basic questions regarding the solutions concern existence, uniqueness, stability and singularity formation. In this thesis, we consider two different classes of equations: the Landau-Lifshitz equations, and nonlinear Dirac equations. There are two different definitions of stationary solutions. For the Landau-Lifshitz equation, the stationary solution is time-independent, while for the Dirac equation, the stationary solution, also called solitary wave solution or ground state solution, is a solution which propagates without changing its shape. The class of Landau-Lifshitz equations (including harmonic map heat flow and Schrödinger map equations) arises in the study of ferromagnets (and anti-ferromagnets), liquid crystals, and is also very natural from a geometric standpoint. Harmonic maps are the stationary solutions to these equations. My thesis concerns the problems of singularity formation vs. global regularity and long time asymptotics when the target space is a 2-sphere. We consider maps with some symmetry. I show that for m-equivariant maps with energy close to the harmonic map energy, the solutions to Landau-Lifshitz equations are global in time and converge to a specific family of harmonic maps for big m, while for m =1, a finite time blow up solution is constructed for harmonic map heat flow. A model equation for Schrödinger map equations is also studied in my thesis. Global existence and scattering for small solutions and local well-posedness for solutions with finite energy are proved. The existence of standing wave solutions for the nonlinear Dirac equation is studied in my thesis. I construct a branch of solutions which is a continuous curve by a perturbation method. It refines the existing results that infinitely many stationary solutions exist, but with uniqueness and continuity unknown. The ground state solutions of nonlinear Schrodinger equations yield solutions to nonlinear Dirac equations. We also show that this branch of solutions is unstable. This leads to a rigorous proof of the instability of the ground states, confirming non-rigorous results in the physical literature.
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Jumarhon, Bartur. "The one dimensional heat equation and its associated Volterra integral equations." Thesis, University of Strathclyde, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342381.

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Banerjee, Paromita. "Numerical Methods for Stochastic Differential Equations and Postintervention in Structural Equation Models." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1597879378514956.

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Wang, Jun. "Integral Equation Methods for the Heat Equation in Moving Geometry." Thesis, New York University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10618746.

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Many problems in physics and engineering require the solution of the heat equation in moving geometry. Integral representations are particularly appropriate in this setting since they satisfy the governing equation automatically and, in the homogeneous case, require the discretization of the space-time boundary alone. Unlike methods based on direct discretization of the partial differential equation, they are unconditonally stable. Moreover, while a naive implementation of this approach is impractical, several efforts have been made over the past few years to reduce the overall computational cost. Of particular note are Fourier-based methods which achieve optimal complexity so long as the time step Δt is of the same order as Δx, the mesh size in the spatial variables. As the time step goes to zero, however, the cost of the Fourier-based fast algorithms grows without bound. A second difficulty with existing schemes has been the lack of efficient, high-order local-in-time quadratures for layer heat potentials.

In this dissertation, we present a new method for evaluating heat potentials that makes use of a spatially adaptive mesh instead of a Fourier series, a new version of the fast Gauss transform, and a new hybrid asymptotic/numerical method for local-in-time quadrature. The method is robust and efficient for any Δt, with essentially optimal computational complexity. We demonstrate its performance with numerical examples and discuss its implications for subsequent work in diffusion, heat flow, solidification and fluid dynamics.

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Grundström, John. "The Sustainability Equation." Thesis, Umeå universitet, Arkitekthögskolan vid Umeå universitet, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-133151.

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Gylys-Colwell, Frederick Douglas. "An inverse problem for the anisotropic time independent wave equation /." Thesis, Connect to this title online; UW restricted, 1993. http://hdl.handle.net/1773/5726.

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Shedlock, Andrew James. "A Numerical Method for solving the Periodic Burgers' Equation through a Stochastic Differential Equation." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103947.

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The Burgers equation, and related partial differential equations (PDEs), can be numerically challenging for small values of the viscosity parameter. For example, these equations can develop discontinuous solutions (or solutions with large gradients) from smooth initial data. Aside from numerical stability issues, standard numerical methods can also give rise to spurious oscillations near these discontinuities. In this study, we consider an equivalent form of the Burgers equation given by Constantin and Iyer, whose solution can be written as the expected value of a stochastic differential equation. This equivalence is used to develop a numerical method for approximating solutions to Burgers equation. Our preliminary analysis of the algorithm reveals that it is a natural generalization of the method of characteristics and that it produces approximate solutions that actually improve as the viscosity parameter vanishes. We present three examples that compare our algorithm to a recently published reference method as well as the vanishing viscosity/entropy solution for decreasing values of the viscosity.
Master of Science
Burgers equation is a Partial Differential Equation (PDE) used to model how fluids evolve in time based on some initial condition and viscosity parameter. This viscosity parameter helps describe how the energy in a fluid dissipates. When studying partial differential equations, it is often hard to find a closed form solution to the problem, so we often approximate the solution with numerical methods. As our viscosity parameter approaches 0, many numerical methods develop problems and may no longer accurately compute the solution. Using random variables, we develop an approximation algorithm and test our numerical method on various types of initial conditions with small viscosity coefficients.
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Books on the topic "Equation"

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Selvadurai, A. P. S. Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000.

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Tam, Kenneth. The earther equation: The fourth equations novel. Waterloo, ON: Iceberg Pub., 2005.

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Tam, Kenneth. The vengeance equation: The sixth equations novel. Waterloo, Ont: Iceberg, 2007.

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Tam, Kenneth. The alien equation: The second equations novel. Waterloo, ON: Iceberg Pub., 2004.

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Tam, Kenneth. The human equation: The first equations novel. Waterloo, ON: Iceberg Pub., 2003.

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Tam, Kenneth. The genesis equation: The fifth equations novel. Waterloo, ON: Iceberg, 2006.

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Bejenaru, Ioan. Near soliton evolution for equivariant Schrödinger maps in two spatial dimensions. Providence, Rhode Island: American Mathematical Society, 2013.

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Jensen, Jane. Dante's equation. London: Orbit, 2003.

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Barbeau, Edward J. Pell’s Equation. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/b97610.

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Dante's equation. London: Orbit, 2004.

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Book chapters on the topic "Equation"

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Horgmo Jæger, Karoline, and Aslak Tveito. "The Cable Equation." In Differential Equations for Studies in Computational Electrophysiology, 79–91. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30852-9_9.

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AbstractIn Chapter 6, we studied a simple version of the cable equation, where a diffusion term was added to the FitzHugh-Nagumo equations. In this chapter, we will revisit the cable equation and go through a simple derivation of the model. In addition, we will consider the numerical solution of the cable equation for a neuronal axon with membrane dynamics modeled by the Hodgkin-Huxley model.
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Horgmo Jæger, Karoline, and Aslak Tveito. "A Simple Cable Equation." In Differential Equations for Studies in Computational Electrophysiology, 47–52. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30852-9_6.

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AbstractThe cable equation was first derived to model transport of electrical signals in telegraphic cables. But it later gained enormous popularity as a model of transport of electrical signals along a neuronal axon. In Chapter 9, we will discuss how this equation is derived and how the different terms in the equation come about. But here, we will just take a simple version of the equations for granted and then try to solve them. We will observe that the few techniques we learned above are actually sufficient to solve the non-linear reaction-diffusion equations we consider here.
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Kurasov, Pavel. "The Characteristic Equation." In Operator Theory: Advances and Applications, 97–122. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/978-3-662-67872-5_5.

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AbstractThis chapter is devoted to compact graphs formed by a finite number of bounded intervals. We already know that the spectrum of the corresponding magnetic Schrödinger operator is discrete and our main goal is to obtain characteristic equations determining the spectrum (eigenvalues) precisely. We describe here three different methods to obtain an explicit characteristic equation.
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Kavdia, Mahendra. "Parabolic Differential Equations, Diffusion Equation." In Encyclopedia of Systems Biology, 1621–24. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_273.

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Sleeman, Brian D. "Partial Differential Equations, Poisson Equation." In Encyclopedia of Systems Biology, 1635–38. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_274.

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Clayton, Richard H. "Partial Differential Equations, Wave Equation." In Encyclopedia of Systems Biology, 1638–40. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_275.

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Brenig, Wilhelm. "Rate Equations (Master Equation, Stosszahlansatz)." In Statistical Theory of Heat, 158–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-74685-7_32.

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Rapp, Christoph. "Basic equations." In Hydraulics in Civil Engineering, 51–69. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-54860-4_5.

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AbstractIn Chapter 5 basic fluid mechanical equations are derived step by step. First, the continuity equation is deduced with the help of a ballon which passes through a constriction. Second, Cauchy’s equation of motion is set up with the stresses acting on a fluid volume which is described once more with a balloon that moves upon application of stress and gravity. The constitutive equation which describes the properties of the fluid considered is elaborated also from the scratch. With the above mentioned steps, it is easy to reach to the Euler and Navier-Stokes equations from which the Bernoulli and the momentum equation are derived.
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Parker, David F. "Laplace’s Equation and Poisson’s Equation." In Springer Undergraduate Mathematics Series, 55–76. London: Springer London, 2003. http://dx.doi.org/10.1007/978-1-4471-0019-5_4.

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Goodair, Daniel, and Dan Crisan. "On the 3D Navier-Stokes Equations with Stochastic Lie Transport." In Mathematics of Planet Earth, 53–110. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-40094-0_4.

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AbstractWe prove the existence and uniqueness of maximal solutions to the 3D SALT (Stochastic Advection by Lie Transport) Navier-Stokes Equation in velocity and vorticity form, on the torus and the bounded domain respectively. In particular we demonstrate the efficacy of Goodair et al. (Existence and Uniqueness of Maximal Solutions to SPDEs with Applications to Viscous Fluid Equations, 2023. Stochastics and Partial Differential Equations: Analysis and Computations, pp.1-64) in showing the well-posedness for both the velocity and vorticity form of the equation, as well as obtaining the first analytically strong existence result for a fluid equation perturbed by Lie transport noise on a bounded domain.
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Conference papers on the topic "Equation"

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Cohen, Leon. "Phase-space equation for wave equations." In ICA 2013 Montreal. ASA, 2013. http://dx.doi.org/10.1121/1.4800400.

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Roy, Subhro, Shyam Upadhyay, and Dan Roth. "Equation Parsing : Mapping Sentences to Grounded Equations." In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2016. http://dx.doi.org/10.18653/v1/d16-1117.

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Mikhailov, M. S., and A. A. Komarov. "Combining Parabolic Equation Method with Surface Integral Equations." In 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring). IEEE, 2019. http://dx.doi.org/10.1109/piers-spring46901.2019.9017786.

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TAKEYAMA, YOSHIHIRO. "DIFFERENTIAL EQUATIONS COMPATIBLE WITH BOUNDARY RATIONAL qKZ EQUATION." In Proceedings of the Infinite Analysis 09. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814324373_0021.

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Isserstedt, Philipp, Christian Fischer, and Thorsten Steinert. "QCD’s equation of state from Dyson-Schwinger equations." In FAIR next generation scientists - 7th Edition Workshop. Trieste, Italy: Sissa Medialab, 2023. http://dx.doi.org/10.22323/1.419.0024.

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Sharifi, J., and H. Momeni. "Optimal control equation for quantum stochastic differential equations." In 2010 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010. http://dx.doi.org/10.1109/cdc.2010.5717172.

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Freire, Igor Leite, and Priscila Leal da Silva. "An equation unifying both Camassa-Holm and Novikov equations." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0304.

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Pang, Subeen, and George Barbastathis. "Robust Transport-of-Intensity Equation with Neural Differential Equations." In Computational Optical Sensing and Imaging. Washington, D.C.: Optica Publishing Group, 2023. http://dx.doi.org/10.1364/cosi.2023.cth4d.4.

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We solve the transport-of-intensity equation by estimating the intensity derivative using the method of neural differential equations. We observe strong robustness to artifacts from ill-conditionedness and measurement noise.
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Bui, T. T., and V. Popov. "Radial basis integral equation method for Navier-Stokes equations." In BEM/MRM 2009. Southampton, UK: WIT Press, 2009. http://dx.doi.org/10.2495/be090131.

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Vălcan, Teodor-Dumitru. "From Diofantian Equations To Matricial Equations (Ii) -Generalizations Of The Pythagorean Equation-." In 9th International Conference Education, Reflection, Development. European Publisher, 2022. http://dx.doi.org/10.15405/epes.22032.63.

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Reports on the topic "Equation"

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Lettau, Martin, and Sydney Ludvigson. Euler Equation Errors. Cambridge, MA: National Bureau of Economic Research, September 2005. http://dx.doi.org/10.3386/w11606.

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Boyd, Zachary M., Scott D. Ramsey, and Roy S. Baty. Symmetries of the Euler compressible flow equations for general equation of state. Office of Scientific and Technical Information (OSTI), October 2015. http://dx.doi.org/10.2172/1223765.

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Mickens, Ronald E. Mathematical and Numerical Studies of Nonstandard Difference Equation Models of Differential Equations. Office of Scientific and Technical Information (OSTI), December 2008. http://dx.doi.org/10.2172/965764.

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Grinfeld, M. A. Operational Equations of State. 1. A Novel Equation of State for Hydrocode. Fort Belvoir, VA: Defense Technical Information Center, September 2011. http://dx.doi.org/10.21236/ada553223.

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Menikoff, Ralph. JWL Equation of State. Office of Scientific and Technical Information (OSTI), December 2015. http://dx.doi.org/10.2172/1229709.

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Grove, John W. xRage Equation of State. Office of Scientific and Technical Information (OSTI), August 2016. http://dx.doi.org/10.2172/1304734.

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SCIENCE AND TECHNOLOGY CORP HAMPTON VA. Analytic Parabolic Equation Solutions. Fort Belvoir, VA: Defense Technical Information Center, November 1989. http://dx.doi.org/10.21236/ada218588.

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Fujisaki, Masatoshi. Normed Bellman Equation with Degenerate Diffusion Coefficients and Its Application to Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada190319.

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Uhlman, J. S., and Jr. An Integral Equation Formulation of the Equations of Motion of an Incompressible Fluid. Fort Belvoir, VA: Defense Technical Information Center, July 1992. http://dx.doi.org/10.21236/ada416252.

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Grinfeld, Michael. The Operational Equations of State, 4: The Dulong-Petit Equation of State for Hydrocode. Fort Belvoir, VA: Defense Technical Information Center, July 2012. http://dx.doi.org/10.21236/ada568915.

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