Relevant bibliographies by topics / Equation

Contents

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

Academic literature on the topic 'Equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Equation"

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Sriram, S., та P. Veeramallan. "On the Integer Solution of the Transcendental Equation √2𝑧−4=√𝑥+√𝐶𝑦± √𝑥−√𝐶𝑦". Indian Journal of Advanced Mathematics (IJAM) 2, № 1 (2022): 1–4. https://doi.org/10.54105/ijam.C1120.041322.

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<strong>Abstract:</strong> Let C be a positive non-square integer. In this paper, we look at the complete solutions of the Transcendental equation &radic;𝟐𝒛&minus;𝟒=&radic;𝒙+&radic;𝑪𝒚&plusmn; &radic;𝒙&minus;&radic;𝑪𝒚 , where 𝒙𝟐&minus;𝑪𝒚𝟐=𝜶𝟐 or 𝟐𝟐𝒕. In addition, we find repeated relationships in the solutions to this figure.
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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 (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
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Zead, Yahya Ali Allawee. "Application New Iterative Method For Solving Nonlinear Burger's Equation And Coupled Burger's Equations." International Journal of Computer Science Issues 15, no. 3 (2018): 31–35. https://doi.org/10.5281/zenodo.1292414.

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In the recent research , the numerical solution of Nonlinear Burger&rsquo;s equation and coupled Burger&rsquo;s equation is obtained Nonlinear using a New Iterative Method (NIM) is being proposed to obtain. We have shown that the NIM solution is more accurate as compared to the techniques like, Burger&rsquo;s equation and coupled Burger&rsquo;s equation method and HPM method. more, results also demonstrate that NIM solution is more reliable, easy to compute and computationally fast as compared to HPM method.
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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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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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Bobylev, Alexander Vasilievich, and Sergei Borisovitch Kuksin. "Boltzmann equation and wave kinetic equations." Keldysh Institute Preprints, no. 31 (2023): 1–20. http://dx.doi.org/10.20948/prepr-2023-31.

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The well-known nonlinear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim – Uehling – Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann equation. To this goal we introduce the generalized kinetic equation that depends on a function of four real variables F(x1; x2; x3; x4). The function F is assumed to satisfy certain commutation relations. The general properties of this equation are studied. It is shown that the above mentioned kinetic equations correspond to different forms of the function (poly
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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 (2023): 1741–43. http://dx.doi.org/10.21275/sr23612082710.

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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 (2014): 156–66. http://dx.doi.org/10.1134/s0081543814090156.

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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 equatio
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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.<br>"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
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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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<p> 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 computation
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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 eq
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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. Springer Berlin Heidelberg, 2000.

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

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

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

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

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

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

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

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Jensen, Jane. Dante's equation. Ballantine Books, 2003.

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Magnus, Wilhelm. Hill's equation. Dover Publications, 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. 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. 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. 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. 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. 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. 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. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-74685-7_32.

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Hamilton, Mark F., and Christopher L. Morfey. "Model Equations." In Nonlinear Acoustics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58963-8_3.

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AbstractThe chapter begins with the full equations of fluid mechanics for viscous, heat conducting, homogeneous fluids. Exact implicit solutions are developed for plane waves in ideal fluids, as well as an exact nonlinear wave equation for nonplanar waves in a perfect gas. Ordering procedures are introduced that permit structured derivations of approximate wave equations accounting for quadratic nonlinearity in thermoviscous fluids. A second-order wave equation that includes both cumulative and local nonlinear effects is derived, from which are obtained the Westervelt, Burgers, and KZK equatio
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Rapp, Christoph. "Basic equations." In Hydraulics in Civil Engineering. 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 Berno
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Goodair, Daniel, and Dan Crisan. "On the 3D Navier-Stokes Equations with Stochastic Lie Transport." In Mathematics of Planet Earth. 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 an
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Conference papers on the topic "Equation"

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Wang, Lihong V. "Derivations of Bloch (Majorana-Bloch) equation, von Neumann equation, and Schrödinger-Pauli equation." In Quantum Sensing, Imaging, and Precision Metrology III, edited by Selim M. Shahriar. SPIE, 2025. https://doi.org/10.1117/12.3045250.

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Metzner, Dominik, and Lukas T. Hiller. "Comparison of Monge-Ampère equation and Poisson’s equation for holographic lighting." In Digital Holography and Three-Dimensional Imaging. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/dh.2024.w5b.3.

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Innovative lighting is an important part in lighting industry to improve safeness and visibility for example in road traffic. Developing lighting systems over the last decades, lighting systems were designed using halogen lamps to LED systems in the present. Modern lighting systems make use of holography. However, in many cases the light source is a fully coherent Laser beam that give us a precise reconstruction of the desired light distribution. In cases where the light source is a non-coherent LED, the accuracy reduces if we consider a holographic phase image created with the Gerchberg-Saxto
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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. 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. 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. 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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Reports on the topic "Equation"

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Guan, Jiajing, Sophia Bragdon, and Jay Clausen. Predicting soil moisture content using Physics-Informed Neural Networks (PINNs). Engineer Research and Development Center (U.S.), 2024. http://dx.doi.org/10.21079/11681/48794.

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Environmental conditions such as the near-surface soil moisture content are valuable information in object detection problems. However, such information is generally unobtainable at the necessary scale without active sensing. Richards’ equation is a partial differential equation (PDE) that describes the infiltration process of unsaturated soil. Solving the Richards’ equation yields information about the volumetric soil moisture content, hydraulic conductivity, and capillary pressure head. However, Richards’ equation is difficult to approximate due to its nonlinearity. Numerical solvers such as
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Lettau, Martin, and Sydney Ludvigson. Euler Equation Errors. National Bureau of Economic Research, 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), 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), 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. Defense Technical Information Center, 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), 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), 2016. http://dx.doi.org/10.2172/1304734.

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SCIENCE AND TECHNOLOGY CORP HAMPTON VA. Analytic Parabolic Equation Solutions. Defense Technical Information Center, 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. Defense Technical Information Center, 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. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada416252.

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