Relevant bibliographies by topics / Equations

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

Academic literature on the topic 'Equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Equations"

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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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Deeba, E. Y., and E. L. Koh. "The Pexider Functional Equations in Distributions." Canadian Journal of Mathematics 42, no. 2 (April 1, 1990): 304–14. http://dx.doi.org/10.4153/cjm-1990-017-6.

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The Cauchy functional equations have been studied recently for Schwartz distributions by Koh in [3]. When the solutions are locally integrate functions, the equations reduce to the classical Cauchy equations (see [1]):(1) f(x+y)=f﹛x)+f(y)(2) f(x+y)=f(x)f(y)(3) f(xy)=f(x)+f(y)(4) f(xy)=f(x)f(y).Earlier efforts to study functional equations in distributions were given by Fenyö [2]for the Hosszu’ equationsf(x + y - xy) +f(xy) =f(x) +f (y ),by Neagu [4]for the Pompeiu equationf(x+y+xy)=f(x)+f(y)+f(x)f(y)and by Swiatak [6].
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Morchało, Jarosław. "Volterra summation equations and second order difference equations." Mathematica Bohemica 135, no. 1 (2010): 41–56. http://dx.doi.org/10.21136/mb.2010.140681.

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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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Hino, Yoshiyuki, and Taro Yoshizawa. "Total stability property in limiting equations for a functional-differential equation with infinite delay." Časopis pro pěstování matematiky 111, no. 1 (1986): 62–69. http://dx.doi.org/10.21136/cpm.1986.118265.

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Kratz, Werner. "Asymptotic behaviour of Riccati's differential equation associated with self-adjoint scalar equations of even order." Czechoslovak Mathematical Journal 38, no. 2 (1988): 351–65. http://dx.doi.org/10.21136/cmj.1988.102230.

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Bosák, Miroslav, and Jiří Gregor. "On generalized difference equations." Applications of Mathematics 32, no. 3 (1987): 224–39. http://dx.doi.org/10.21136/am.1987.104253.

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Egger, Joseph, and Mauro Dall'Amico. "Empirical master equations: Numerics." Meteorologische Zeitschrift 16, no. 2 (May 7, 2007): 139–47. http://dx.doi.org/10.1127/0941-2948/2007/0196.

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Budochkina, Svetlana, and Hue Vu. "ON AN INDIRECT REPRESENTATION OF EVOLUTIONARY EQUATIONS IN THE FORM OF BIRKHOFF'S EQUATIONS." Eurasian Mathematical Journal 13, no. 3 (2022): 23–32. http://dx.doi.org/10.32523/2077-9879-2022-13-3-23-32.

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Dissertations / Theses on the topic "Equations"

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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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Moyano, Garcia Iván. "Controllability of of some kinetic equations, of parabolic degenerated equations and of the Schrödinger equation via domain transformation." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX062/document.

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Ce mémoire présente les travaux réalisés au cours de ma thèse dans le but d'étudier la contrôlabilité de quelques équations aux dérivées partielles. La première partie de cette thèse est consacrée à l'étude de la contrôlabilité de quelques équations cinétiques en différents régimes. Dans un régime collisionnel, nous étudions la contrôlabilité de l'équation de Kolmogorov, un modèle de type Fokker-Planck cinétique, posée dans l'espace de phases $R^d times R^d$. Nous obtenons la contrôlabilité à zéro de cette équation grâce à l'utilisation d'une inégalité spectrale associée à l'opérateur Laplacien dans tout l'espace. Dans un régime non-collisionnel, nous étudions la contrôlabilité de deux systèmes de couplage fluide-cinétique, les systèmes de Vlasov-Stokes et de Vlasov-Navier-Stokes, comportant des non-linéarités dues au terme de couplage. Dans ces cas, l'approche repose sur la méthode du retour.Dans la deuxième partie nous étudions la contrôlabilité d'une famille d'équations paraboliques dégénérées 1-D par la méthode de platitude, qui permet la constructions de contrôles explicites. La troisième partie porte sur le problème de la contrôlabilité de l'équation de Schrödinger par la forme du domaine, c'est-à-dire, en utilisant le domaine comme variable de contrôle. Nous obtenons un résultat de ce type dans le cas du disque unité bidimensionnel. Nos méthodes sont basées sur un résultat de contrôle exact local autour d'une certaine trajectoire, obtenu grâce au théorème d'inversion locale
This memoir presents the results obtained during my PhD, whose goal is the study of the controllability of some Partial Differential Equations.The first part of this thesis is concerned with the study of the controllability of some kinetic equations undergoing different regimes. Under a collisional regime, we study the controllability of the Kolmogorov equation, a particular case of kinetic Fokker-Planck equation, in the phase space $R^d times R^d$. We obtain the null-controllability of this equation thanks to the use of a spectral inequality associated to the Laplace operator in the whole space. Under a non-collisional regime, we study the controllability of two fluid-kinetic models, the Vlasov-Stokes system and the Vlasov-Navier-Stokes system, which exhibe nonlinearities due to the coupling terms. In those cases, the strategy relies on the Return method.In the second part, we study the controllability of a family of 1-D degenerate parabolic equations by the flatness method, which allows the construction of explicit controls.The third part is focused on the problem of the controllability of the Schrödinger equation via domain deformations, i.e., using the domain as a control. We obtain a result of this kind in the case of the two-dimensional unit disk, for radial data. Our methods are based on a local exact controllability result around a certain trajectory, obtained thanks to the Inverse Mapping theorem
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Yesilyurt, Deniz. "Solving Linear Diophantine Equations And Linear Congruential Equations." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-19247.

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This report represents GCD, euclidean algorithm, linear diophantine equation and linear congruential equation. It investigates the methods for solving linear diophantine equations and linear congruential equations in several variables. There are many examples which illustrate the methods for solving equations.
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Baker, Linda Margaret. "The companion equations and the Moyal-Nahm equations." Thesis, Durham University, 2000. http://etheses.dur.ac.uk/4257/.

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The first part of this thesis is concerned with the companion equations. These are equations of motion for the companion Lagrangian which is proposed to be the Lagrangian for a field theory associated with strings and branes, similar to the Klein-Gordon field description for particles. The form of this Lagrangian can be related to the Hamilton-Jacobi formalism for strings and branes. Some solutions to the companion equations are found and their integrability is discussed. There is an equivalence between the equations of motion for different companion Lagrangians when some constraints are applied. Under these constraints, the companion equations for a Lagrangian without a square root are equivalent to the companion equations for a Lagrangian with a square root but in one dimension less. The appearance of Universal Field Equations, generalised Bateman equations, in the companion equations leads to the study of an iterative procedure for Lagrangians which are homogeneous of weight one in the first derivatives in the fields the theory describes. The Universal Field equations appear after several iterations. Also, it is shown how Lagrangians for a large family of field theories are a divergence or vanish on the space of solutions of the equations of motion. Such theories could be called 'pseudo-topological'.The second part of this thesis is concerned with finding solutions to the Moyal-Nahm equations in four and eight dimensions. These equations are the Nahm equations, which give a set of solutions to self-dual Yang-Mills, but with the commutators replaced with Moyal brackets. Solutions are found in terms of generalised Wigner functions. Also, matrix representations of the algebra generated by the equivalent Nahm equations in eight dimensions are obtained. Solutions to the Nahm equations in eight dimensions are also given.
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Chen, Huyuan. "Fully nonlinear elliptic equations and semilinear fractional equations." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/115532.

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Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática
Esta tesis esta dividida en seis partes. La primera parte está dedicada a probar propiedades de Hadamard y teoremas del tipo de Liouville para soluciones viscosas de ecuaciones diferenciales parciales elípticas completamente no lineales con término gradiente \begin{equation}\label{eq06-10-13 1} \mathcal{M}^{-}(|x|,D^2u)+\sigma(|x|)|Du|+f(x,u)\leq 0,\quad \ x\in\Omega, \end{equation} donde $\Omega=\mathbb{R}^N$ o un dominio exterior, las funciones $\sigma:[0,\infty)\to\mathbb{R}$ y $f:\Omega\times (0,\infty)\to (0,\infty)$ son continuas las cuales satisfacen algunas condiciones extras. En la segunda parte se estudia la existencia de soluciones que explotan en la frontera para ecuaciones elípticas fraccionarias semilineales \begin{equation}\label{eq06-10-13 2} \arraycolsep=1pt \begin{array}{lll} (-\Delta)^{\alpha} u(x)+|u|^{p-1}u(x)=h(x),\quad & x\in\Omega,\\[2mm] \phantom{ (-\Delta)^{\alpha} u(x)+|u|^{p-1}} u(x)=0,\quad & x\in\bar\Omega^c,\\[2mm] \phantom{ (-\Delta)^{\alpha} \ } \lim_{x\in\Omega, x\to\partial\Omega}u(x)=+\infty, \end{array} \end{equation} donde $p>1$, $\Omega$ es un dominio abierto acotado $C^2$ de $\mathbb{R}^N(N\geq2)$, el operador $(-\Delta)^{\alpha}$ con $\alpha\in(0,1)$ es el Laplaciano fraccionario y $h:\Omega\to\R$ es una función continua la cual satisface algunas condiciones extras. Por otra parte, analizamos la unicidad y el comportamiento asimptótico de soluciones al problema (\ref{eq06-10-13 2}). El objetivo principal de la tercera parte es investigar soluciones positivas para ecuaciones elípticas fraccionarias \begin{equation}\label{eq06-10-13 3} \arraycolsep=1pt \begin{array}{lll} (-\Delta)^{\alpha} u(x)+|u|^{p-1}u(x)=0,\quad & x\in\Omega\setminus\mathcal{C},\\[2mm] \phantom{ (-\Delta)^{\alpha} u(x)+|u|^{p-1}} u(x)=0,\quad & x\in\Omega^c,\\[2mm] \phantom{ (-\Delta) \ } \lim_{x\in\Omega\setminus\mathcal{C}, \ x\to\mathcal{C}}u(x)=+\infty, \end{array} \end{equation} donde $p>1$ y $\Omega$ es un dominio abierto acotado $C^2$ de $\mathbb{R}^N(N\geq2)$, $\mathcal{C}\subset \Omega$ es el frontera de dominio $G$ que es $C^2$ y satisface $\bar G\subset\Omega$. Consideramos la existencia de soluciones positivas para el problema (\ref{eq06-10-13 3}). Mas aún, analizamos la unicidad, el comportamiento asimptótico y la no existencia al problema (\ref{eq06-10-13 3}). En la cuarta parte, estudiamos la existencia de soluciones débiles de (F) $ (-\Delta)^\alpha u+g(u)=\nu $ en un dominio $\Omega$ abierto acotado $C^2$ de $\R^N (N\ge2)$ el cual se desvanece en $\Omega^c$, donde $\alpha\in(0,1)$, $\nu$ es una medida de Radon y $g$ es una función no decreciente satisfaciendo algunas hipótesis extras. Cuando $g$ satisface una condición de integrabilidad subcrítica, probamos la existencia y unicidad de una solución débil para el problema (F) para cualquier medida. En el caso donde $\nu$ es una masa de Dirac, caracterizamos el comportamiento asimptótico de soluciones a (F). Asimismo, cuando $g(r)=|r|^{k-1}r$ con $k$ supercrítico, mostramos que una condición de absoluta continuidad de la medida con respecto a alguna capacidad de Bessel es una condición necesaria y suficiente para que (F) sea resuelta. El propósito de la quinta parte es investigar soluciones singulares débiles y fuertes de ecuaciones elípticas fraccionarias semilineales. Sean $p\in(0,\frac{N}{N-2\alpha})$, $\alpha\in(0,1)$, $k>0$ y $\Omega\subset \R^N(N\geq2)$ un dominio abierto acotado $C^2$ conteniendo a $0$ y $\delta_0$ la masa de Dirac en $0$, estudiamos que la solución débil de $(E)_k$ $ (-\Delta)^\alpha u+u^p=k\delta_0 $ en $\Omega$ la cual se desvanece en $\Omega^c$ es una solución débil singular de $(E^*)$ $ (-\Delta)^\alpha u+u^p=0 $ en $\Omega\setminus\{0\}$ con el mismo dato externo. Por otra parte, estudiamos el límite de soluciones débiles de $(E)_k$ cuando $k\to\infty$. Para $p\in(0, 1+\frac{2\alpha}{N}]$, el límite es infinito en $\Omega$. Para $p\in(1+\frac{2\alpha}N,\frac{N}{N-2\alpha})$, el límite es una solución fuertemente singular de $(E^*)$. Finalmente, en la sexta parte estudiamos la ecuación elíptica fraccionaria semilineal (E1) $(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu $ en un dominio $\Omega$ abierto acotado $C^2$ de $\R^N (N\ge2)$, el cual se desvanece en $\Omega^c$, donde $\epsilon=\pm1$, $\alpha\in(1/2,1)$, $\nu$ es una medida de Radon y $g:\R_+\mapsto\R_+$ es una funci\'on continua. Probamos la existencia de soluciones débiles para el problema (E1) cuando $g$ es subcrítico. Además, el comportamiento asimptótico y la unicidad de soluciones son descritas cuando $\epsilon=1$, $\nu$ es una masa de Dirac y $g(s)=s^p$ con $p\in(0,\frac)$.
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Knaub, Karl R. "On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6772.

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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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Ludvigsson, Gustav. "Kolmogorov Equations." Thesis, Uppsala universitet, Analys och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202845.

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Books on the topic "Equations"

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Zhuoqun, Wu, ed. Nonlinear diffusion equations. River Edge, NJ: World Scientific, 2001.

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Lancaster, Peter. Algebraic Riccati equations. Oxford: Clarendon Press, 1995.

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

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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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Sibal, Shivani. Equations. Noida: HarperCollins Publishers India, 2021.

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Equations, ed. Equations. Bangalore): Equations, 1992.

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Farr, Raymond, ed. Equations. Ocala, Fla-Conshohocken, Pa-Plymouth Meeting, Pa: Blue & Yellow Dog Press, 2013.

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Book chapters on the topic "Equations"

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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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Seifert, Christian, Sascha Trostorff, and Marcus Waurick. "The Fourier–Laplace Transformation and Material Law Operators." In Evolutionary Equations, 67–83. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89397-2_5.

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AbstractIn this chapter we introduce the Fourier–Laplace transformation and use it to define operator-valued functions of ∂t,ν; the so-called material law operators. These operators will play a crucial role when we deal with partial differential equations. In the equations of classical mathematical physics, like the heat equation, wave equation or Maxwell’s equation, the involved material parameters, such as heat conductivity or permeability of the underlying medium, are incorporated within these operators. Hence, these operators are also called “material law operators”. We start our chapter by defining the Fourier transformation and proving Plancherel’s theorem in the Hilbert space-valued case, which states that the Fourier transformation defines a unitary operator on $$L_2(\mathbb {R};H)$$ L 2 ( ℝ ; H ) .
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Ehling, Georg, and Temur Kutsia. "Solving Quantitative Equations." In Automated Reasoning, 381–400. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-63501-4_20.

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AbstractQuantitative equational reasoning provides a framework that extends equality to an abstract notion of proximity by endowing equations with an element of a quantale. In this paper, we discuss the unification problem for a special class of shallow subterm-collapse-free quantitative equational theories. We outline rule-based algorithms for solving such equational unification problems over generic as well as idempotent Lawvereian quantales and study their properties.
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Lipton, Richard J., and Kenneth W. Regan. "George Dantzig: Equations, Equations, and Equations." In People, Problems, and Proofs, 139–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-41422-0_27.

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Hasanov, Fakhri J., Frederick L. Joutz, Jeyhun I. Mikayilov, and Muhammad Javid. "KGEMM Behavioral Equations and Identities." In SpringerBriefs in Economics, 41–83. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-12275-0_7.

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AbstractThis chapter reports the estimated long-run equations and identities in Sects. 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, and 7.9 while the estimated short-run equations, i.e., final ECM specifications associated with the long-run equations are reported in Appendix B to save space in the main text. Note that the long-run and ECM equations are estimated till 2019 in the fifth version of KGEMM. Starting years of the estimations range from the 1970s to the 1990s dictated by the data availability. For the readers ease, we describe one of the long-run equations below and the rest equations here follow the same context. As an example, we select the first appeared long-run equation, i.e., Eq. (7.43).
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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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Seifert, Christian, Sascha Trostorff, and Marcus Waurick. "Exponential Stability of Evolutionary Equations." In Evolutionary Equations, 167–88. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89397-2_11.

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AbstractIn this chapter we study the exponential stability of evolutionary equations. Roughly speaking, exponential stability of a well-posed evolutionary equation $$\displaystyle \left (\partial _{t,\nu }M(\partial _{t,\nu })+A\right )U=F $$ ∂ t , ν M ( ∂ t , ν ) + A U = F means that exponentially decaying right-hand sides F lead to exponentially decaying solutions U. The main problem in defining the notion of exponential decay for a solution of an evolutionary equation is the lack of continuity with respect to time, so a pointwise definition would not make sense in this framework. Instead, we will use our exponentially weighted spaces $$L_{2,\nu }(\mathbb {R};H)$$ L 2 , ν ( ℝ ; H ) , but this time for negative ν, and define the exponential stability by the invariance of these spaces under the solution operator associated with the evolutionary equation under consideration.
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Conference papers on the topic "Equations"

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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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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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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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Reports on the topic "Equations"

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Young, C. W. Penetration equations. Office of Scientific and Technical Information (OSTI), October 1997. http://dx.doi.org/10.2172/562498.

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Gear, C. W. Differential algebraic equations, indices, and integral algebraic equations. Office of Scientific and Technical Information (OSTI), April 1989. http://dx.doi.org/10.2172/6307619.

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Knorrenschild, M. Differential-algebraic equations as stiff ordinary differential equations. Office of Scientific and Technical Information (OSTI), May 1989. http://dx.doi.org/10.2172/6980335.

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Ostashev, Vladimir, Michael Muhlestein, and D. Wilson. Extra-wide-angle parabolic equations in motionless and moving media. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/42043.

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Wide-angle parabolic equations (WAPEs) play an important role in physics. They are derived by an expansion of a square-root pseudo-differential operator in one-way wave equations, and then solved by finite-difference techniques. In the present paper, a different approach is suggested. The starting point is an extra-wide-angle parabolic equation (EWAPE) valid for small variations of the refractive index of a medium. This equation is written in an integral form, solved by a perturbation technique, and transformed to the spectral domain. The resulting split-step spectral algorithm for the EWAPE accounts for the propagation angles up to 90° with respect to the nominal direction. This EWAPE is also generalized to large variations in the refractive index. It is shown that WAPEs known in the literature are particular cases of the two EWAPEs. This provides an alternative derivation of the WAPEs, enables a better understanding of the underlying physics and ranges of their applicability, and opens an opportunity for innovative algorithms. Sound propagation in both motionless and moving media is considered. The split-step spectral algorithm is particularly useful in the latter case since complicated partial derivatives of the sound pressure and medium velocity reduce to wave vectors (essentially, propagation angles) in the spectral domain.
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Yagi, M., and W. Horton. Reduced Braginskii equations. Office of Scientific and Technical Information (OSTI), November 1993. http://dx.doi.org/10.2172/10105700.

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Attanasio, Orazio, and Hamish Low. Estimating Euler Equations. Cambridge, MA: National Bureau of Economic Research, May 2000. http://dx.doi.org/10.3386/t0253.

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Dresner, L. Nonlinear differential equations. Office of Scientific and Technical Information (OSTI), January 1988. http://dx.doi.org/10.2172/5495671.

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Luc, Brunet. Systematic Equations Handbook : Book 1-Energy. R&D Médiation, May 2015. http://dx.doi.org/10.17601/rd_mediation2015:1.

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The energy equation handbook is the complete collection of physically coherent expression of energy computed using from 2 to 7 physical units among: density(ML-3) energy (ML2T-2) time (T) force (MLT-2) power (ML2T-3) current (I) temperature (Th) quantity (N) mass (M) length (L) candela (J) surface (L2) volume (L3) concentration (ML-3) frequency (T-1) acceleration (LT- 2) speed (LT-1) pressure (ML-1T-2) viscosity (ML-1T-1) luminance (L- 2J) MolarMass (MN-1) MassicEnergy (L2T-2) resistance (ML2T-3I-2) voltage (ML2T-3I-1) Farad (M-1L-2T4I2) Thermal- Conductivity (MLT-3Th-1) SpecificHeat (L2T-2Th-1) MassFlux (MT-1) SurfaceTension (MT-2) Charge (TI) Resistivity (ML3T-3I-2) The complete list of 4196 equations is sorted by number of variable required to obtain an energy in Joules. All the units are in MKSA.
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Baader, Franz, Pavlos Marantidis, and Alexander Okhotin. Approximately Solving Set Equations. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.227.

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Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the number of violations, and investigate the complexity of the respective decision problem, i.e., the problem of deciding whether there is an assignment that solves the system with at most l violations for a given threshold value l.
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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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