Relevant bibliographies by topics / Gaussian equation

Contents

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

Academic literature on the topic 'Gaussian equation'

Author: Grafiati
Published: 5 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Gaussian equation"

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Bojdecki, Tomasz, and Luis G. Gorostiza. "Gaussian and Non–Gaussian Distribution–Valued Ornstein–Uhlenbeck Processes." Canadian Journal of Mathematics 43, no. 6 (1991): 1136–49. http://dx.doi.org/10.4153/cjm-1991-066-6.

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Generalized (distribution-valued) Ornstein-Uhlenbeck processes, which by definition are solutions of generalized Langevin equations, arise in many investigations on fluctuation limits of particle systems (eg. Bojdecki and Gorostiza [1], Dawson, Fleischmann and Gorostiza [5], Fernández [7], Gorostiza [8,9], Holley and Stroock [10], Itô [12], Kallianpur and Pérez-Abreu [16], Kallianpur and Wolpert [14], Kotelenez [17], Martin-Löf [19], Mitoma [22], Uchiyama [25]). The state space for such a process is the strong dual Φ′ of a nuclear space Φ. A generalized Langevin equation for a Φ′-valued proces
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Vyas, Ujjval B., Varsha A. Shah, Athul Vijay P.K., and Nikunj R. Patel. "Gaussian exponential regression method for modeling open circuit voltage of lithium-ion battery as a function of state of charge." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 41, no. 1 (2021): 64–80. http://dx.doi.org/10.1108/compel-03-2021-0113.

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Purpose The purpose of the article is to develop an equation to accurately represent OCV as a function of SoC with reduced computational burden. Dependency of open circuit voltage (OCV) on state of charge (SoC) is often represented by either a look-up table or an equation developed by regression analysis. The accuracy is increased by either a larger data set for the look-up table or using a higher order equation for the regression analysis. Both of them increase the memory requirement in the controller. In this paper, Gaussian exponential regression methodology is proposed to represent OCV and
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TAQQU, MURAD S., and MARK VEILLETTE. "MULTIVARIATE PARTIAL DIFFERENTIAL EQUATION DESCRIBING THE EVOLUTION OF A GAUSSIAN PROCESS." Stochastics and Dynamics 09, no. 04 (2009): 493–518. http://dx.doi.org/10.1142/s0219493709002750.

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If {X(t), t ≥ 0} is a Gaussian process, the diffusion equation characterizes its marginal probability density function. How about finite-dimensional distributions? For each n ≥ 1, we derive a system of partial differential equations which are satisfied by the probability density function of the vector (X(t1), …, X(tn)). We then show that these differential equations determine uniquely the finite-dimensional distributions of Gaussian processes. We also discuss situations where the system can be replaced by a single equation, which is either one member of the system, or an aggregate equation obt
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Selvaratnam, A. R., M. Vlieg-Hulstman, B. van-Brunt, and W. D. Halford. "On the solution of a class of second-order quasi-linear PDEs and the Gauss equation." ANZIAM Journal 42, no. 3 (2001): 312–23. http://dx.doi.org/10.1017/s1446181100011962.

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AbstractGauss' Theorema Egregium produces a partial differential equation which relates the Gaussian curvature K to components of the metric tensor and its derivatives. Well-known partial differential equations (PDEs) such as the Schrödinger equation and the sine-Gordon equation can be derived from Gauss' equation for specific choices of K and coördinate systems. In this paper we consider a class of Bäcklund Transformations which corresponds to coördinate transformations on surfaces with a given Gaussian curvature. These Bäcklund Transformations lead to the construction of solutions to certain
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Misra, Shikha, Sanjay K. Mishra, and P. Brijesh. "Coaxial propagation of Laguerre–Gaussian (LG) and Gaussian beams in a plasma." Laser and Particle Beams 33, no. 1 (2015): 123–33. http://dx.doi.org/10.1017/s0263034615000142.

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AbstractThis paper investigates the non-linear coaxial (or coupled mode) propagation of Laguerre–Gaussian (LG) (in particular L01 mode) and Gaussian electromagnetic (em) beams in a homogeneous plasma characterized by ponderomotive and relativistic non-linearities. The formulation is based on numerical solution of non-linear Schrödinger wave equation under Jeffreys–Wentzel–Kramers–Brillouin approximation, followed by paraxial approach applicable in the vicinity of intensity maximum of the beams. A set of coupled differential equations for spot size (beam width) and phase evolution with space co
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Noble, J. M. "Evolution equation with Gaussian potential." Nonlinear Analysis: Theory, Methods & Applications 28, no. 1 (1997): 103–35. http://dx.doi.org/10.1016/0362-546x(95)00037-v.

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Hu, Y. "Schrödinger equation with Gaussian potential." Theory of Probability and Mathematical Statistics 98 (August 19, 2019): 115–26. http://dx.doi.org/10.1090/tpms/1066.

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Vashpanova, N., O. Lesechko, and T. Podousova. "INFINITESIMAL DEFORMATIONS OF SURFACES WITH A GIVEN CHANGE OF THE RICCI TENSOR." Mechanics And Mathematical Methods 5, no. 1 (2023): 97–109. http://dx.doi.org/10.31650/2618-0650-2023-5-1-97-109.

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In three-dimensional Euclidean space, we study the problem of the existence of an infinitesimal first-order deformation of single-connected regular surfaces with a predetermined change in the Ricci tensor. It is shown that for surfaces of nonzero Gaussian curvature, this problem is reduced to the study and solution of a system of seven equations (including differential equations) with respect to seven unknown functions, each solution of which determines a vector field that is a univariate function (with an accuracy of a constant vector) and can be interpreted as a moment-free stress state of e
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BRACKEN, PAUL. "ON TWO-DIMENSIONAL MANIFOLDS WITH CONSTANT GAUSSIAN CURVATURE AND THEIR ASSOCIATED EQUATIONS." International Journal of Geometric Methods in Modern Physics 09, no. 03 (2012): 1250018. http://dx.doi.org/10.1142/s0219887812500181.

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The components for the frame field of a two-dimensional manifold with constant Gaussian curvature are determined for arbitrary nonzero curvature. The components of the frame fields are found from the structure equations and lead to specific nonlinear equations which pertain to surfaces with specific values of the Gaussian curvature. For negative curvature, the equation is of sine-Gordon type, and for positive curvature it is of sinh-Gordon type. The integrability and Bäcklund properties of these equations are then investigated by studying a differential ideal of two-forms which leads to the eq
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DUBKOV, ALEXANDER, and BERNARDO SPAGNOLO. "GENERALIZED WIENER PROCESS AND KOLMOGOROV'S EQUATION FOR DIFFUSION INDUCED BY NON-GAUSSIAN NOISE SOURCE." Fluctuation and Noise Letters 05, no. 02 (2005): L267—L274. http://dx.doi.org/10.1142/s0219477505002641.

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We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker–Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov–Feller equation for discontinuous Markovian processes, and the fractional Fokker–Pl
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Dissertations / Theses on the topic "Gaussian equation"

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Chiu, Y. D. "Exploratory studies for Gaussian process structural equation models." Thesis, University College London (University of London), 2014. http://discovery.ucl.ac.uk/1437626/.

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Latent variable models (LVMs) are widely used in many scientific fields due to the ubiquitousness and feasibility of latent variables. Conventional LVMs, however, have limitations because they model relationships between covariates and latent variables or among latent variables with a parametric fashion. A more flexible model framework is therefore needed, especially without prior knowledge of sensible parametric forms. This thesis proposes a new non-parametric LVM for the need. We define a model structure with particular features, including a multi-layered structure constituting of non-parame
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Hocquet, Antoine. "The Landau-Lifshitz-Gilbert equation driven by Gaussian noise." Palaiseau, Ecole polytechnique, 2015. https://theses.hal.science/tel-01265433/document.

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Cette thèse porte sur l'influence d'un bruit Gaussien dans l'équation de Landau-Lifshitz-Gilbert Stochastique (SLLG). Il s'agit d'une équation aux dérivées partielles stochastique, non linéaire, avec une contrainte non convexe sur le module des solutions. Le chapitre 1 se consacre tout d'abord à la solvabilité locale de SLLG. Utilisant les propriétés classiques de l'intégration stochastique dans un espace de Banach, nous proposons une formulation mild, et donnons l'existence et l'unicité d'une solution locale en dimension quelconque, pour un bruit Gaussien régulier en espace, dans le cas sur-a
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Knani, Habiba. "Backward stochastic differential equations driven by Gaussian Volterra processes." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0014.

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Cette thèse porte sur les équations différentielles stochastiques rétrogrades (EDSR) dirigées par une classe de processus de Volterra qui contient le mouvement brownien multifractionnaire et le processus Ornstein-Uhlenbeck multifractionnaire. Dans la première partie, nous étudions la solution des EDSRs multidimensionnelles avec des générateurs linéaires. Par la formule d’Itô pour les processus de Volterra nous réduisons l’EDSR à une équation aux dérivées partielles (EDP) de second ordre linéaire avec la condition terminale. Sous une condition d’intégrabilité dans un voisinage du temps terminal
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Haydar, Adel, and Imad Akeab. "Simulation of wave propagation in terrain using the FMM code Nero2D." Thesis, Linnaeus University, School of Computer Science, Physics and Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-8767.

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<p>In this report we describe simulation of the surface current density on a PEC cylinder and the diffracted field for a line source above a finite PEC ground plane as a means to verify the Nero2D program. The results are compared with the exact solution and give acceptable errors. A terrain model for a communication link is studied in the report and we simulate the wave propagation for terrain with irregular shapes and different materials. The Nero2D program is based on the fast multipole method (FMM) to reduce computation time and memory. Gaussian sources are also studied to make the terrain
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Moreira, Heloisa Beatriz Cordeiro. "AplicaÃÃo da teoria fuzzy em um modelo de transporte de massa, para avaliar o risco da dispersÃo dos poluentes atmosfÃricos." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11331.

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nÃo hÃ<br>Os problemas de poluiÃÃo do ar se tornam cada vez mais crÃticos, necessitando de controles e monitoramentos contÃnuos, a fim de assegurar um ambiente adequado à comunidade em geral. O impacto das fontes de poluiÃÃo do ar existente ou de novas fontes pode ser avaliado, atravÃs de modelos matemÃticos ou modelos de qualidade do ar. Esta ferramenta permite avaliar os riscos (efeitos) dos poluentes atmosfÃricos ao meio ambiente sob diversas variÃveis, como condiÃÃes de estabilidade atmosfÃricas e pontos de lanÃamento. Neste contexto, a teoria Fuzzy desponta como uma soluÃÃo viÃvel para es
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Huang, Jeffrey. "Numerical solutions of continuous wave beam in nonlinear media." PDXScholar, 1987. https://pdxscholar.library.pdx.edu/open_access_etds/3742.

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Deformation of a Gaussian beam is observed when it propagates through a plasma. Self-focusing of the beam may be observed when the intensity of the laser increases the index of refraction of plasma gas. Due to the difficulties in solving the nonlinear partial differential equation in Maxwell's wave equation, a numerical technique has been developed in favor of the traditional analytical method. Result of numerical solution shows consistency with the analytical method. This further suggests the validity of the numerical technique employed. A three dimensional graphics package was used to depict
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Croix, Jean-Charles. "A new decomposition of Gaussian random elements in Banach spaces with application to Bayesian inversion." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEM019.

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L'inférence est une activité fondamentale en sciences et en ingénierie: elle permet de confronter et d'ajuster des modèles théoriques aux données issues de l'expérience. Ces mesures étant finies par nature et les paramètres des modèles souvent fonctionnels, ilest nécessaire de compenser cette perte d'information par l'ajout de contraintes externes au problème, via les méthodes de régularisation. La solution ainsi associée satisfait alors un compromis entre d'une part sa proximité aux données, et d'autre part une forme de régularité.Depuis une quinzaine d'années, ces méthodes intègrent un forma
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Mouysset, Sandrine. "Contributions à l'étude de la classification spectrale et applications." Phd thesis, Institut National Polytechnique de Toulouse - INPT, 2010. http://tel.archives-ouvertes.fr/tel-00573433.

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La classification spectrale consiste à créer, à partir des éléments spectraux d'une matrice d'affinité gaussienne, un espace de dimension réduite dans lequel les données sont regroupées en classes. Cette méthode non supervisée est principalement basée sur la mesure d'affinité gaussienne, son paramètre et ses éléments spectraux. Cependant, les questions sur la séparabilité des classes dans l'espace de projection spectral et sur le choix du paramètre restent ouvertes. Dans un premier temps, le rôle du paramètre de l'affinité gaussienne sera étudié à travers des mesures de qualités et deux heuris
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L'hour, Charles-Antoine. "Modélisation de la propagation électromagnétique en milieux inhomogènes basée sur les faisceaux gaussiens : application à la propagation en atmosphère réaliste et à la radio-occultation entre satellites." Thesis, Toulouse 3, 2017. http://www.theses.fr/2017TOU30069/document.

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La thèse, dont le sujet est "Modélisation de la propagation électromagnétique en milieux à gradient d'indice basée sur les faisceaux gaussiens - Application à la propagation en atmosphère réaliste et à la radio-occultation entre satellites" a été commencée le 2 décembre 2013, au Département ÉlectroMagnétisme et Radar (DEMR) de l'Onera de Toulouse et avec le laboratoire LAPLACE de l'Université Paul Sabatier. Elle est co-financée par l'ONERA et par la Région Midi-Pyrénées. L'encadrement a été assuré par Jérôme Sokoloff (Laplace/UPS, directeur de thèse), Alexandre Chabory (ENAC, co-directeur) et
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Sarkar, Sanket. "Extending the Time Scale in Atomistic Simulations: The Diffusive Molecular Dynamics Method." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1321282489.

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Books on the topic "Gaussian equation"

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Link, Carol L. An equation for one-sided tolerance limits for normal distributions. U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1985.

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Link, Carol L. An equation for one-sided tolerance limits for normal distributions. U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1985.

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Link, Carol L. An equation for one-sided tolerance limits for normal distributions. U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1985.

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Link, Carol L. An equation for one-sided tolerance limits for normal distributions. U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1985.

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Link, Carol L. An equation for one-sided tolerance limits for normal distributions. U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1985.

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Link, Carol L. An equation for one-sided tolerance limits for normal distributions. U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 1985.

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Dyall, Kenneth G. Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets. NASA Ames Research Center, 1990.

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Grigoryan, A. Heat kernel and analysis on manifolds. American Mathematical Society, 2009.

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Grigoryan, A. Heat kernel and analysis on manifolds. American Mathematical Society, 2009.

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1957-, Adamian Armen, and Langley Research Center, eds. Approximation theory for LQG optimal control of flexible structures. National Aeronautics and Space Administration, Langley Research Center, 1988.

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Book chapters on the topic "Gaussian equation"

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Chirikjian, Gregory S. "Gaussian Distributions and the Heat Equation." In Stochastic Models, Information Theory, and Lie Groups, Volume 1. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4803-9_2.

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Kanazawa, Kiyoshi. "Microscopic Derivation of Linear Non-Gaussian Langevin Equation." In Springer Theses. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6332-9_7.

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Kanazawa, Kiyoshi. "Analytical Solution to Nonlinear Non-Gaussian Langevin Equation." In Springer Theses. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6332-9_8.

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Schuch, Dieter. "Time-Dependent Schrödinger Equation and Gaussian Wave Packets." In Fundamental Theories of Physics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-65594-9_2.

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Shimizu, Shohei. "Non-Gaussian Structural Equation Models for Causal Discovery." In Statistics and Causality. John Wiley & Sons, Inc., 2016. http://dx.doi.org/10.1002/9781118947074.ch7.

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Benth, Fred Espen, and Ludwig Streit. "The Burgers Equation with a Non-Gaussian Random Force." In Stochastic Analysis and Related Topics VI. Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-2022-0_6.

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Gawarecki, L., and V. Mandrekar. "On the Zakai Equation of Filtering with Gaussian Noise." In Stochastics in Finite and Infinite Dimensions. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0167-0_8.

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Lawrence, Neil, Magnus Rattray, Antti Honkela, and Michalis Titsias. "Gaussian Process Inference for Differential Equation Models of Transcriptional Regulation." In Handbook of Statistical Systems Biology. John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9781119970606.ch19.

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Kim, Jin Won, and Sebastian Reich. "On Forward–Backward SDE Approaches to Conditional Estimation." In Mathematics of Planet Earth. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-70660-8_6.

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AbstractIn this chapter, we investigate the representation of conditional expectation values for partially observed diffusion processes in terms of appropriate estimators. The work of Kalman and Bucy has established a duality between filtering and estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an optimization problem constrained by a backward stochastic partial differential equation. Here we revisit this problem from the perspective of appropriate forward-backward stochastic differential equa
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Hamilton, Mark F. "Sound Beams." In Nonlinear Acoustics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58963-8_8.

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AbstractDiffraction in sound beams is analyzed using the KZK nonlinear parabolic wave equation. General integral solutions are presented for generation of the second harmonic, sum, and difference frequencies in weakly nonlinear axisymmetric sound beams. Analytical solutions are obtained for sources with Gaussian amplitude distributions, both unfocused and focused. Asymptotic solutions are presented for far-field radiation from circular pistons, and the appearance of additional sidelobes is explained. Solutions for difference-frequency radiation in the far field of a parametric array, and the a
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Conference papers on the topic "Gaussian equation"

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Nigam, Unnati, Radhendushka Srivastava, Michael Burke, and Faezeh Marzbanrad. "A Dynamical Equation Approach For Quasi-Periodic Gaussian Processes." In ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2025. https://doi.org/10.1109/icassp49660.2025.10888984.

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Nieto-Chaupis, Huber. "The Gaussian and Weibull Manifestations of Friis Transmission Equation." In 2024 International Conference on Computing, Networking, Telecommunications & Engineering Sciences Applications (CoNTESA). IEEE, 2024. https://doi.org/10.1109/contesa64738.2024.10891272.

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Parmantier, J. P., X. Ferrières, S. Bertuol, and C. E. Baum. "Optimization of the BLT Equation Based on a Sparse Gaussian Elimination." In 13th International Zurich Symposium and Technical Exhibition on Electromagnetic Compatibility. IEEE, 1999. https://doi.org/10.23919/emc.1999.10791776.

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Kumar, Kailash, Govind Sharma, and Ajit Kumar Chaturvedi. "Application of Friis Transmission Equation for the Power Delay Profile in Gaussian Scattering." In 2025 National Conference on Communications (NCC). IEEE, 2025. https://doi.org/10.1109/ncc63735.2025.10983213.

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Kosut, Oliver, Michelle Effros, and Michael Langberg. "Nobody Expects a Differential Equation: Minimum Energy-Per-Bit for the Gaussian Relay Channel with Rank-1 Linear Relaying." In 2024 IEEE International Symposium on Information Theory (ISIT). IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619129.

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Erikson, W. L., and Surendra Singh. "Maxwell-Gaussian optical beams." In OSA Annual Meeting. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.wa1.

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Paraxial Gaussian-beam-like solutions of the scalar wave equation, often used to model laser beams, do not satisfy Maxwell's equations. Paraxial-beam-like solutions that satisfy Maxwell's equations are constructed from the solutions of the scalar wave equation. Polarization properties of these Maxwell-Gaussian beams in free space are discussed. It is found that a Maxwell-Gaussian beam linearly polarized in the x direction and propagating in the z direction has a weak cross polarization component in the y direction in addition to a longitudinal component in the direction of propagation. These p
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Drühl, Kai J. "Solutions of the Raman wave equation for focused pump beams." In OSA Annual Meeting. Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.tua7.

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We solve the wave equation for stimulated Raman and Brillouin scattering from Gaussian pump beams by a transformation to a system of coexpanding and contracting coordinates in which the pump beam has constant radius. The resulting equation has a quadratic potential term and is equivalent to the Schrödinger equation for a harmonic oscillator in two dimensions. If the typical gain length is small compared to the Rayleigh range of the pump, the decrease of pump intensity away from the center will lead to strong narrowing of the amplified Stokes beam. The pump intensity distribution can then be ex
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Li, Siwei, Sergey Fomel, and Alexander Vladimirsky. "Improving wave‐equation fidelity of Gaussian beams by solving the complex eikonal equation." In SEG Technical Program Expanded Abstracts 2011. Society of Exploration Geophysicists, 2011. http://dx.doi.org/10.1190/1.3628005.

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English, R. Edward, and Nicholas George. "Diffraction under Gaussian illumination: a Gaussian beam expansion approach." In OSA Annual Meeting. Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.fq2.

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A conventional approach to solving diffraction problems involves integrating an input field multiplied by the Fresnel diffraction kernel. Alternately, one can solve the associated differential equation subject to certain boundary conditions. The Hermite- and Laguerre-Gaussian beam modes are complete and orthogonal sets of functions for this differential equation suited, respectively, for Cartesian and cylindrical geometries. Proceeding in this way, we describe a Gaussian beam expansion approach that is suitable for solving certain diffraction problems.
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Kiselev, Aleksei P., and Alexandr B. Plachenov. "Astigmatic Gaussian beam: Exact solution of the Helmholtz equation." In 2018 Days on Diffraction (DD). IEEE, 2018. http://dx.doi.org/10.1109/dd.2018.8553170.

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Reports on the topic "Gaussian equation"

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Gardiner, Thomas, and Allen Robinson. Gaussian Mixture Model Solvers for the Boltzmann Equation. Office of Scientific and Technical Information (OSTI), 2022. http://dx.doi.org/10.2172/2402991.

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