Log in

Relevant bibliographies by topics / Gaussian equation / Journal articles

To see the other types of publications on this topic, follow the link: Gaussian equation.

Journal articles on the topic 'Gaussian equation'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Gaussian equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

2

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

3

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

4

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

5

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

6

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

9

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

10

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

11

Su, Zhiyong, and Jeffrey M. Falzarano. "Gaussian and non-Gaussian cumulant neglect application to large amplitude rolling in random waves." International Shipbuilding Progress 58, no. 2-3 (2011): 97–113. https://doi.org/10.3233/isp-2011-0071.

Full text

Abstract:

Large amplitude rolling in random beam seas is studied by moment equations and stochastic excitation is represented through a cascading filter driven by pure Gaussian white noise in order to apply Markov approximation. The moment equation is generated from a six state space rolling model using the Itô differential rule. The Gaussian and non-Gaussian cumulant neglect method is applied to close the infinite hierarchy of moment equations. In this paper, an automatic neglect tool is developed to handle the complex and untraceable higher-order cumulant neglect closure method to capture the non-Gaus

APA, Harvard, Vancouver, ISO, and other styles

12

Başpınar, Dila, Ela BAŞPINAR, Nesrin BAŞPINAR, and Umut Aldoğan. "Derivative and partial integral methods and Gauss integral's indefinite integral solution and its use in wave function in quantum mechanics and exact solutions of the wave function depending on position and time." Kuantum Teknolojileri ve Enformatik Araştırmaları Dergisi 1, no. 1 (2023): 55–63. http://dx.doi.org/10.70447/ktve.2239.

Full text

Abstract:

This study, , solution of Gaussian Integral with differential equation [18,19]; By using the partial integral method, the indefinite integral solution by taking x under the differential [29,30,31] and the indefinite integral solution by taking the Gaussian integral under the differential [33,38,39] both harmonic series and function solutions are found. Indefinite integral solution of Gaussian Integral [38] In Quantum Physics, the wave function solution f(x,α) in terms of α variable in x position and k space by substituting it in wave function [44,45] and in one-dimensional time dependent Schrö

APA, Harvard, Vancouver, ISO, and other styles

13

Ünal, Gazanfer. "Stochastic symmetries of Wick type stochastic ordinary differential equations." International Journal of Modern Physics: Conference Series 38 (January 2015): 1560079. http://dx.doi.org/10.1142/s2010194515600794.

Full text

Abstract:

We consider Wick type stochastic ordinary differential equations with Gaussian white noise. We define the stochastic symmetry transformations and Lie equations in Kondratiev space [Formula: see text]. We derive the determining system of Wick type stochastic partial differential equations with Gaussian white noise. Stochastic symmetries for stochastic Bernoulli, Riccati and general stochastic linear equation in [Formula: see text] are obtained. A stochastic version of canonical variables is also introduced.

APA, Harvard, Vancouver, ISO, and other styles

14

Demskoi, Dmitry K., and Wolfgang K. Schief. "On steady motions of an ideal fibre-reinforced fluid in a curved stratum. Geometry and integrability." Journal of Physics A: Mathematical and Theoretical 54, no. 50 (2021): 505205. http://dx.doi.org/10.1088/1751-8121/ac38eb.

Full text

Abstract:

Abstract It is shown that the kinematic equations governing steady motions of an ideal fibre-reinforced fluid in a curved stratum may be expressed entirely in terms of the intrinsic Gauss equation, which assumes the form of a partial differential equation of third order, for the surface representing the stratum. In particular, the approach adopted here leads to natural non-classical orthogonal coordinate systems on surfaces of constant Gaussian curvature with one family of coordinate lines representing the fibres. Integrable cases are isolated by requiring that the Gauss equation be compatible

APA, Harvard, Vancouver, ISO, and other styles

15

Dila, Başpınar, BAŞPINAR Ela, and Aldoğan Umut. "Derivative and partial integral methods and Gauss integral's indefinite integral solution and its use in wave function in quantum mechanics and exact solutions of the wave function depending on position and time." Journal of Quantum Technologies and Informatics Research 1, no. 1 (2023): 55–63. https://doi.org/10.5281/zenodo.10259636.

Full text

Abstract:

This study, , solution of Gaussian Integral with differential equation [18,19]; By using the partial integral method, the indefinite integral solution by taking x under the differential [29,30,31] and the indefinite integral solution by taking the Gaussian integral under the differential [33,38,39] both harmonic series and function solutions are found. Indefinite integral solution of Gaussian Integral [38] In Quantum Physics, the wave function solution f(x,α) in terms of α variable in x position and k space by substituting it in wave function [44,45] and in one-dimensional time dependent Schrö

APA, Harvard, Vancouver, ISO, and other styles

16

Gonzalez-Lee, Mario, Hector Vazquez-Leal, Luis J. Morales-Mendoza, Mariko Nakano-Miyatake, Hector Perez-Meana, and Juan R. Laguna-Camacho. "Statistical Assessment of Discrimination Capabilities of a Fractional Calculus Based Image Watermarking System for Gaussian Watermarks." Entropy 23, no. 2 (2021): 255. http://dx.doi.org/10.3390/e23020255.

Full text

Abstract:

In this paper, we explore the advantages of a fractional calculus based watermarking system for detecting Gaussian watermarks. To reach this goal, we selected a typical watermarking scheme and replaced the detection equation set by another set of equations derived from fractional calculus principles; then, we carried out a statistical assessment of the performance of both schemes by analyzing the Receiver Operating Characteristic (ROC) curve and the False Positive Percentage (FPP) when they are used to detect Gaussian watermarks. The results show that the ROC of a fractional equation based sch

APA, Harvard, Vancouver, ISO, and other styles

17

Stroock, Daniel W. "Cauchy's functional equation and Gaussian measures." High Frequency 2, no. 3-4 (2019): 142–46. http://dx.doi.org/10.1002/hf2.10043.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Blackledge, Jonathan, Derek Kearney, Marc Lamphiere, Raja Rani, and Paddy Walsh. "Econophysics and Fractional Calculus: Einstein’s Evolution Equation, the Fractal Market Hypothesis, Trend Analysis and Future Price Prediction." Mathematics 7, no. 11 (2019): 1057. http://dx.doi.org/10.3390/math7111057.

Full text

Abstract:

This paper examines a range of results that can be derived from Einstein’s evolution equation focusing on the effect of introducing a Lévy distribution into the evolution equation. In this context, we examine the derivation (derived exclusively from the evolution equation) of the classical and fractional diffusion equations, the classical and generalised Kolmogorov–Feller equations, the evolution of self-affine stochastic fields through the fractional diffusion equation, the fractional Poisson equation (for the time independent case), and, a derivation of the Lyapunov exponent and volatility.

APA, Harvard, Vancouver, ISO, and other styles

19

Christodoulou, Dimitris M., and Silas G. T. Laycock. "Clarifying the Optical Thin-lens Equations of Gravitational Self-lensing." Research Notes of the AAS 7, no. 6 (2023): 115. http://dx.doi.org/10.3847/2515-5172/acdad3.

Full text

Abstract:

Abstract We exploit an analogy between gravitational lenses and optical lenses to determine the Gaussian form of the optical thin-lens equation of gravitational self-lensing (this is not the deflection-angle equation which is also called the “ray-tracing equation”). As in magnifying glasses, this Gaussian form determines the location of the virtual image in front of the lens and behind the source. Some confusion exists in the literature because a similar-looking equation of totally different substance is often written down, creating the false impression that this may be the equivalent optical

APA, Harvard, Vancouver, ISO, and other styles

20

Kolokol'tsov, Vassili N. "Localization and Analytic Properties of the Solutions of the Simplest Quantum Filtering Equation." Reviews in Mathematical Physics 10, no. 06 (1998): 801–28. http://dx.doi.org/10.1142/s0129055x98000264.

Full text

Abstract:

The paper deals with the quantum Langevin equation describing a quantum particle with continuously observed position. Special Banach spaces of entire analytic functions are introduced and studied (including a theorem of Paley–Wiener type for them), which comprise all solutions of this equation and in which the uniform convergence (as time tends to infinity) of the solutions to the Gaussian function with a fixed dispersion (selflocalisation or continuous collapse) is proved. The asymptotic behavior at infinity of the mean position and momentum of the limit Gaussian wave packet (which satisfy cl

APA, Harvard, Vancouver, ISO, and other styles

21

Saad, Mohamed, Hossam Abdel-Aziz, and Haytham Ali. "Investigation of Affine Factorable Surfaces in Pseudo-Galilean Space." WSEAS TRANSACTIONS ON MATHEMATICS 22 (September 26, 2023): 666–73. http://dx.doi.org/10.37394/23206.2023.22.73.

Full text

Abstract:

In this paper, we investigate affine factorable surfaces of the second kind in the three-dimensional pseudo-Galilean space G1 3. We use the invariant theory and theory of diffeerential equations to study the geometric properties of these surfaces, namely, the first and second fundamental forms, Gaussian and mean curvatures. Also, we present some special cases by changing the partial diffeerential equation into the ordinary diffeerential equation to simplify our special cases. Furthermore, we give some theorems according to zero and non-zero Gaussian and mean curvatures of the meant surfaces. F

APA, Harvard, Vancouver, ISO, and other styles

22

Zhang, Lei, and Yao Wen Yang. "Three-Dimensional Charge Redistribution of Ionic Polymer-Metal Composites with Uncertainty in Surface Conductivity." Advanced Materials Research 47-50 (June 2008): 379–82. http://dx.doi.org/10.4028/www.scientific.net/amr.47-50.379.

Full text

Abstract:

In this paper, the three-dimensional charge redistribution of IPMC material under dynamic electric potentials with uncertainty in surface conductivity is studied. The governing equations of charge redistribution are derived from the Nernst-Planck equation, the Poisson equation, the mass conservation equation and the basic electrostatic equations. The surface conductivity is viewed as a Gaussian distribution. A travelling wave type analytical solution is obtained to account for the three-dimensional cation movement under the applied electric potentials.

APA, Harvard, Vancouver, ISO, and other styles

23

QIAO, HUIJIE, and JINQIAO DUAN. "TOPOLOGICAL EQUIVALENCE FOR DISCONTINUOUS RANDOM DYNAMICAL SYSTEMS AND APPLICATIONS." Stochastics and Dynamics 14, no. 01 (2013): 1350007. http://dx.doi.org/10.1142/s021949371350007x.

Full text

Abstract:

After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an Itô stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman–Grobman theorem is proved for the linearization of the Itô stochastic differential equation. Furthermore, for Marcus stochastic differential equations, this topological e

APA, Harvard, Vancouver, ISO, and other styles

24

ABDELWAHAB, M., KHALEDS M. ESSA, M. EMBABY, and SAWSANE M. ELSAID. "Some characteristic parameters of Gaussian plume model." MAUSAM 63, no. 1 (2021): 123–28. http://dx.doi.org/10.54302/mausam.v63i1.1461.

Full text

Abstract:

The Gaussian solution of the diffusion equation for line source is used to have the first four moments of the vertical concentration distribution (centroid, variance, skewness, and kurtosis). The magnitude and position of maximum concentration level were evaluated. Also the plume advection wind speed is estimated. Equations for the ground level concentration were compared with wind tunnel measurements.

APA, Harvard, Vancouver, ISO, and other styles

25

Jiang, X., P. Cooper, and P. J. Scott. "Freeform surface filtering using the diffusion equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2127 (2010): 841–59. http://dx.doi.org/10.1098/rspa.2010.0307.

Full text

Abstract:

The measurement of texture for geometric surfaces is well established for surfaces that are of a planar (Euclidean) nature. Gaussian filtering is the fundamental base for scale-limited surfaces used in surface texture, but cannot be applied to non-Euclidean surfaces without distortion of the results. A link exists between Gaussian filtering and solutions of the PDE that models linear isotropic diffusion. In particular, an analytical solution of this diffusion equation over a planar region at a time t is given by the continuous convolution of the initial distribution of the diffused quantity wi

APA, Harvard, Vancouver, ISO, and other styles

26

Bracken, Paul. "Determination of surfaces in three-dimensional Minkowski and Euclidean spaces based on solutions of the Sinh-Laplace equation." International Journal of Mathematics and Mathematical Sciences 2005, no. 9 (2005): 1393–404. http://dx.doi.org/10.1155/ijmms.2005.1393.

Full text

Abstract:

The relationship between solutions of the sinh-Laplace equation and the determination of various kinds of surfaces of constant Gaussian curvature, both positive and negative, will be investigated here. It is shown that when the metric is given in a particular set of coordinates, the Gaussian curvature is related to the sinh-Laplace equation in a direct way. The fundamental equations of surface theory are found to yield a type of geometrically based Lax pair for the system. Given a particular solution of the sinh-Laplace equation, this Lax can be integrated to determine the three fundamental ve

APA, Harvard, Vancouver, ISO, and other styles

27

Dabrowska, Anita, and John Gough. "Quantum Trajectories for Squeezed Input Processes: Explicit Solutions." Open Systems & Information Dynamics 23, no. 01 (2016): 1650004. http://dx.doi.org/10.1142/s1230161216500049.

Full text

Abstract:

We consider the quantum (trajectories) filtering equation for the case when the system is driven by Bose field inputs prepared in an arbitrary non-zero mean Gaussian state. The a posteriori evolution of the system is conditioned by the results of a single or double homodyne measurements. The system interacting with the Bose field is a single cavity mode taken initially in a Gaussian state. We show explicit solutions using the method of characteristic functions to the filtering equations exploiting the linear Gaussian nature of the problem.

APA, Harvard, Vancouver, ISO, and other styles

28

Sun, Wenqing, Jinqian Feng, Jin Su, and Yunyun Liang. "Data driven adaptive Gaussian mixture model for solving Fokker–Planck equation." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 3 (2022): 033131. http://dx.doi.org/10.1063/5.0083822.

Full text

Abstract:

The Fokker–Planck (FP) equation provides a powerful tool for describing the state transition probability density function of complex dynamical systems governed by stochastic differential equations (SDEs). Unfortunately, the analytical solution of the FP equation can be found in very few special cases. Therefore, it has become an interest to find a numerical approximation method of the FP equation suitable for a wider range of nonlinear systems. In this paper, a machine learning method based on an adaptive Gaussian mixture model (AGMM) is proposed to deal with the general FP equations. Compared

APA, Harvard, Vancouver, ISO, and other styles

29

Sun, Xu, Xiaofan Li, and Yayun Zheng. "Governing equations for probability densities of Marcus stochastic differential equations with Lévy noise." Stochastics and Dynamics 17, no. 05 (2016): 1750033. http://dx.doi.org/10.1142/s0219493717500332.

Full text

Abstract:

Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Lévy processes and have wide applications in engineering and physical sciences. The probability density of the solution to an SDE offers complete statistical information on the underlying stochastic process. Explicit formula for the Fokker–Planck equation, the governing equation for the probability density, is well-known when the SDE is driven by a Brownian motion. In this paper, we address the open question of finding the Fokker–Planck equations for Marcus SDEs

APA, Harvard, Vancouver, ISO, and other styles

30

Qian, Jianliang, and Lexing Ying. "Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation." Journal of Computational Physics 229, no. 20 (2010): 7848–73. http://dx.doi.org/10.1016/j.jcp.2010.06.043.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Albert, Christopher G., and Katharina Rath. "Gaussian Process Regression for Data Fulfilling Linear Differential Equations with Localized Sources." Entropy 22, no. 2 (2020): 152. http://dx.doi.org/10.3390/e22020152.

Full text

Abstract:

Specialized Gaussian process regression is presented for data that are known to fulfill a given linear differential equation with vanishing or localized sources. The method allows estimation of system parameters as well as strength and location of point sources. It is applicable to a wide range of data from measurement and simulation. The underlying principle is the well-known invariance of the Gaussian probability distribution under linear operators, in particular differentiation. In contrast to approaches with a generic covariance function/kernel, we restrict the Gaussian process to generate

APA, Harvard, Vancouver, ISO, and other styles

32

Qiao, Huijie. "Uniqueness for measure-valued equations of nonlinear filtering for stochastic dynamical systems with Lévy noise." Advances in Applied Probability 50, no. 2 (2018): 396–413. http://dx.doi.org/10.1017/apr.2018.19.

Full text

Abstract:

Abstract In the paper we study the Zakai and Kushner–Stratonovich equations of the nonlinear filtering problem for a non-Gaussian signal-observation system. Moreover, we prove that under some general assumption, the Zakai equation has pathwise uniqueness and uniqueness in joint law, and the Kushner–Stratonovich equation is unique in joint law.

APA, Harvard, Vancouver, ISO, and other styles

33

Xie, Hongling. "High-Order Spectral Method of Density Estimation for Stochastic Differential Equation Driven by Multivariate Gaussian Random Variables." Advances in Mathematical Physics 2023 (August 16, 2023): 1–10. http://dx.doi.org/10.1155/2023/9974539.

Full text

Abstract:

There are some previous works on designing efficient and high-order numerical methods of density estimation for stochastic partial differential equation (SPDE) driven by multivariate Gaussian random variables. They mostly focus on proposing numerical methods of density estimation for SPDE with independent random variables and rarely research density estimation for SPDE is driven by multivariate Gaussian random variables. In this paper, we propose a high-order algorithm of gPC-based density estimation where SPDE driven by multivariate Gaussian random variables. Our main techniques are (1) we bu

APA, Harvard, Vancouver, ISO, and other styles

34

IZADI, FARZALI, RASOOL FOROOSHANI NAGHDALI, and PETER GEOFF BROWN. "SOME QUARTIC DIOPHANTINE EQUATIONS IN THE GAUSSIAN INTEGERS." Bulletin of the Australian Mathematical Society 92, no. 2 (2015): 187–94. http://dx.doi.org/10.1017/s0004972715000465.

Full text

Abstract:

In this paper we examine solutions in the Gaussian integers to the Diophantine equation $ax^{4}+by^{4}=cz^{2}$ for different choices of $a,b$ and $c$. Elliptic curve methods are used to show that these equations have a finite number of solutions or have no solution.

APA, Harvard, Vancouver, ISO, and other styles

35

Jin, Shi, Hao Wu, and Xu Yang. "Semi-Eulerian and High Order Gaussian Beam Methods for the Schrödinger Equation in the Semiclassical Regime." Communications in Computational Physics 9, no. 3 (2011): 668–87. http://dx.doi.org/10.4208/cicp.091009.160310s.

Full text

Abstract:

AbstractA novel Eulerian Gaussian beam method was developed in [8] to compute the Schrödinger equation efficiently in the semiclassical regime. In this paper, we introduce an efficient semi-Eulerian implementation of this method. The new algorithm inherits the essence of the Eulerian Gaussian beam method where the Hessian is computed through the derivatives of the complexified level set functions instead of solving the dynamic ray tracing equation. The difference lies in that, we solve the ray tracing equations to determine the centers of the beams and then compute quantities of interests only

APA, Harvard, Vancouver, ISO, and other styles

36

Podousova, T., and N. Vashpanova. "DEFORMATIONS OF SURFACES FROM STATIONARY RICCI TENSOR." Mechanics And Mathematical Methods 2, no. 2 (2020): 51–62. http://dx.doi.org/10.31650/2618-0650-2020-2-2-51-62.

Full text

Abstract:

In this paper, we consider infinitesimal (n. m.) first-order deformations of single-connected regular surfaces in three-dimensional Euclidean space. The search for the vector field of this deformation is generally reduced to the study and solution of a system of four equations (among them there are differential equations) with respect to seven unknown functions. To avoid uncertainty, the following restriction is imposed on a given surface: the Ricci tensor is stored (mainly) on the surface. A mathematical model of the problem is created: a system of seven equations with respect to seven unknow

APA, Harvard, Vancouver, ISO, and other styles

37

Gray, Samuel H., and Norman Bleistein. "True-amplitude Gaussian-beam migration." GEOPHYSICS 74, no. 2 (2009): S11—S23. http://dx.doi.org/10.1190/1.3052116.

Full text

Abstract:

Gaussian-beam depth migration and related beam migration methods can image multiple arrivals, so they provide an accurate, flexible alternative to conventional single-arrival Kirchhoff migration. Also, they are not subject to the steep-dip limitations of many (so-called wave-equation) methods that use a one-way wave equation in depth to downward-continue wavefields. Previous presentations of Gaussian-beam migration have emphasized its kinematic imaging capabilities without addressing its amplitude fidelity. We offer two true-amplitude versions of Gaussian-beam migration. The first version comb

APA, Harvard, Vancouver, ISO, and other styles

38

Wang, Hui, and Tian-Tian Zhang. "Stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 3 (2019): 878–89. http://dx.doi.org/10.1108/hff-08-2018-0448.

Full text

Abstract:

Purpose The purpose of this paper is to study stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms, which can be used to describe the propagation properties of optical soliton solutions. Design/methodology/approach The authors apply the ansatz method and the Hamiltonian system technique to find its bright, dark and Gaussian wave solitons and analyze its modulation instability analysis and stability analysis solution. Findings The results imply that the generalized nonlinear Schrödinger equation has bright, dark a

APA, Harvard, Vancouver, ISO, and other styles

39

Cheshkova, М. A., and A. A. Pavlova. "Example of Bianchi Transformation of Kuen’s Surface." Izvestiya of Altai State University, no. 1(117) (March 17, 2021): 126–28. http://dx.doi.org/10.14258/izvasu(2021)1-22.

Full text

Abstract:

The work is devoted to the study of the Bianchi transformation for surfaces of constant negative Gaussian curvature. The surfaces of rotation of constant negative Gaussian curvature are the Minding top, the Minding coil, and the pseudosphere (Beltrami surface). Surfaces of constant negative Gaussian curvature also include Kuen’s surface and the Dini’s surface. Studying the surfaces of constant negative Gaussian curvature (pseudospherical surfaces) is of great importance for the interpretation of Lobachevsky planimetry. Geometric characteristics of pseudospherical surfaces are found to be relat

APA, Harvard, Vancouver, ISO, and other styles

40

NUALART, DAVID, and LLUÍS QUER-SARDANYONS. "OPTIMAL GAUSSIAN DENSITY ESTIMATES FOR A CLASS OF STOCHASTIC EQUATIONS WITH ADDITIVE NOISE." Infinite Dimensional Analysis, Quantum Probability and Related Topics 14, no. 01 (2011): 25–34. http://dx.doi.org/10.1142/s0219025711004286.

Full text

Abstract:

In this note, we establish optimal lower and upper Gaussian bounds for the density of the solution to a class of stochastic integral equations driven by an additive spatially homogeneous Gaussian random field. The proof is based on the techniques of the Malliavin calculus and a density formula obtained by Nourdin and Viens. Then, the main result is applied to the mild solution of a general class of SPDEs driven by a Gaussian noise which is white in time and has a spatially homogeneous correlation. In particular, this covers the case of the stochastic heat and wave equations in ℝd with d ≥ 1 an

APA, Harvard, Vancouver, ISO, and other styles

41

Herianto, Tulus Joseph, and Adventus Manurung. "Solution of the Likelihood Equation System on Generalized Inverse Gaussian Distribution Parameter Estimation with Newton-Raphson Method." Journal of Mathematics Technology and Education 2, no. 2 (2023): 145–61. https://doi.org/10.32734/jomte.v2i2.9650.

Full text

Abstract:

This study aims to solve the likelihood equation resulting from the estimation ofthe generalized inverse Gaussian distribution parameter estimation. The likelihood equationresulting from the estimation of the generalized inverse Gaussian distribution parameter cannot be solved analytically. The equation cannot be solved because the resulting equation is non linear. So, the Newton-Raphson method was chosen as the right method to be able tosolve the equation. The results obtained from the estimation of the generalized inverse Gaussian distribution parameters with the maximum likelihood method on

APA, Harvard, Vancouver, ISO, and other styles

42

Piela, Lucjan. "Search for the Most Stable Structures on Potential Energy Surfaces." Collection of Czechoslovak Chemical Communications 63, no. 9 (1998): 1368–80. http://dx.doi.org/10.1135/cccc19981368.

Full text

Abstract:

Smoothing techniques for global optimization in search for the most stable structures (clusters or conformers) have been a novel possibility for the last decade. The techniques turned out to be related to a variety of fundamental laws: Fick's diffusion equation, time-dependent and time-independent Schrodinger equations, Smoluchowski dynamics equation, Bloch equation of canonical ensemble evolution with temperature, Gibbs free-energy principle. The progress indicator of global optimization in those methods takes different physical meanings: time, imaginary time, Planck constant, or the inverse

APA, Harvard, Vancouver, ISO, and other styles

43

Hu, Jingjing, Weipeng Hu, Fan Zhang, Han Zhang, and Zichen Deng. "Structure-preserving analysis on Gaussian solitary wave solution of logarithmic-KdV equation." Physica Scripta 96, no. 12 (2021): 125268. http://dx.doi.org/10.1088/1402-4896/ac3efb.

Full text

Abstract:

Abstract The existence of the Gaussian solitary wave solution in the logarithmic-KdV equation has aroused considerable interests recently. Focusing on the defects of the reported multi-symplectic analysis on the Gaussian solitary wave solution of the logarithmic-KdV equation and considering the dynamic symmetry breaking of the logarithmic-KdV equation, new approximate multi-symplectic formulations for the logarithmic-KdV equation are deduced and the associated structure-preserving scheme is constructed to simulate the evolution of the Gaussian solitary wave solution. In the structure-preservin

APA, Harvard, Vancouver, ISO, and other styles

44

Feldman, Raisa E., and Srikanth K. Iyer. "Non-Gaussian Density Processes Arising from Non-Poisson Systems of Independent Brownian Motions." Journal of Applied Probability 35, no. 1 (1998): 213–20. http://dx.doi.org/10.1239/jap/1032192564.

Full text

Abstract:

The Brownian density process is a Gaussian distribution-valued process. It can be defined either as a limit of a functional over a Poisson system of independent Brownian particles or as a solution of a stochastic partial differential equation with respect to Gaussian martingale measure. We show that, with an appropriate change in the initial distribution of the infinite particle system, the limiting density process is non-Gaussian and it solves a stochastic partial differential equation where the initial measure and the driving measure are non-Gaussian, possibly having infinite second moment.

APA, Harvard, Vancouver, ISO, and other styles

45

Feldman, Raisa E., and Srikanth K. Iyer. "Non-Gaussian Density Processes Arising from Non-Poisson Systems of Independent Brownian Motions." Journal of Applied Probability 35, no. 01 (1998): 213–20. http://dx.doi.org/10.1017/s0021900200014807.

Full text

Abstract:

The Brownian density process is a Gaussian distribution-valued process. It can be defined either as a limit of a functional over a Poisson system of independent Brownian particles or as a solution of a stochastic partial differential equation with respect to Gaussian martingale measure. We show that, with an appropriate change in the initial distribution of the infinite particle system, the limiting density process is non-Gaussian and it solves a stochastic partial differential equation where the initial measure and the driving measure are non-Gaussian, possibly having infinite second moment.

APA, Harvard, Vancouver, ISO, and other styles

46

Kumar, Vivek. "Stochastic fractional heat equation perturbed by general Gaussian and non-Gaussian noise." Statistics & Probability Letters 184 (May 2022): 109381. http://dx.doi.org/10.1016/j.spl.2022.109381.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Cheshkova, M. A. "Bianchi transformation of the Minding coil." Differential Geometry of Manifolds of Figures, no. 55(1) (2024): 81–88. http://dx.doi.org/10.5922/0321-4796-2024-55-1-9.

Full text

Abstract:

The work is devoted to the study of the Bianchi transform for surfaces of constant negative Gaussian curvature. The surfaces of rotation of constant negative Gaussian curvature are the Mining top, the Minding coil, the pseudosphere (Beltrami surface). Surfaces of constant negative Gaussian curvature also include Kuens surface and the Dinis surface. The study of surfaces of constant negative Gaussian curvature (pseudospherical surfaces) is of great importance for the interpretation of Lobachevsky planimetry. The connection of the geometric characteristics of pseudospherical surfaces with the

APA, Harvard, Vancouver, ISO, and other styles

48

Ibrahim, R. A., and H. Heo. "Autoparametric Vibration of Coupled Beams Under Random Support Motion." Journal of Vibration and Acoustics 108, no. 4 (1986): 421–26. http://dx.doi.org/10.1115/1.3269365.

Full text

Abstract:

The dynamic response of a two degree-of-freedom system with autoparametric coupling to a wide band random excitation is investigated. The analytical modeling includes quadratic nonlinearity, and a general first-order differential equation of the moments of any order is derived. It is found that the moment equations form an infinite hierarchy set which is closed via two different closure methods. These are the Gaussian closure and the non-Gaussian closure schemes. The Gaussian closure solution shows that the system does not reach a stationary response while the non-Gaussian closure solution giv

APA, Harvard, Vancouver, ISO, and other styles

49

Smith, Steven T. "On Gaussian Beams Described by Jacobi's Equation." SIAM Journal on Applied Mathematics 74, no. 5 (2014): 1637–56. http://dx.doi.org/10.1137/130915996.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Liu, Hailiang, James Ralston, Olof Runborg, and Nicolay M. Tanushev. "Gaussian Beam Methods for the Helmholtz Equation." SIAM Journal on Applied Mathematics 74, no. 3 (2014): 771–93. http://dx.doi.org/10.1137/130916072.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!