Results 1 - 10 of 16,568

On Miura Transformations and Volterra-Type Equations Associated with the Adler–Bobenko–Suris Equations

by Decio Levi, Matteo Petrera, Christian Scimiterna, Ravil Yamilov - SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS , 2008
"... We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler–Bobenko–Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund ..."
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We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler–Bobenko–Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund

LOTKA–VOLTERRA TYPE EQUATIONS AND THEIR EXPLICIT INTEGRATION

by Jean-loup Gervais , 1994
"... In the present note we give an explicit integration of some two–dimensionalised Lotka–Volterra type equations associated with simple Lie algebras possessing a representation without branching. ..."
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In the present note we give an explicit integration of some two–dimensionalised Lotka–Volterra type equations associated with simple Lie algebras possessing a representation without branching.

Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics

by Geir Evensen - J. Geophys. Res , 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
Abstract - Cited by 800 (23 self) - Add to MetaCart
. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error

Elastically deformable models

by Demetri Terzopoulos - Computer Graphics , 1987
"... The goal of visual modeling research is to develop mathematical models and associated algorithms for the analysis and synthesis of visual information. Image analysis and synthesis characterize the domains of computer vision and computer graphics, respectively. For nearly three decades, the vision an ..."
Abstract - Cited by 883 (20 self) - Add to MetaCart
The goal of visual modeling research is to develop mathematical models and associated algorithms for the analysis and synthesis of visual information. Image analysis and synthesis characterize the domains of computer vision and computer graphics, respectively. For nearly three decades, the vision

An almost ideal demand system.

by Angus Deaton , John Muellbauer - American Economic Review, , 1980
"... Ever since Richard Stone (1954) first estimated a system of demand equations derived explicitly from consumer theory, there has been a continuing search for alternative specifications and functional forms. Many models have been proposed, but perhaps the most important in current use, apart from the ..."
Abstract - Cited by 636 (0 self) - Add to MetaCart
hope to be able to reveal more clearly the problems and potential solutions associated with the usual approach. I. Specification of the AIDS In much of the recent literature on systems of demand equations, the starting point has been the specification of a function which is general enough to act as a

A Signal Processing Approach To Fair Surface Design

by Gabriel Taubin , 1995
"... In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing, or fai ..."
Abstract - Cited by 654 (15 self) - Add to MetaCart
, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities

Convex Analysis

by R. Tyrrell Rockafellar , 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
Abstract - Cited by 5411 (68 self) - Add to MetaCart
progressed also to the study of so-called stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.

A HYBRID VOLTERRA-TYPE EQUATION WITH TWO TYPES OF IMPULSES

by S. A. Belbas, Jong Seo Park , 2005
"... We formulate and analyze a hybrid system model that involves Volterra integral operators with multiple integrals and two types of impulsive terms. We give a constructive proof, via an iteration method, of existence and uniqueness of solutions. I. ..."
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We formulate and analyze a hybrid system model that involves Volterra integral operators with multiple integrals and two types of impulsive terms. We give a constructive proof, via an iteration method, of existence and uniqueness of solutions. I.

A Unified Approach to Convergence Analysis of Discretization Methods for Volterra-type Equations

by Jennifer Dixon, Sean Mckee , 1983
"... This paper presents a general convergence analysis of numerical methods for solving ordinary differential equations and non-linear Voltcrra integral and integro-differential equations. The concept of analytic and discrete fundamental forms is introduced. Prolongation and restriction operators reduce ..."
Abstract - Cited by 2 (2 self) - Add to MetaCart
collocation method for solving Volterra integral equations of the second kind. 1.

The Variational Formulation of the Fokker-Planck Equation

by Richard Jordan, David Kinderlehrer, Felix Otto - SIAM J. Math. Anal , 1999
"... The Fokker--Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of time--dependent systems in which randomness plays a role. In this paper, ..."
Abstract - Cited by 282 (22 self) - Add to MetaCart
The Fokker--Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of time--dependent systems in which randomness plays a role. In this paper
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