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In this paper we show that if one writes down the structure equations for the evolution of a curve embedded in an n-dimensional Riemannian manifold with constant curvature this leads to a symplectic, a Hamiltonian and an hereditary operator. This gives us a natural connection between finite dimensional geometry, infinite dimensional geometry and integrable… (More)

- Elizabeth Mansfield, Gloria Marí Beffa, Jing Ping Wang
- Foundations of Computational Mathematics
- 2013

Group-based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group-based moving frame, which is essentially a sequence of moving frames with overlapping domains. We demonstrate a small set of… (More)

- Alexander V. Mikhailov, Vladimir S. Novikovand, Jing Ping Wang
- 2008

We study partial differential equations of second order (in time) that possess a hierarchy of infinitely many higher symmetries. The famous Boussinesq equation is a member of this class after the extension of the differential polynomial ring. We develop the perturbative symmetry approach in symbolic representation. Applying it, we classify the integrable… (More)

We introduce the notion of a ghost characteristic for nonlocal differential equations. Ghosts are essential for maintaining the validity of the Jacobi identity for the characteristics of nonlocal vector fields. The local theory of symmetries of differential equations has been well-established since the days of Sophus Lie. Generalized, or higher order… (More)

- Gloria Marí Beffa, Jan A. Sanders, Jing Ping Wang
- J. Nonlinear Science
- 2002

- Jing Wang, Lijian Yang, JING WANG, LIJIAN YANG
- 2007

Asymptotically exact and conservative confidence bands are obtained for a nonparametric regression function, using piecewise constant and piecewise linear spline estimation, respectively. Compared to the pointwise confidence interval of Huang (2003), the confidence bands are inflated by a factor proportional to {log (n)} 1/2 , with the same width order as… (More)

This paper is devoted to the complete classiication of integrable one-component evolution equations whose eld variable takes its values in an associative algebra. The proof that the list of noncommutative inte-grable homogeneous evolution equations is complete relies on the symbolic method. Each equation in the list has innnitely many local symmetries and… (More)

- Jing Ping WANG, J P Wang
- 2001

This paper contains a list of known integrable systems. It gives their recursion-, Hamiltonian-, symplectic-and cosymplectic operator, roots of their symmetries and their scaling symmetry.

- Willy Hereman, Jan A. Sanders, Jack Sayers, Jing Ping Wang, JING PING WANG
- 2004

Algorithms for the symbolic computation of polynomial conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of the Fréchet and variational derivatives and the Euler and homotopy operators. The algorithms are illustrated… (More)

- Jing Wang, Lijian Yang
- 2009

A great deal of effort has been devoted to the inference of additive model in the last decade. Among existing procedures, the kernel type are too costly to implement for high dimensions or large sample sizes, while the spline type provide no asymptotic distribution or uniform convergence. We propose a one step backfitting estimator of the component function… (More)