In this paper we study generalized classes of volume preserving multidimensional integrable systems via Nambu-Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close resemblance to the self dual Einstein equation. Recently Takasaki-Takebe provided the twistor construction of dispersionless KP and dToda type equations by us...

A certain non-Noetherian connection between symmetry and integrability properties of nonlinear field equations in conservation-law form is studied. It is shown that the symmetry condition alone may lead, in a rather straightforward way, to the construction of a Lax pair, a doubly infinite set of (generally nonlocal) conservation laws, and a recursion operator for symmetries. Applications includ...

We introduce a data-efficient approach for solving the linear Bellman equation, which corresponds to a class of Markov decision processes (MDPs) and stochastic optimal control (SOC) problems. We show that this class of control problem can be cast as a stochastic composition optimization problem, which can be further reformulated as a saddle point problem and solved via dual kernel embeddings [1...

The extended boundary node method (X-BNM) has been applied to a boundary-value problem of the Grad-Shafranov (G-S) equation and its performance has been numerically investigated by comparing with the dual reciprocity boundary element method (DRM). The result of computations shows that the accuracy of the X-BNM is higher than that of the DRM. Therefore, it is found that the X-BNM might be a powe...

We reformulate the self-dual Einstein equation as a trio of di erential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2D sigma models valued in in nite-dimensional group, which was shown by Park and Husain earlier. We also derive other eld theories including the 2D Higgs bundle equation. This formulation elucidates the relation among thos...

• Slits, li • Intersection of 2 planes, defined by their parametric coordinates ui and vi ; • For horizontal slit, in the pox-slits model, • For vertical slit, in the pox-slits model, • Z1 and Z2 are the distance that each slit are from the image plane. • Equation, represented by the dual Plücker matrices, is • Projection ray, • Intersection of the planes formed by a 3D Point, P, and each slit;...

the asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. the rigid disk is assumed to be in frictionless contact with the elastic half-space. by virtue of appropriate green's functions, the mixed boundary value problem is written as a dual integral equation. employing further mathematica...

The paper begins with a review of screw algebra including dual numbers, unit line vectors, dual vectors, screws, line coordinates, and screw coordinates and summarizes the essential rules of operation for screw algebra. A significant advantage of the algebra is that geometric, kinematic, and dynamic equations of a rigid body can be expressed in a concise and compact form. Several physical quant...

This work addresses the numerical approximation of distributed null controls (with small support) for the 1D heat equation, with Dirichlet boundary conditions: the goal is to compute a control that drives the solution from a prescribed initial state at t = 0 to zero at t = T . The earlier contribution by Carthel, Glowinski and Lions [3] considers boundary controls and exhibits numerical instabi...

We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax− |x| = b, where A is an n× n square matrix. The algorithm, which makes no assumptions on AVE other than solvability, consists of a finite number of linear programs terminating at a solution of the AVE or at a stationary point of the bilinear program. The...