The fundamental quantities of classical dynamics, such as position, velocity and acceleration, are expressed in terms of the Cartan tetrad, and the first Cartan structure equation is used to develop classical dynamics. The velocity is defined as the covariant exterior derivative of the position, and the acceleration as the exterior covariant derivative of the velocity. The resulting terms are a...

9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objects A and B. It transforms the topological relationships between two simple spatial objects A and B into point-set topology problem in terms of the intersections of A’s boundary (symbol 182 \f "Symbol" \s 11∂}A), interior (A) and exterior (A) with B’s boundary ( symbol 182 \f "S...

9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objects A and B. It transforms the topological relationships between two simple spatial objects A and B into point-set topology problem in terms of the intersections of A’s boundary (A), interior (A) and exterior (A) with B’s boundary ( B), interior (B) and exterior (B). It was sh...

We review the notion of the deformation of the exterior wedge product. This allows us to construct the deformation of the algebra of exterior forms over a vector space and also over an arbitrary manifold. We relate this approach to the generalized statistics. we study quons, as a particular case of these generalized statistics. We also give their statistical properties. A large part of the work...

Given a strictly convex plane curve, the dual billiard transformation is the transformation of its exterior defined as follows: given a point x outside the curve, draw a support line to it from the point and reflect x at the support point. We show that the dual billiard transformation far from the curve is well approximated by the time 1 transformation of a Hamiltonian flow associated with the ...

Given a collection of unorganised points in space, we present a new method of constructing a surface which approximates this point cloud. The surface is defined implicitly as the isosurface of a trivariate volume model. The volume model is piecewise linear and obtained as a least squares fit to data derived from the point cloud. The original point cloud input is assigned a zero value. Additiona...

The exterior of a bounded closed point set b in E will mean the unbounded region of the complementary set E — b. The remainder of E — b, if not vacuous, will be called the interior of b. (A) As a corollary to the above theorem, c is intersected by any simple arc with one end point interior and one exterior to c. This paper contains an elementary constructive proof of the Jordan-Schoenflies Theo...

Let X = G=K be an odd-dimensional semisimple Riemannian symmetric space of the noncompact type, and suppose that all Cartan subgroups of G are conjugate. Let u be a real-valued classical solution of the modiied wave equation u tt = ((+ k)u on R X, the Cauchy data of which are supported in a closed metric ball of radius a at time t = 0. Here t is the coordinate on R, is the (nonpositive deenite)...

In joint work with S.-T. Yau, we construct new cohomologies of differential forms and elliptic operators on symplectic manifolds. Their construction can be described simply following a symplectic decomposition of the exterior derivative operator into two first-order differential operators, which are analogous to the Dolbeault operators in complex geometry. These first-order operators lead to ne...