Some Invariant Solutions of Two-Dimensional Elastodynamics in Linear Homogeneous Isotropic Materials

Invariant solutions of two-dimensional elastodynamics in linear homogeneous isotropic materials are considered via the group theoretical method. The second order partial differential equations of elastodynamics are reduced to ordinary differential equations under the infinitesimal operators. Three invariant solutions are constructed. Their graphical figures are presented and physical meanings are elucidated in some cases.

New Approach for Dynamic Modelling of Flexible Manipulators

This paper deals with the dynamic modelling of flexible manipulators. Expressing such models analytically is extremely useful in simulation, design, control, and identification. To this end, an efficient and systematic approach is proposed for symbolic derivation of dynamic equations. A kinematic formulation based on homogeneous transformations and infinitesimal operators is used. In order to obtain simplified model equations for sufficiently stiff manipulators, infinitesimal displacement terms of the order of ≤ 2 are systematically eliminated by using an appropriate algorithm. Lagrangian formalism is adopted to obtain dynamic equations. A serial and a parallel manipulator are considered to verify and illustrate the proposed approach.

Markov Dilation of Diffusion Type Processes and its Application to the Financial Mathematics

The Markov dilation of diffusion type processes is defined. Infinitesimal operators and stochastic differential equations for the obtained Markov processes are described. Some applications to the integral representation for functionals of diffusion type processes and to the construction of a replicating portfolio for a non-terminal contingent claim are considered.

BRAIDS, LINK POLYNOMIALS AND TRANSFORMATIONS OF SOLVABLE MODELS

It is shown that braid matrices and link polynomials can be systematically constructed from exactly solvable models in statistical mechanics. Through symmetry breaking transformations, different braid matrices are derived from a solvable model. By associating the Markov traces with multi-variable representations, multi-variable link polynomials are obtained. Infinitesimal operators for braid matrices are constructed. Connection of our approach to the conformal field theories and the topological quantum field theory is discussed.