For N-coupled generalized time-dependent oscillators, primary invariants and a generalized invariant are found in terms of classical solutions. Exact quantum motions satisfying the Heisenberg equation of motion are also found. For number states and coherent states of the generalized invariant, the uncertainties in positions and momenta are obtained.

We present a novel approach for segmenting different motions from 3D trajectories. Our approach uses the theory of transformation groups to derive a set of invariants of 3D points located on the same rigid object. These invariants are inexpensive to calculate, involving primarily QR factorizations of small matrices. The invariants are easily converted into a set of robust motion affinities and ...

Master character of the multidimensional homogeneous Euler equation is discussed. It shown that under restrictions to lower dimensions certain subclasses its solutions provide us with various hydrodynamic type equations. Integrable one dimensional systems in terms Riemann invariants and extensions, equations describing isoenthalpic polytropic motions shallow water are among them.

In this work we study in detail new kinds of motions of the metric tensor. The work is divided into two main parts. In the first part we study the general existence of Kerr-Schild motions —a recently introduced metric motion. We show that generically, Kerr-Schild motions give rise to finite dimensional Lie algebras and are isometrizable, i.e., they are in a one-to-one correspondence with a subs...

Construction of an efficient perception and action mechanism is the most crucial issue for creation of intelligent robots. Our objective is to apply the robot’s own experience for developing the robot’s perception and action mechanism based on human development. In this talk, I present my work on development of robot’s perception mechanism based on affordance theory and motion generation using ...

Moment invariants are important shape descriptors in computer vision. In this paper, we give a general and systematic method to derive moment invariants of any order and for k-dimensional space (invariants to scale, to orthogonal transformation and to translation). This result is applied to the selection of adequate features for visual servoing. To elaborate the control law, we also determine t...

Quantum mechanics may loose its weirdness if systematically geometric algebra methods would be used more. Crucial aspect is to find laws of quantum mechanics be present in macroworld in form of description of motions rather than objects. To help to reach this goal we suggest to use double rotation as one of base invariants in quantum mechanics. We suggest to consider geometric algebra as algebr...

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.