Under the assumption that a residually finite-dimensional Hopf algebra H has an Artinian ring of fractions, it is proved flat module over any right coideal subalgebra satisfying polynomial identity and faithfully subalgebra. As consequence we find large class algebras which are all subalgebras subalgebras.

Developed Navier-Stokes turbulence is simulated with varying wave-vector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents zp of the pth order velocity stru...

A generalized theory of two-dimensional isotropic turbulence is developed based on con-formal symmetry. A number of minimal models of conformal turbulence are solved under an extended constraint including both the enstrophy cascade by Kraichnan and the discontinuity of vorticity by Saffman. There are an infinite number of solutions which fall into two different categories. An explicit relation ...

When optimizing the performance of constrained robotic system, the motion trajectory plays a crucial role. In this research the motion planning problem for systems that admit a polynomial description of the system dynamics through differential flatness is tackled by parameterizing the system’s so-called flat output as a polynomial spline. Using basic properties of B-splines, sufficient conditio...

Ahs~aet-A new technique is presented for the design of digital FIR filters, with a prescribed degree of flatness in the passband, and a prescribed (equiripple) attenuation in the stopband. The design is based entirely on an appropriate use of the well-known Rem&-exchange algorithm for the design of weighted Chebyshev FIR filters. The extreme versatility of this algorithm is combined with certai...