Yu. G. Palii

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Entangling properties of a mixed 2-qubit system can be described by the local homogeneous unitary invariant polynomials in elements of the density matrix. The structure of the corresponding invariant polynomial ring for the special subclass of states, the so-called mixed X−states, is established. It is shown that for the X−states there is an injective ring(More)
Algorithmic methods of commutative algebra based on the involutive and Gröbner bases technique are efficient means for completion of equations governing dynamical systems to involution. At the same time, when working with high-dimensional tensor quantities, direct use of standard functions for calculating Gröbner bases, which are built in computer algebra(More)
The drift of numerical solution of a dynamical system off the integral and constraint surface is eliminated with the help of a gradient supplement to the equations of motion. This supplement makes the image point in the phase space to move along the normal to a given surface. The solution is compared with those obtained by integrating the generalized(More)
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