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Year 2017

S. E. Vaganov, S. I. Khashin A comparison of the effectiveness of different versions of Lucas–Kanade method

The modification of the classical Lucas–Kanade method for find optical flow between two frames using the Hessian matrix for the second frame was proposed. The convegence radius definition of the algorithm was given. The effectiveness analyze of the various Lucas–Kanade algorithms was produced.

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Yu. A. Kremeshkova, S. V. Puhov, E. A. Tumanova On the geometric interpretation of Â-splines of degree 2

It is known that, for any B-spline S of degree 2, there exist a triangle pyramid \tau and a family \gamma of all planes parallel to a given plane \pi such that the dependence of the square of the cross section of \tau by a plane of \gamma on the parameter defining the position of the plane in the space coincides with S. In the present paper, for an arbitrary triangle pyramid \tau and a family \gamma of parallel planes, all the cases of their mutual arrangement are fully described when the converse is true: the above dependence is proportional to a B-spline of degree 2.

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D. I. Moldavanskii On the separability of cyclic subgroups in the direct product of groups

The sufficient condition for any \pi'-isolated cyclic subgroup of a direct product of two groups to be separable in the class of all finite \pi-groups is obtained. An example showing that this condition is not necessary is constructed.

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E. V. Sokolov Key agreement protocols based on groups with nontrivial identities

We obtain the generalizations of two known key agreement cryptographic protocols based on an arbitrary group satisfying certain nontrivial identity.

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J. A. Khashina Biquadratic functions and their presentation as a sum of the quadrates

If the biquadratic function can be represented as a sum of several complete squares of bilinear functions, than it can be represent in the form of a sum of not more than three such terms and non-negative constant. If the biquadratic function with positive leading coefficient bounded from below, than it can be represented as a sum of three squares of bilinear functions with common zero and biquadratic functions minimum.

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