Interrelation of families of points of high order on the Edwards curve over a prime field

We propose a modification of the addition law on the Edwards curve over a prime field. We prove three theorems on properties of coordinates of high-order points and on a degenerate pair of twisted curves. We propose an algorithm for reconstructing all unknown points kP of the Edwards curve when only 1/8 of the points are known.     

A model for generation of directed graphs of information by the directed graph of metainformation for a two-level model of information units with a complex structure

A model for generation of directed graphs of information by the directed graph of metainformation for a two-level connected directed graph model of information units is described. It can be used as a basis in computer tools for editing information with a complex structure with different levels of abstraction and invariance to technological spaces (subject domains) in a common conceptual framework for carriers of this information, making it unnecessary to organize specialized training for these carriers or to involve professional intermediaries.     

Increase of the speed of operation of scalar neural network tree when solving the nearest neighbor search problem in binary space of large dimension

In the binary space of large dimension we analyze the nearest neighbor search problem where the required point is a distorted version of one of the patterns. Previously it was shown that the only algorithms able to solve the set problem are the exhaustive search and the neural network search tree. For the given problem the speed of operation of the last algorithm is dozens of times larger comparing with the exhaustive search. Moreover, in the case of large dimensions the neural network tree can be regarded as an accurate algorithm since the probability of its error is so small that cannot be measured. In the present publication, we propose a modification of the scalar neural network tree allowing the speeding of the algorithm’s operation up to hundred times without losses in its reliability.     

Modeling Close Packing of 3D Objects

The paper represents the concept of Φ-functions and quasi Φ-functions as an efficient tool for mathematical modeling of three-dimensional packing problems for convex geometrical objects with continuous translations and rotations. A mathematical model of close packing of convex geometrical objects is formulated and its basic properties are considered. A solution method is proposed, which includes the following stages: constructing initial points, computing local extrema, and passing from one local minimum to another. The solution approach is efficient to solve optimization packing problems. Numerical examples are given.     

Mathematical modeling of the dynamics of anomalous migration fields within the framework of the model of distributed order

The authors perform mathematical modeling of the dynamics of a locally nonequilibrium (in time) geomigration process in a geoporous medium saturated with a salt solution, on the basis of a sub-diffusion model described by a distributed-order system of equations.     

Trajectory control of a high altitude hypervelocity flying vehicle in the midcourse active phase of the flight

An approach to the control of the motion of the center of mass of a high altitude hypervelocity flying vehicle whose engine thrust and aerodynamics strongly depend on the angle of attack in the midcourse active phase of the flight is proposed. This approach provides a basis for the method of the trajectory control of motion. The motion of this flying vehicle is simulated with regard to the disturbed atmosphere. It is shown that the proposed approach can be used to form launching zones of high altitude hypervelocity flying vehicles.     

Development of algorithms for feature matching in the method for reconstucting high-precision digital surface models

The method for reconstructing high-precision digital surface models baseed on stereo matching of point and contour features is presented. Methods for extracting points and contours in images, and their subsequent matching are considered. Additionally the specific items of the proposed method are underlined from the point of view of using these image features for solving the final problem of detection features of the surface relief. Special attention is paid to the transition from local stereo matching to the global one. The necessity of this transition for successful solving the problem of a qualitative relief model with a minimal number of outliers is shown. The advantages of the developed method are demonstrated by the example of reconstructing a surface relief based on two stereo pairs of aerial images of different resolutions.     

Fast rank algorithms based on multiscale histograms and lazy calculations

Rank algorithms allow effective solutions for image smoothing and impulse noise suppression, but most of them are computationally complex. On the base of multiscale histograms, we propose algorithms for fast computations of EV and KNV neighborhood average, sliding equalization and search for an arbitrary element in a rank series (median filtering is a particular case of this algorithm). An approach using lazy calculations for fast updating of multiscale histograms is proposed. Using the developed algorithms, we have achieved a processing speed for EV and KNV neighborhood average algorithms that is close to the fastest known median filtering algorithm.