Search

Results:

Vol. 13 (2010 year), No. 3

Zharkikh A.A., Bychkova S.M.
On distribution of Euclidean distances between ordered set of

The paper contains the solution of the Cermelo navigational problem for a free axial field of velocities obtained in analytical and integral form by means of the principle of the Pontryagin maximum. As an example the results of concrete solutions of problems with different forms of the velocities' profile and given correlation of its base velocity and velocities of the moving object have been given. The management function has been received analytically, trajectory solutions have been built as integrals using MathCad software package. Some examples have been shown when the maximum principle does not give the optimum decision.

(in Russian, стр.15, fig. 0, tables. 0, ref 8, Adobe PDF, Adobe PDF 0 Kb)

Vol. 13 (2010 year), No. 4

Zharkikh A.A., Bychkova S.M.
Recognition of direction of point random shift accounting random rotation

The observation of the point on a plane is being made in order to determine the direction of its parallel shift. The point performs a complex motion which includes a parallel shift in a certain direction and rotation at a random angle. The observation begins at a random moment of time. Point coordinates are measured and recorded after each step of the random motion. Mathematical models have been constructed for the point motion and decisive rule of recognition. Expressions for calculating the probability of correct recognition of the parallel shift direction have been presented in the form of theorems.

(in Russian, стр.5, fig. 0, tables. 0, ref 7, Adobe PDF, Adobe PDF 0 Kb)

Vol. 16 (2013 year), No. 1

Zharkikh A.A., Bychkova S.M.
Probabilities of recognition of direction of point shift on a plane on a random rotations background

The complex motion of a point on a plane has been considered. The observed point and the center of point rotation carry out a parallel shift with the probability p in one of m equidistant on an angle of directions at each discrete time moment and, simultaneously, the observed point rotates relatively to this center on a random angle. The decision rule for determining the direction of shift has been justified. Expressions for conditional probability densities distribution of sample means of coordinates of the observed point have been derived. Formulas for the probabilities of correct recognition of the shift direction have been derived by two ways. One way uses the resulting conditional probability density functions. The second way is realized by averaging over random parameters of motion.

(in Russian, стр.12, fig. 0, tables. 1, ref 7, Adobe PDF, Adobe PDF 0 Kb)