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2004 year, number 3

Nonparametric tests in testing composite hypotheses on goodness of fit to exponential family distributions

B.Yu. Lemeshko and A.A. Maklakov
Pages: 3–18

Abstract >>
Statistical modeling methods are used to investigate statistic distributions of nonparametric Kolmogorov, and also and Mises tests for composite hypotheses on goodness of fit of empirical data to the exponential family distributions. Models of limiting distributions of statistics of the considered goodness of fit tests are constructed for different values of the parameter of form of exponential family and are recommended for application to problems of statistical analysis.

Estimation of Quantities by Means of Fuzzy Arithmetic

I.A .Hodashinsky
Pages: 19–28

Abstract >>
Procedures for estimation of quantities expressed as fuzzy numbers are considered. A fuzzy triangular number is chosen as a base for estimation. Examples of estimation of fuzzy trapezoid and parabolic numbers by triangular equivalents are given. Problems of finding an average value of several fuzzy triangular numbers are considered. Operations for estimation of complex properties are determined.

Extreme accessible probabilities of true recognition of multi-dimensional vector signals

Y.A. Furman and A.A .Rozhentsov
Pages: 29–41

Abstract >>
The problem of definition of extreme accessible probabilities of true signal recognition by means of an ordered set of k-dimensional vectors is solved. The choice of a space for signal presentation, the criterion of decision making, the kind of reference signals of the alphabet and its volume, as well as the model of a signal recognized are substantiated. An expression for calculating the extreme accessible probability of true recognition of a k-dimensional signal is obtained as a -multiple definite integral of the normal probability distri- bution density. Validity of analytically obtained results is experimentally verified.

Object recognition algorithms invariant to geometrical distortions: translation, scale, and rotation

I.S. Gruzman and V.G. Nikitin
Pages: 42–47

Abstract >>
To solve the problem of object recognition with geometrical distortions, it is proposed to use central moments of inertia of edge line segments occurred in the sector while radial-circle scanning of objects. The scanning center is located in the central moments of inertia of each observed object. Such a scanning ensures scale invariance of size of the feature vector and robustness of recognition algorithms. This feature vector is used to obtain an algorithm of simultaneous recognition and estimation of geometrical distortion parameters, and a correlation recognition algorithm. Both of them are very robust.

Factorization of matrices of Walsh transforms

A.I. Litvin and L.A. Pisarenko
Pages: 48–54

Abstract >>
Techniques for factorization of matrices of Walsh transforms are considered. The proposed algorithms for matrices factorization are convenient for their implementation in real time as well as in the vector mode for single-instruction/multiple-data computing devices.

Application of the artificial neural network technology to predicting floristic parameters of herbarium labels

V.I. Krasinsky
Pages: 55–62

Abstract >>
Results of classifying documents of a botanical database of herbarium labels in terms of two qualitative features on the basis of one mathematical method of artificial intelligence, theory of artificial neural networks, are presented. The values of the qualitative target feature of other documents in this database were predicted, which revealed several errors in the documents.

The effect of recording material shrinkage on the dispersion characteristic of a reflective phase hologram

P.V. Troshchanovich, N.A .Kostrov and E.F. Pen
Pages: 63–72

Abstract >>
Some effects of recording material shrinkage on the properties of a volume reflective phase hologram are investigated. A method is proposed for solving the inverse problem of experimental determination of the value of material shrinkage by the optimal hologram reconstruction conditions that have been changed by its effect. Conditions for a solution of the inverse problem are presented. The theoretical and experimental results are in good agreement. The proposed model can be applied with account for the material shrinkage in the course of designing holographic optical elements and holograms of diffused objects.

To the problem of light diffraction on ultrasonics

S.V. Bogdanov
Pages: 73–78

Abstract >>
The problem concerns light diffraction on ultrasonics in the Raman-Nath and Bragg modes in relation to the law of impulse conservation. It is shown that the commonly used approximation of plane acoustic waves in the Raman-Nath diffraction results in violation of this law, leading to errors in determination of angles of diffraction.

The equation for an imaging optical system with an axicon

V.V. Kotlyar and A.A. Kovalev
Pages: 79–87

Abstract >>
A Fourier correlator with a spatial filter in the form of an axicon is considered. A convolution-type integral expression that relates complex amplitudes at the input and output of the optical system is obtained.

Correction of rigid gradient-index endoscope aberrations

E.G. Ezhov, S.A. Stepanov, and G.I. Greisukh
Pages: 88–92

Abstract >>
Results on investigating the possibilities of color and monochromatic aberrations of the needle-shaped unit of a rigid endoscope, which includes gradient-index optical elements: an objective and a translator, are presented. It is shown that a hybrid compensator consisting of a Wood lens and a homogeneous meniscus can serve as an effective corrector of its aberrations.

Fourier-Fresnel transform in speckle interferometry

E.A. Krasnopevtsev
Pages: 93–102

Abstract >>
The Fourier-Fresnel transform based on geometrical optics, which is performed by converging and diverging lenses, and used in speckle interferometry to determine with a variable sensitivity the shift in the plane and the inclination of elements of the surface of deformed objects is considered.

Reduction of the zone shadowing effect in diffractive optical elements on curvilinear surfaces

I.V. Minin and O.V. Minin
Pages: 103–112

Abstract >>
Results of theoretical investigation of the zone shadowing effect in focusing diffractive optical elements are presented. It is shown that fabrication of a diffractive optical element on a curvilinear surface will substantially reduce this effect and increase the coefficient of usage of element surface.