2019
Том 71
№ 11

# Volume 52, № 8, 2000

Anniversaries (Ukrainian)

### On the 75th Birthday of Vladimir Semenovich Korolyuk

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1011-1013

Article (Ukrainian)

### On the Creative Contribution of V. S. Korolyuk to the Development of Probability Theory

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1014-1030

We present a brief survey of the main results obtained by V. S. Korolyuk in probability theory and mathematical statistics.

Article (Ukrainian)

### Some Remarks on the Article “On the Creative Contribution of V. S. Korolyuk to the Development of Probability Theory”

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1031-1033

Article (Ukrainian)

### Exact Formulas for $E^{θ}/G/1/N$-Type Queuing Systems

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1034-1044

We investigate E θ/G/1/N-type queuing systems with limited queue. The investigation is based on the potential method proposed by Korolyuk

Article (Russian)

### Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1045-1061

We establish the strong law of large numbers with operator normalizations for vector martingales and sums of orthogonal random vectors. We describe its applications to the investigation of the strong consistency of least-squares estimators in a linear regression and the asymptotic behavior of multidimensional autoregression processes.

Article (Russian)

### Stochastic Integrals with Respect to Consistent Random Measures

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1062-1074

We consider integrals of random mappings with respect to consistent random measures in C([0; 1]).

Article (Russian)

### On the Distribution of the Number of Calls in the Queuing System $D_{η}|D_{ξ}^{\kappa}|1$

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1075-1081

For the queuing system D η|D ξ k|1, we determine the distribution of the number of calls in transient and stationary modes.

Article (Ukrainian)

### Estimation of Parameters of Homogeneous Gaussian Random Fields

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1082-1088

On the basis of the limit theorem for quadratic variation, we construct a consistent estimator for parameters of a homogeneous Gaussian random field of a certain class. We find confidence ellipsoids for estimators of this sort.

Article (Russian)

### Structural Analysis of One Class of Dynamical Systems

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1089-1096

We develop the method of structural transformations of dynamical systems (proposed earlier by Koshlyakov) for systems containing nonconservative positional structures. The method under consideration is based on structural transformations that enable one to eliminate nonconservative positional terms from the original system without changing its stability properties.

Article (Ukrainian)

### A Test for the Homogeneity of Mixtures with Varying Concentrations

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1097-1102

We construct a generalized version of the Kolmogorov–Smirnov test for the verification of a hypothesis concerning the homogeneity of a sample against an alternative sample from a mixture with varying concentrations. We obtain asymptotic formulas and nonasymptotic upper bounds for the probabilities of errors of the first and second kinds.

Article (Russian)

### On Strong Summability of Fourier Series of Summable Functions

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1103-1111

In the metric of L, we obtain estimates for the generalized means of deviations of partial Fourier sums from an arbitrary summable function in terms of the corresponding means of its best approximations by trigonometric polynomials.

Article (Russian)

### Controlled Pulse Influence in Games with Fixed Termination Time

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1112-1118

We construct optimal strategies for players and determine the sets of initial positions favorable for one player or another.

Article (Ukrainian)

### Differentiation of Multivalued Mappings. $T$-Derivative

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1119-1126

We consider several approaches to the differentiation of multivalued mappings and introduce a new definition of derivative (T-derivative), which generalizes the Hukuhara derivative.

Brief Communications (Russian)

### A Probability Method for the Solution of the Telegraph Equation with Real-Analytic Initial Conditions

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1127-1134

We propose a method for the construction of an analytic solution of the Cauchy problem for the telegraph equation that is based on its simulation by a one-dimensional Markov random evolution.

Brief Communications (Ukrainian)

### α-Primitive Elements in the Generalized Verma Modules

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1135-1140

We present explicit formulas for α-primitive elements in the generalized Verma module, which generalize the known formulas for primitive elements in the Verma modules.

Brief Communications (Russian)

### Quotient Groups of Groups of Certain Classes

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1141-1143

For an arbitrary variety $\mathfrak{X}$ of groups and an arbitrary class $\mathfrak{Y}$ of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with $\mathfrak{X}$ - and $\mathfrak{Y}$ -factors (respectively, is a residually $\mathfrak{Y}$ -group) if G possesses an invariant system with $\mathfrak{X}$ - and $\mathfrak{Y}$ -factors (respectively, is a residually $\mathfrak{Y}$ -group) and N $\mathfrak{X}$ (respectively, N is a maximal invariant $\mathfrak{X}$ -subgroup of the group G).

Brief Communications (Ukrainian)

### Extremum Problem for the Wiener–Hopf Equation

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1144-1147

The extremum problem for the Wiener–Hopf equation obtained by replacing the condition u(x) = 0, x < 0, by the condition of the minimum of the quadratic functional of the function u(x)exp(−x), −∞ < x < ∞, is solved in closed form.

Article (Russian)

### Statistical Tests for the Order of a Regression Model Based on a Single Series of Observations

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1148-1152

We construct a test for the determination of the order of a linear regression model on the basis of a single series of observations in the case of normally distributed noise with mean value zero and bounded variance. We propose a new equilibrium statistic for the model with infinite (but single) series of observations; by using this statistic, we construct a test for the determination of the order of this model.