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Vol 72, No 2 (2017)
- Year: 2017
- Articles: 9
- URL: https://journal-vniispk.ru/0027-1322/issue/view/10017
Article
45-48
Characterization of ℝ-factorizable G-spaces
Abstract
The ℝ-factorizability of G-spaces is characterized in the paper and the equivalence of ℝ-factorizability and ω-U property is proved for G-spaces with d-open actions of ω-narrow groups. It is shown that the ℝ-factorizability characterizes those compact coset spaces which are coset spaces of ω-narrow groups. The concepts of m- and M-factorizable G-spaces are introduced, which generalizes the corresponding concepts for topological groups.
49-54
Constructive theory of enumerable species
Abstract
A constructive semantics for the language of set theory with atoms based on interpreting set variables by enumerable species is defined. The soundness of the axioms of the Zermelo–Fraenkel set theory with this semantics is completely studied.
55-60
Estimates for the number of Boolean functions realized by an initial Boolean automaton with three constant states
Abstract
The problem of realization of Boolean functions by initial Boolean automata with constant states and n inputs is considered. Such automata are those whose output function coincides with one of n-ary constant Boolean functions 0 or 1 in all states. The exact value of the maximum number of n-ary Boolean functions, where n > 1, realized by an initial Boolean automaton with three constant states and n inputs is obtained.
61-69
Brief Communications
Graded prime Goldie rings
Abstract
Prime Goldie rings graded by a group are studied. It is proved that there exists a completely gr-reducible graded ring of fractions in the case of a grading group with a finite commutator subgroup (which enhances the results of Goodearl–Stafford obtained for Abelian groups). An example where such ring does not exist is constructed (a counterexample for a semi-prime ring was already known).
70-72
Stability of solutions in optimal reinsurance problem
Abstract
A discrete-time insurance model with stop-loss reinsurance is considered. One-period insurance claims form a sequence of independent identically distributed nonnegative random variables with finite mean. The insurer maintains the company surplus above a chosen level a by capital injections. We study the stability of optimal capital injections to the variability of claims distribution. The term “optimal” means the minimal amount of injections that can be found from the corresponding Bellman equation.
73-76
Estimates and asymptotic properties of solutions and their derivatives for a weakly nonlinear third order ordinary differential equation
Abstract
Sufficient conditions are established for the estimate, boundedness, power absolute integrability on the semiaxis, tending to zero including exponential and power laws for solutions and their first and second derivatives to a weakly nonlinear third order ordinary differential equation.
77-80
The absence of residual property for total hyper-frequencies of solutions to third order differential equations
Abstract
It is established that total hyper-frequencies considered as functionals on the set of solutions to third order homogeneous linear differential equations with continuous coefficients bounded on the semiaxis are not residual (i.e. can be changed when changing the solution on a finite interval).
81-83
The rate of convergence of weak greedy approximations over orthogonal dictionaries
Abstract
The convergence rate of a weak orthogonal greedy algorithm is studied for the subspace ℓ1 ⊂ ℓ2 and orthogonal dictionaries. It is shown that general results on convergence rate of weak orthogonal greedy algorithms can be essentially improved in the studied case. It is also shown that this improvement is asymptotically sharp.
84-87