Vol. 49 No. 1 (236) (2015)

It is well-known that $N -1$ $n$-independent nodes uniquely determine curve of degree $n$, where $N = (1/2)(n + 1)(n + 2)$. We are interested in finding the minimal number of $n$-independent nodes determining uniquely curve of degree $k\leq1$. In this paper we show that this number for $k=n-1$ is $N-4$.

Using the finite-sheeted unbranched covering maps between the topological spaces, we define the notion of the blowup of a topological space and show the existence of the blowups of certain covering spaces.

It is proved that the inner automorphisms group of the group A(m, n) are characteristic subgroup in Aut(A(m, n)) for all m > 1 and odd $n \geq$1003, where the groups A(m, n) are known non-commutative analogues of the additive group of rational numbers.

The paper introduces an alternative approach to the bonus-malus system construction. In the presented model the premium calculation is based on the previous premium and on the claim severity component as well. Following to the concept of an optimal bonus-malus system the necessary and sufficient condition for the aggregate premiums to be a martingale series have been found out. Thus the presented approach differs totally from the usual bonus-malus classes as well as from the systems, where the severity of the claim is omitted.

We prove that if $P(D)=P(D_1,D_2)=\sum_\alpha\gamma_\alpha D_1^{\alpha_1}D_2^{\alpha_2}$ is almost hippoelliptic regular operator, then for enough small $\delta>0$, all solutions of equation $P(D)u=0$ from $L_{2,\delta}(R^2)$ are entire analytical functions.

For the equation $x_1x_2\ldots x_n+x_{n+1}x_{n+2}\ldots x_{2n}+x_{2n+1}x_{2n+2}\ldots x_{3n}=1$ over the finite field $F_2$ we estimate the minimal number of systems of linear equations over the same field such that the union of their solutions exactly coincides with the set of solutions of the equation. We prove in this article that the number in the question is not greater than $9n^{\log_{2} 3}+4$.

The dynamical sampling problem is a new problem in sampling theory dealing with reconstruction of a function from its spatio-temporal samples. The question of reconstructing the signal, when the positions of measuring devices or sensors are not changing over time has been studied earlier. The focus of this paper is on the case when devices are allowed to move. This, for example, may happen when devices are placed on moving cars and measure the air pollution as they travel within a polluted area.

In thе paper characters of propagation of elastic waves in layer with continuously changing periodical heterogeneity along layer are investigated. Numerical results of dependence of wave propagation phase velocity from determining parameters of heterogeneity of wavelength are shown.

Multibiometric systems are kind of systems, where multiple templates from different biometric sources for the same user are stored. The authentication based on biometrics is a very good mechanism; however, such authentication technology needs large storage of biometric data, which should be protected. Fuzzy Vault is one of the most popular biometric encryption schemes, which aims to encode users’ critical information in such a way that only the legitimate users are able to access it. In this paper multimodal biometric template protection scheme is combined with biometrics, which results a high security. In particular, the approach of feature-level fusion for obtaining single multibiometric template is described and construction of fuzzy vault scheme for the palm veins and fingerprints is presented. The proposed fuzzy vault scheme has been implemented and tested on the publicly available databases.

We consider undirected, simple, finite, connected graphs. Some relations between the μ-parameters are obtained for the case of regular graphs.

Definition of arithmetical functions with indeterminate values of arguments is given. Notions of computability, strong computability and λ-definability for such functions are introduced. Monotonicity and computability of every λ-definable arithmetical function with indeterminate values of arguments is proved. It is proved that every computable, naturally extended arithmetical function with indeterminate values of arguments is λ-definable. It is also proved that there exist strong computable, monotonic arithmetical functions with indeterminate values of arguments, which are not λ-definable. The δ-redex problem for strong computable, monotonic arithmetical functions with indeterminate values of arguments is defined. It is proved that there exist strong computable, λ-definable arithmetical functions with indeterminate values of arguments, for which the δ-redex problem is unsolvable.

Light propagation (reflection, refraction and transmission) through homogeneous uniaxial medium layer with a finite thickness having double anisotropy (i.e. with anisotropy of both dielectric and magnetic permittivities) and an arbitrary orientation of its optical axis in the plane of incidence are investigated. Conditions when layer works as an omnidirectional reflector (independent from incident light polarization and angle) and also conditions for total transmission (independent from incident light polarization and for fixed incident angle) are considered. In purpose of getting laser cavity applications we have discussed certain case of anisotropic layer in which the light accumulation reaches two hundred times more than the intensity of incident light.