Vol. 53 No. 2 (249) (2019)

We consider the problem of identification of the position and the moment of the beginning of a radioactive source emission on the plane. The acts of emission constitute inhomogeneous Poisson processes and are registered by $ K $ detectors on the plane. We suppose that the moments of arriving of the signals at the detectors are measured with some small errors. Then, using these estimate, we construct the estimators of the position of source and the moment of the beginning of emission. We study the asymptotic properties of these estimators for large signals and prove their consistency.

We consider sets of word tuples accepted by multitape finite automata. We use the known notation for regular expressions that describes languages accepted by one-tape automata. Nevertheless, the interpretation of the "concatenation" operation is different in this case. The algebra of events for multitape finite automata is defined in the same way as for one-tape automata. It is shown that the introduced algebra is a Kleene algebra. It is also, shown that some known results for the algebra of events accepted by one-tape finite automata are valid in this case too.

Let the set of nodes $ \LARGE{x} $ in the plain be $ n $-independent, i.e., each node has a fundamental polynomial of degree $ n $. Suppose also that $ \vert \LARGE{x} \normalsize \vert \mathclose{=} (n \mathclose{+} 1) \mathclose{+} n \mathclose{+} \cdots \mathclose{+} (n \mathclose{-} k \mathclose{+} 4) \mathclose{+} 2 $ and $ 3 \mathclose{\leq} k \mathclose{\leq} n \mathclose{-} 1 $. We prove that there can be at most 4 linearly independent curves of degree less than or equal to $ k $ passing through all the nodes of $ \LARGE{x} $. We provide a characterization of the case when there are exactly 4 such curves. Namely, we prove that then the set $ \LARGE{x} $ has a very special construction: all its nodes but two belong to a (maximal) curve of degree $ k \mathclose{-} 2 $. At the end, an important application to the Gasca-Maeztu conjecture is provided.

In this paper we obtain explicit expressions for the covariogram and the orientation-dependent chord length distribution of a right parallelepiped with square base.

This article deals with the problem of an elastic infinite strip, which is strengthened along its free boundary by a finite number of finite overlays with different elastic characteristics and small constant thicknesses. The interaction between the strip and the overlays is mediated by adhesive shear layers. The overlays are deformed under the action of horizontal forces. The problem of determination of unknown stresses acting between the strip and overlays are reduced to a system of Fredholm integral equations of the second kind for a finite number of unknown functions defined on different finite intervals. It is shown that in the certain domain of variation of the characteristic parameter of the problem this system of integral equations in Banach space may be solved by the method of successive approximations. Particular cases are discussed and the character and behaviour of unknown shear stresses are investigated.

We obtain lower bounds for the complexity of linearized coverings for some sets of special solutions of the equation $$ x_{1}x_{2}x_{3} \mathclose{+} x_{2}x_{3}x_{4} \mathclose{+} \cdots \mathclose{+} x_{3n}x_{1}x_{2} \mathclose{+} x_{1}x_{3}x_{5} \mathclose{+} x_{4}x_{6}x_{8} \mathclose{+} \cdots \mathclose{+} x_{3n-2}x_{3n}x_{2} \mathclose{=} b $$ over an arbitrary finite field.

In this paper we investigate a class of equation systems with determinable partial (not everywhere defined) Boolean functions. We found the asymptotic estimate of the number of solutions of equation systems in the “typical” case (for the whole range of changes in the number of equations).

In this study we present a microwave sensor based on the quadratic-shape and designed for detecting glucose concentration in aqueous solutions by using a microwave near-field electromagnetic interaction technique. We found a linear relationship between the microwave $ S_{11} $ reflection coefficient of the suggested system and the concentration of glucose in solution. Due to this linear relationship we were able to determine the glucose concentration in the range of 0–250 mg/dL at an operating frequency near 3.6 GHz. The measured minimum detectable signal was 0.0044 dB/(mg/dL) and the measured minimum detectable concentration was 6.8 mg/dL. These results suggest that the system we offer has a high enough accuracy for non-contact glucose monitoring and provides a promising basis for developing a non-invasive glucometer.

In the article exact analytical and invariant solutions for both spinless and half-spin relativistic charged particles in crossed constant electric and magnetic fields, when $ H \mathclose{>} E $ have been found. It is shown that in both cases the problem reduces to that of quantum harmonic oscillator.