Using recurrence relations between any three consecutive polynomial eigenfunctions of second-order linear differential equations, the Christoffel–Darboux formulas are derived for the system of ...polynomial eigenfunctions of these equations.
A system of third-order recurrence relations for the coefficients of polynomial eigenfunctions (PEFs) of a differential equation is solved. A recurrence relation for three consecutive PEFs and a ...formula for differentiating PEFs are obtained. We consider differential equations one of which generalizes the Hermite and Laguerre differential equations and the other is a generalization of the Jacobi differential equation. For these equations, we construct functions bringing them to self-adjoint form and find conditions under which these functions become weight functions. Examples are given where the PEFs for nonweight functions do not have real zeros.
The paper is devoted to the vision system for determining the grain-size distribution of finely crushed particles (∼ 0.1mm in size) of bulk material moving on a conveyor belt. A block diagram of the ...system and data exchange protocol are presented. The commands for high-speed LED pulse backlight control are provided. The functional diagram and principle of the LED matrix control are described. The results of a full-scale testing of the system at the mining and processing plant are presented. As a result of the full-scale testing of the system at the mining and processing plant, the absolute error varies from 1.2% for the class "+ 4.0mm" to 5.2% for the class "-0.1mm". The absolute error for the target "+ 1.0mm" is 2.5%.
We suggest a modified solution to the Riemann boundary value problem on a Riemann surface of an algebraic function of genus
. This allows us to to reduce the problem of finding the number
l
of ...linearly independent algebraic functions (LIAF), that are multiples of a fractional divisor
Q
, to finding the number of LIAF that are multiples of an effective divisor
J
(
); this provides a solution to the Jacobi inversion problem given in this paper. We study the case, where the exponents of the normal basis elements coincide, and solve the problem of finding the number of LIAF, multiples of an effective divisor. The definitions of conjugate points of Riemann surface and hyperorder of an effective divisor are introduced. Depending on the structure of divisor
J
, exact formulas are obtained for number
l
; they are expressed in terms of the order of divisor
Q
, the hyperorder of divisor
J
, and numbers
and
n
, where
n
is the number of sheets of the algebraic Riemann surface.
The thermal conductivities for the traditional fuel UO2 and for the Accident Tolerant Fuel (uranium Molybdenum alloy, U-10Mo and uranium silicide, U3Si2) are calculated and compared. Then the ...temperature distributions on these core reactor, namely on the surface of the rod and in the center line of the rod were determined. The calculation is carried out using MATHCAD program. The calculations showed enhancement of thermal conductivity of the Accident Tolerant Fuel as they increased linearly with increasing temperature, and reduction of their center line temperatures of the rods. Beside, their steep thermal gradient, which may reduce the induced heat stresses in the core of the reactor.
Gradient-like flows on surfaces have simple dynamics, which inspired many mathematicians to search for invariants of their topological equivalence. Under assumptions of different generality on the ...class of gradient-like flows under consideration, such classical invariants as the Leontovich–Mayer scheme, the Peixoto graph, the equipped Peixoto graph, the two-color Wang graph, the three-color Oshemkov–Sharko graph, the Fleitas circular scheme, etc. were obtained. Thus, the problem of classifying gradient-like flows on surfaces from the point of view of topological equivalence has been solved in an exhaustive way. In recent works by Kruglov, Malyshev, and Pochinka, it was proved that for gradient-like flows the topological equivalence classes coincide with the topological conjugacy ones. The obtained result allows us to use any invariants of their equivalence for topological conjugacy of gradient-like flows. The present study is a review of results on topological conjugacy of gradient-like flows on surfaces and efficient algorithms for its distinction, that is, algorithms whose running time is limited by some polynomial in the length of the input information.
The article presents an algorithm of automated determination of fan influence zones under conditions of their dynamic change. The use of fuzzy logic enables stabilization of crossing influence zones ...of fans and allows compensating impossibility of their strict differentiation when determining the most difficult-to-ventilate direction. The solution to the problem of the real-time air distribution control in a mine ventilation network is stable and close to optimality. The practical relevance of the proposed fan control algorithm and the correctness of the formulas are proved by the result of simulation modeling of automated ventilation control operation in mine 4RU of Belaruskali.
A system for determining the grain size composition of particles of bulk material is described using the example of measurement the geometry of prills of crushed iron ore. The hardware and algorithm ...peculiarities are given. The stages of the image processing algorithm for crushed particles detection and analyzing are illustrated. The results of full-scale testing of the system at the ore mining and processing enterprise are analyzed. The maximum absolute error of the designed hardware-software appliance is 4.2% and the average error is 3% for the "+150mm" class which is of most importance for the given task of primary crushing quality control.
Abstract
In the modern world, sequencing is an integral part of medicine, biology and other scientific fields. The Illimina / Solexa method is a new generation method and relates to methods of mass ...parallel sequencing. One of the features of using this method is the sequential pumping of various chemicals through the flow cell in which the reaction occurs. For uniformity and high quality of DNA sequencing, it is necessary that the amount of gas in liquids be minimized. Because many it can adversely affect both during chemical reactions and at the stage of recording reaction results. This article will examine the sequencing system using the Illumina\Solexa method using bubble sensors. An algorithm was developed that periodically receives information from bubble sensors in a microfluidic tube. The information received is processed and allows at certain stages to report deviations from the normal conditions for sequencing. The experimental results are presented.
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