Projects in Computer Science Training – An Example with Numerical Series

When it comes to teaching computer science, working on software projects is a quite natural pedagogical approach. Its main advantage is the increased motivation for learning, which arises from the opportunity to immediately see the application of acquired knowledge. In this paper, the authors share their experience of creating a project in computer science for high school students, making a cross-curricular connection with mathematics. Emphasis is placed on interactive teaching methods in the classroom.

Principal Components of Genetic Sequences: Correlations and Significance

Any numerical series can be decomposed into principal components using singular spectral analysis. We have recently proposed a new analysis method ‒ PCA-Seq, which allows calculating numerical principal components for a sequence of elements of any type. In particular, the sequence may be composed of nucleotide base pairs or amino acid residues. Two questions inevitably arise about interpretation of the obtained principal components and about the assessment of their reliability. For interpretation of the symbolic sequence principal components, it is reasonable to evaluate their correlations with numerical characteristics of the sequence elements. To assess the significance of correlations between sequences, one should bear in mind that standard significance criteria are based on the assumption of independence of observations, which, as a rule, is not fulfilled for real sequences. The article discusses the use of an anchor bootstrap technique for these purposes also previously developed by the authors of the article. In this approach it is assumed, that points of a metric space can represent the objects. When taken together they make up some fixed structure in it, in particular, a sequence. The objects are assigned the same random integer weights as in the classical bootstrap. This is sufficient to obtain the bootstrap distribution of the correlation coefficients and assess their significance. The coding sequence of the SLC9A1 gene (synonyms APNH, NHE1, PPP1R143) were taken as an example of use the anchor bootstrap technique in the genetic sequence analysis. Significant correlations of the first principal component were revealed with the hydrophobicity/“transmembraneity” of the corresponding fragments of the amino acid sequence, the phenylalanine content in them, as well as the difference in the T- and A-content in the corresponding nucleotide fragments. Earlier a similar pattern was found by other authors for other genes. Very likely, that it is of a more general nature.

Forecast of cattle leukemia virus epizootic development in West Kazakhstan region

Bovine leukemia is a chronic viral infectious disease that is widespread in many countries of the world, including the Republic of Kazakhstan. Based on our spectral and combinatorial analysis, this paper presents the results of supposed scenarios of leukemia infection development in the territory of West Kazakhstan region, where there is the alternating change of ups and downs virus level having a direct dependence on solar activity. To solve this problem, we used previously developed computer programs to decompose the dynamics of the cattle infection rate in the West Kazakhstan region for 2006-2016 into a Fourier series, then generate all possible combinations, create a database table with forecast values for several years and select the best numerical series. As a result of this research, it was noted that the computer mathematical model simulating the dynamics of bovine leukemia virus (BLV) carrier, based on the properties of the trigonometric Fourier polynomial, has 100% coincidence with the actual trend. Then in order to identify trends that would maximally reflect the real trend, we conducted a combinatorial analysis of the spectral model which allowed us to increase the number of alternative scenarios for the development of BLV infection for the next five years (2021-2026). According to the above mentioned mathematical model, based on combinatorial analysis, in 2022 the forecast of infectability corridor will average from 4.15 to 11.01%; in 2023 from 3.89 to 9.76%; in 2024 from 8.04 to 16.47%; in 2025 from 6.86 to 15.23% and in 2026 from 3.98 to 8.79%.

On Transcendental Systems of Equations

Several types of transcendental systems of equations are considered: the simplest ones, special, and general. Since the number of roots of such systems, as a rule, is infinite, it is necessary to study power sums of the roots of negative degree. Formulas for finding residue integrals, their relation to power sums of a negative degree of roots and their relation to residue integrals (multidimensional analogs of Waring’s formulas) are obtained. Various examples of transcendental systems of equations and calculation of multidimensional numerical series are given

Series based on the new order in intuitionistic fuzzy environment

Intuitionistic fuzzy number (IFN) is an effective tool for dealing with the uncertain information, and it has been applied to various fields. According to IFNs, the intuitionistic fuzzy calculus has been developed, which can effectively integrate the continuous uncertain information. Series in intuitionistic fuzzy environment is a part of the intuitionistic fuzzy calculus theory, of which core idea is limit. However, the order used in the existing limit theory is not the one used in intuitionistic fuzzy calculus, causing the separation of the limit theory and intuitionistic fuzzy calculus. Thus, series in intuitionistic fuzzy environment is not closely related to the intuitionistic fuzzy calculus. In order to solve the above problem, we construct the related theories. There are mainly the following three aspects: (1) the limit theory including the sequence limit and the function limit is studied based on the new order. (2) we re-examine the numerical series according to the new tool of researching IFNs: the basis and the coordinates. (3) we discuss the function series and put forward the uniform convergence in intuitionistic fuzzy environment.

ABOUT ONE CLASS OF FUNCTIONS WITH FRACTAL PROPERTIES

We consider one generalization of functions, which are called as «binary self-similar functi- ons» by Bl. Sendov. In this paper, we analyze the connections of the object of study with well known classes of fractal functions, with the geometry of numerical series, with distributions of random variables with independent random digits of the two-symbol $Q_2$-representation, with theory of fractals. Structural, variational, integral, differential and fractal properties are studied for the functions of this class.

READING COMPREHENSION OF EDUCATIONAL TEXTS AMONG 4–8 GRADES STUDENTS AS INDICATOR OF THEIR ABILITY TO LEARN

Introduction. Within the framework of the actual problem of the ability to learn for a modern school the peculiarities of children’s reading comprehension of edu-cational texts were studied. The analysis showed that the problem of reading com-prehension is not sufficiently developed from the standpoint of Cultural Activity Approach, since in existing studies (I.I. Ilyasov, I.V. Usacheva, O.E., Malskaya, etc.), the activity aspect is expressed only in a detailed description of the actions that provide reading comprehension and their structure, but these works do not “grasp” the general meaning of these actions related to the students’ understanding of the indicative purpose of educational texts — that it is from their content that the indicative basis of the subject actions performed should be ex-tracted. The most clearly indicative purpose of a special type of educational text — the definition of a concept — is justified in studies of the formation of the recogni-tion action (RA) (P. Ya. Galperin, N.F. Talyzina, L.F. Obukhova, etc.), where the “understanding” of the definition is the ability to recognize the objects that are described by it. The goal: to study the ability of students to perceive educational texts (ordinary educational texts and definitions of concepts) as tools for completing of specific tasks. Methods and sample. A sample of students in grades 4–8 (N = 280) was conducted: 1) assessment of the formation of the ability to work with definitions of concepts (concept’ recognition tasks, developed on the basis of the principles of diagnostics by N.F. Talyzina), 2) assessment of the ability to highlight the main thing in the text (the method of O.E. Malskaya and A.A. Sidelnikova “Selection of main sentences” for grades 4–8), 3) assessment of the ability to structure the text (the task of selecting paragraphs and their heading), 4) two GIT subtests (“Execution of rules” and “Numerical series”). Results and conclusions. It was shown that the understanding of definitions significantly and positively correlates with the understanding of educational texts. It was also revealed that the level of formation of both the ability to work with definitions and the ability to work with texts does not significantly increase after the 4th grade and up to the 8th grade there is a “failure” in these parameters, despite the smooth positive dynamics in some intellectual abilities.

STRUCTURE AND TYPOLOGY OF INTELLECTUAL-PERSONAL POTENTIAL OF EMPLOYEES OF THE FEDERAL PENITENTIARY SERVICE OF RUSSIA AT THE INITIAL STAGE OF SERVICE ACTIVITIES

The article presents the results of an empirical study of the intellectual and personal potential of employees of the FPS of Russia who are at the initial stage of official activity in an educational organization. The study involved 275 employees of 4 specializations ("Penitentiary psychology", "Logistics in the penitentiary system", "organization of the regime in the penitentiary system", "Operational search activity"). To assess the intellectual and personal potential of employees of the FPS of Russia, the following methods were used: "Career orientation questionnaire" by E. Shane in adaptation by V.A. Chiker, V.E. Vinokurova "career Anchors";" Personal profile " by G. Eysenck (Eysenck Personality Profiler) in the adaptation of K. Sugonyaev; test "word Exclusion"; subtest "Numerical series" of the intelligence structure test by R. Amthauer in the adaptation of K. Sugonyaev; "Advanced progressive matrices" by J. Raven. The structure of the intellectual and personal potential of employees of the FPS of Russia includes the following factors: verbal intelligence, nonverbal intelligence, high-speed intellectual, aggressiveness-impulsivity, sociability-anxiety, autonomy, service-motivational. Employees of the FPS of Russia who are at the initial stage of official activity can be classified into separate personality types that differ in intellectual and personal potential: constructive, mediocre and unbalanced. After analyzing the average intellectual-personal potential of each of the three personality types according to objective performance criteria implementation, service and educational and professional activities, revealed the most favorable service activities of the FPS of Russia personality type.