Obtaining a criterion of boundedness of L-index in direction for functions f(hz;mi). Finding sufficient conditions of boundedness L-index in direction for some class of entire functions with "plane" zeros. Proving existence theorems of entire function.

Research of the level of informatization of the main spheres of life activity of citizens of foreign countries. Analyse the peculiarities and problems of the development of higher education in Ukraine in the context of information and digital inequality.

Study recurrent factions fourth order. Contacting algebra fourth order. Building a sustainable rate calculation algorithms recurrent factions. Definition of communication between periodic recurrent about fractions and real positive roots of equations.

Peculiarities of calculating the photoionization cross sections for ions of the isoelectronic sequence of cesium by the Dirac-Fock method. Analysis of the dependence of the photoionization cross sections on energy. Photoelectron distribution methods.

Johann Carl Friedrich Gauss - a German mathematician. His outstanding scientific achievements. The fundamentals of modern balancing and mathematical statistics (the least squares method). Developing number theory, analysis, differential geometry.

Comparative analysis for the algorithm for solving two-parameter game models. Comparison of the values of the game price and the probabilities of strategies. The accuracy and reliability of the results are analyzed with the help of a numeric example.

Absolute value of a complex number, and conjugate complex number. Integral powers and roots of complex numbers. Taylor’s and Laurent’s theorems. Evaluation of integral of meromorphic function. Fundamental elementary functions of complex variables.

Sums, floors and recurrences. Finite and infinite calculus. Hypergeometric functions and transformations. Special, exponential generating functions. Euler’s summation formula. Domino theory and change. Partial hypergeometric sums. Stirling numbers.

The basics of cryptography and its levels of reliability. Secret key cryptosystem and symmetric ciphers, message authentication codes. Fundamentals of discrete mathematics, homomorphisms and isomorphisms. Modular arithmetic and function Euler's Totient.

The importance of research approach to a choice of model and to the search of alternative decisions. Some various methodically important approaches to the decision of elementary problems of search of the minimal speed allowing in "vacuum" conditions.

Дослідження регулярних цілих вектор-функцій половинного порядку зростання та відповідних їм безумовних базисів гільбертових просторів. Розв’язання задачі інтерполяціі функціями з вагових класів цілих вектор-функцій половинного порядку зростання.

Использование независимых событий в качестве результатов измерений, наблюдений, испытаний, опытов, анализа данных - основа вероятностно-статистических моделей. Установление критерия независимости событий - одна из важнейших задач теории вероятностей.

Определение и анализ положения главных центральных осей инерции составного сечения. Вычисление и характеристика главных центральных моментов инерции сечения. Изучение координат центров тяжести профилей и координат центра тяжести сечения на чертеже.

Correct solution of the location problems as one of most important tools of the operations research. The aim of location problem involves the location of one or more new facilities in the plane, when the number of possible locations is usually infinite.

Yangian for gln is the associative algebra historically first example of the quantum group. Bethe subalgebras in Yangians, theories and concepts used in this problem. Analysis and proof of lemmas. The Cartan subalgebra of the regular diagonal matrices.

The algorithm of the basic components of a linear analysis. Work on nonlinear PCA, or NLPCA, autoassociative's neural networks, principal curves and manifolds, kernel the combination's of these approaches. The problem areas that require research.

The results of the participants of the scientific seminar "Problems of elementary divisor rings" concerning the Bezout rings of finite stable range. The conditions under which these rings are elementary divisor rings. These rings introduced Kaplansky.

Mathematics as a fundamental science. The place in its structure of differential equations is one of the most harmonious ways of knowing the universe. Study of the algorithm for constructing compartmental (SIR) models, based on differential equations.

Analyzing multi-dimensional data with complex geometry and to identify low-dimensional "principal objects" that relate to the optimal projection while losing the least amount of information. The methods for dimensionality reduction of microarray data.

The textbook includes topics of discrete mathematics. Relations: binary relations, pictorial representatives of relations, inverse relation, functional relation. Mathematical logic: propositions and compound statements, basic laws of logical operations.

Using a generalized Dunkl translation, we obtain an analog of theorem 5.2 in Younis’ paper for the Dunkl transform for functions satisfying the (d, g)-Dunkl Lipschitz condition in the space L2(R,|x|2a+1dx). Consideration generalized Dunkl translation.

Arithmetic operations and properties of decimals, proportion and percents. Fundamental concepts of algebra, functions and graphs. The fundamental operations with complex numbers. Limits of function values, one-sided limits, infinitesimal functions.

Further examples of population dynamics. Representation of real numbers in an arbitrary base. A geometrical model for continued fractions. The idea of computational complexity. Elementary applications of congruence. The fundamental theorem of arithmetic.

The quart formula - a tool for describing the composition of functions, the modification of which directly changes properties, which are easily detected by numerical modeling. A complete infinite power-factorial functional series of the exponent.

Properties of Probability Distributions. Conditional Distributions and Expectation. Characteristic Functions, Moments and Cumulants. Parametric Families of Distributions. Distribution Theory for Functions of Random Variables, Approximation of Integrals.

Affine plane curves. A brief introduction to the p-adic numbers. Regular functions on projective curves. Plane projective cubic curves with a rational inflection point. Reduction of an elliptic curve. Cohomology of finite, infinite Galois groups.

Names of Greek letters and their pronunciation in formulas. Some facts on the development of the number system. Abbreviation and mathematical dictionary for the telecommunications specialists. Expressions and constructions used while retelling texts.

Combinatorial description. Teichmuller curves. Recurrence relation. Asymptotics of numbers of branched coverings of a torus, volumes of moduli spaces of holomorphic differentials. The character of the infinite wedge representation. Cylinder decomposition.

The concept, nature and purpose of mathematics. The process of identifying the "unknowns" in the process of solving the equation. Characteristic and distinctive features of types of equations, examples of possible solutions. Features Diophantine equation.

Аналіз функціонально-дискретного методу розв’язування задач з крайовими умовами третього роду, періодичними і антиперіодичними умовами. Розгляд обставин геометричної прогресії. Дослідження асимптотичних розвинень для значень задачі Штурма-Ліувілля.