Написание Трактата по арифметике ("Liber abaci") европейским математиком эпохи Средневековья Л. Фибоначчи. Содержание книги: признаки делимости, дроби и смешанные числа, свойства пропорции и др. Наиболее интересные арифметические задачи из Трактата.
Изучение достижений математической науки в период Древней Греции. Изучение основных идей Александрийской школы. Анализ биографии Диофанта. Анализ "Арифметики" Диофанта – сборника задач, каждая из которых снабжена решением и необходимыми пояснениями.
Принято считать, что понятие о золотом сечении ввел в научный обиход Пифагор, древнегреческий философ и математик (VI в. до н.э.). Есть предположение, что Пифагор свое знание золотого сечения позаимствовал у египтян и вавилонян. Золотая пропорция.
Изложение универсального метода построения трёхмерных проекций гиперкубов любых n-мерных измерений (3ПГК-n) любых проекций и ракурсов. Алгебраические формулы для определения количества единичных геометрических элементов n-мерных гиперкубов, их проекций.
Квадратные уравнения в Древнем Вавилоне, Индии и Европе, история их возникновения и развития. Структура и содержание теоремы Виета, принципы и направления ее практического применения. Способы решения квадратных уравнений, их содержание и принципы.
Изучение матриц и линейных уравнений как основных элементов линейной алгебры. Описание элементов векторной алгебры. Исследование основ аналитической геометрии на плоскости и в пространстве. Составляющие производных, функций и математического анализа.
The paper attempts to state and prove a completeness theorem for the system S5 of supplemented by first-order quantifiers and the sign of equality. The basic modal language. A general strategy for proving completeness theorems for quantified modal logics.
Consideration of the Shannon's mathematical theory of communication as the technology processing of information. Problems associated with the transmission of messages: eliminate redundancy, perform coding and messaging communication channels with noise.
Prime and composite numbers. The fundamental theorem of arithmetic states. Sample factorizations. Review of elementary number theory. Some essential algorithms. RSA public-key cryptosystem. Finding squares through products. Large prime variations.
Separating the foundations of mathematics from philosophy. Difference between the theory of formal systems theory and evidence. Classical first order predicate logic. Elementary and full analysis. Existing proof theory. Infinitely long expressions.
The Graphical Modeling and Bayesian Networks. Some Properties of Incomplete Repair and Maintenance Models. The Theoretical Advances in Modeling, Inference and Computation. Network Reliability Evaluation with Propositional Directed Acyclic Graphs.
- 12. Algorithms to determine solvability of linear integro-differential equations with analytic functions
Further, we found sufficient conditions on linear Volterra integro-differential equations of the third kind to be correct in analytical functions which generalize the well-known fact of correctness of a Volterra integral equation of the second kind.
The study of the problem of how remains unchanged if the expected value according to probability distribution determined by minimizing the deviations among the fixed N values of a factor object. The set of all optimal strategies of the second player.
The calculation of fuzzy controllers, subject to the definition of control actions on the controller output for given membership functions. Algorithm Mumdanee for an indistinct conclusion. The linguistic rule of management of an indistinct regulator.
Solving Linear Systems with the Inverse. Transposes and Symmetric Matrices. General Linear Systems. The Fundamental Matrix Subspaces. Minimization of Quadratic Functions. Computations in Orthogonal Bases. Orthogonal Polynomials and Least Squares.
Modeling the static deformation of a circular plate with discrete variable thickness. The use of a matrix green type and algebraic matrices to create an algorithm for compact computing solutions for deformation of circular plates of variable thickness.
The definitions which characterize a problem of parameters of DL-based assumptions related to discrete logarithms and impact of granularity of them. Difficulties of the generic model that identify the parameters relevant to cryptographic assumptions.
The spectral properties of a fourth-order functional-differential operator with a summable potential are studied. The boundary conditions are separated. The solution of the functional-differential equation. The solution of the Volterra integral equation.
An Introduction to Bayesian Inference in Process Monitoring, Control. Modern Numerical Methods in Bayesian Computation. A Bayesian Approach to Statistical Process Control. Bayes’ Rule of Information and Monitoring in Manufacturing Integrated Circuits.
The methods used in the subsequent proofs. The usefulness of the side-by-side multiplication. Proving geometric inequalities where is the area, an arbitrary triangle ABC and what follows: sides, semi-perimeter, medians, angle-bisectors, altitudes.
Multidimensional data distributions with complex topologies and variable local dimensions. A new type of low-dimensional "principal object": a principal cubic complex. The method of topological grammars with the minimization of an elastic energy.
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.
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.
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.
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.
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.
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.
