The mathematical principles of the operation of cryptocurrencies. Mathematical formulas for calculating the public key from the private key. Properties of elliptic curves and the principle of their application during the creation of cryptocurrency.

Dynamic Modeling with Difference Equations. Linear Models of Structured Populations. Nonlinear Models of Interactions. Modeling Molecular Evolution. Constructing Phylogenetic Trees. Infectious Disease Modeling. Curve Fitting and Biological Modeling.

Characteristics of laminar and turbulent fluid flows. Analysis of the relationship between the Reynolds number and turbulence. Solution of the Navier-Stokes hydrodynamic equations. Investigation of the structure and inhomogeneities of a cellular flame.

Consideration of the process of evolution and prospects of mathematical methods and models in economic research. Characterization of advantages and identification of disadvantages of mathematical formalization in the conditions of a new economic paradigm.

Fundamentals of the method of least squares for the case of vector and matrix of observations. Advantages of MNCs to predict performance in the telemedia business. MNCs use algorithm for the matrix of observations with the ability to scale the data.

The methods developed by Hamilton 1989 and Chib 1996 to identied multiple-equation models. It details Bayesian estimation and inference for a class of models with different degrees of time variation and discuss analytical and computational difculties.

Teaching students of mathematical fields of training to inverse problems. Implementation of the scientific, educational potential of teaching university students inverse problems for differential equations. Computational methods of mathematical physics.

Examination of unlimited closed convex subsets of Banach space X, having the same recessive cone, and metric spaces, which they form with the Hausdorff metric. Receiving an analog of the theorem of approximation of convex compacts by normal polyhedrons.

The discussion about boolean algebras and their application to switching circuits. The rotation groups of the regular solids are investigated. New material on order of an element and cyclic groups, more details about the lattice of divisors of an integer.

Studies objects of geometric nature by means of some algebraic invariants defined over the category of these objects. Algebraic K-theory spectrum of DG-category. Definding the different versions of cyclic homology are via the mixed complex functor.

The self regulation of the parameters of the algorithm is a major step towards the establishment of the method as a general tool of nonlinear data analysis. Algorithms for the general task of extracting nonlinear principal manifolds from high dimensional.

Description of combinatorial DG-Hopf color cooperadic models for configuration spaces of points in the first quarter and in the N-gon. The proof version of the formality theorem of Kontsevich to the two subspaces in the vector space and for the morphism.

Generalization old result of Bowman system. Study of homomorphisms between topological Clifford semigroups. Ditopological unosemigroup in the mathematics. The main class of compact topological Clifford semigroups. The theory of partial symmetries.

An optimal boundary control problem associated to the linear parabolic equation. The characteristic feature of this equation, skew-symmetric. A unique solution to the original optimal boundary control problem, singular character of the original matrix.

The study of optimal control problems for linear parabolic equations with unbounded coefficients in the main part of elliptic operator. The peculiarities of this type of equations. Setting of the optimal control problem and its preliminary analysis.

Korobov polynomials as paradeterminants of triangular matrices. Some of the formulas of interpolation of functions of many variables and the discrete analogue of the summation formula of Euler - basic use of mathematical polynomials of this type.

Definition of artinian-by-(finite rank). Characteristic of features of artinian-by-(finite rank). Study of the structure of generalized soluble groups and nilpotent-by-finite modules. Analysis of the structure of artinian-by-(finite rank) modules.

One of the effective methods for solving such problems in case of piecewise-homogeneous environments is a one of hybrid integral transforms. It solves the problem of torsion of semi-bounded piecewise homogeneous elastic cylinder with various features.

Linear Principal Components. A linear model formulation. The Principal Curve and Surface models. Theory for principal curves and surfaces. Algorithmic details. Estimation of curves and surfaces. Gold assay pairs. Generalized linear principal components.

The construction of lower-dimensional manifolds from high-dimensional data is an important task in data mining, machine learning and statistics. The authors consider principal manifolds as a regularized, non-linear empirical quantization error functional.

An analytic univalent convex function. Solution the Gauss equation with negative exponents. Meromorphic starlike and meromorphic convex solutions. Series with negative powers. l-index boundedness. Example of the general solution of Gauss equation.

Study of gastroesophageal reflux disease, the main causes of refractory heartburn. Examples of drugs used for various comorbidities in GERD patients and their adverse events in the upper gastrointestinal tract. Autoimmune Skin Disorders, poor compliance.

Rules for binary addition, multiplication, subtraction and division. Time complexity of extended Euclidean algorithm. Existence of multiplicative inverse. Cancellation law of congruence. Introduction to finite field theory. Corollary of Euler’s theorem.

Reducing the cardinality of the set shared by f and g from 7 to 6 under weaker condition on ramification index. Noise-power distribution multitude values 4 and weakening ramification index enter Saving with Banerjee. Notion of weighted sharing of sets.

Thin and sparse metric spaces as asymptotic counterparts of discrete and very close to discrete metric spaces respectively. Classify thin metric spaces up to coarse equivalence. The types of sparse spaces and construct the spaces of distinct types.

Investigation analytically specificity of numerical integration of ordinary second-order differential equations for systems with Coulomb and viscous friction. Developing and extending of modification of Runge-Kutta formulas for mentioned systems.

A generalization of the classical theorem of T. Kato on similarity for sequences of projections in Hilbert spaces to the case of unconditional Schauder decompositions. Refinement of the theorem of V.N. Vizitei on the stability of Schauder decompositions.

Fundamentals of Probability and Judgement. Random variables and probability distributions. Bayes’ Theorem and Elicitation. Aleatory, epistemic uncertainty. Roles within the elicitation process. The naive intuitive statistician metaphor. "The middle way".

Characterization of symmetric linear functionals as the simplest polynomials. The proof of the theory that every symmetric continuous linear functional on the complex space L (0,1) can be represented as the Lebesgue integral, multiplied by a constant.

An application of mathematical models in transport infrastructure and the field of road construction. The problems of traffic jams, road accident, overload, underload of transport nodal points and their solving with the help of mathematical modeling.