• Дослідження властивостей L-пiдгруп на скiнченних групах. Характеристика множини L-пiдгруп на циклічних групах деяких порядків з простими числами, квазіциклічній та нециклічній групі. Доведення математичних тверджень та приклади деяких L-пiдгруп.

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  • Complete discrete valuation fields. Extensions of discrete valuation fields. Cyclic extensions of prime degree. The Hasse–Herbrand function. The norm and Ramication groups. The milnor K-groups of a local field. The group of units of local number fields.

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  • Вивчення пар класів неспадних тотальних одномісних арифметичних функцій. Встановлення критеріїв рефлективності, транзитивності. Вивчення ґрат m-звідностей з інформаційними обмеженнями. Дослідження структури рекурсивно перераховних ступенів нерозв’язності.

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  • Measure theory, discrete time martingales and discrete time option pricing. Continuous time martingales. Stochastic integrals, calculus and differential equations. Option pricing in continuous time. Random measures, stochastic calculus (characteristics).

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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