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.

Normed linear spaces and Banach spaces. Basic properties of inner-products. Best approximation and orthogonal projections. Compact operators on a Banach space. Boundary value problems. Dierential calculus in Banach spaces and the calculus of variations.

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.

Первая и вторая квадратичная форма. Построение проекции вектора кривизны линии на нормаль поверхности в точке, через которую проходит эта кривая. Изучение кривизны всех линий на поверхности, рассмотрение плоских сечений. Уравнение индикатрисы Дюпена.

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.

Using methods of discrete mathematics in the field of virtual isolation and its application in the scientific theory of numbers, groups, combinatorics and graph theory. Specifics arithmetic methods data comparisons. Construction of a matrix atom.

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.

Search of the Dirichlet series with zero abscissa of absolute convergence. Study of asymptotic equality features. The convergence at different points. The role of the Dirichlet series in number theory. The behavior of the three-dimensional function.

Characteristics of the main principles of construction of cubic maps and base points. Planarizations, their common properties. The proof of the theorem determine a cubic, quadratic and normal forms of planarizations. Complex and real classification.

Characteristic of a Krull–Schmidt Theorem for nonassociative algebras. Definition of the upper annihilating series. Study of some families of nilpotent evolution algebras. Classification of four- and five-dimensional nilpotent evolution algebras.

Determination of p-groups with nilpotency class 3 where all proper subgroups have nilpotency class less or equal 2. The necessary and sufficient condition for finite p-group to be a minimal group of nilpotency class 3.

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.

The order and lower order of an entire function. Using the Fourier series method to study the properties of subharmonic functions. The subharmonic function in the complex plane. The finite system of rays. The class of delta-subharmonic functions.

Mathematical methods of optimizing statistical research. Solution the problem of computation the entropy value of binary messages of increased length generated by Bernoulli information sources. Development of methods to reduce the number of calculations.

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.

The optimal method of teaching trigonometric equations in the high school mathematics course based on the curriculum. The place and meaning of trigonometric equations and inequalities in the school mathematics course, features of their solution.

Formulation of the lemma before solving the problem. The search for the principle of solving the paradox. Mathematical problem solving. Philosophical proof of the theorem. Justification of conclusions that can be applied in solving paradoxical problems.

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.

Putnam argues that, by reinterpretation, the Axiom of Constructibility can be saved from empirical refutation. This paper contends that this argument fails, which leaves Putnam’s sweeping appeal to the Lowenheim - Skolem Theorem inadequately motivated.

Hilbert scheme of points and induction scheme. Cellular decompositions for various nested Hilbert schemes of points. Hodge classes on self-products of K3 surfaces. On the cotangent sheaf of Quot-schemes. Algebraic families on an algebraic surface.

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.

Approximations in Scientic Computation, сomputer Arithmetic, mathematical Software. Linear Systems, solving Linear Systems, Iterative Methods for Linear Systems. Linear Least Squares, eigenvalues and Singular Values, Nonlinear Equations, optimization.

The notion of weighted sharing of sets improving theorem A.I. Lahiri. Idea of gradation of sharing of values and sets known as weighted sharing. The definitions of the value distribution theory. Nonconstant meromorphic functions having no simple poles.

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.

Consideration the results of simulation definition spectral analysis of signals, which consist of harmonic signals with noninteger periods. Studied the change of spectral components by changing width of Fourier transformation by discarding samples.