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.
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.
- 103. Scientific computing
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.
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".
Overview of constraint solving. Term algebra. Attacker model. Constraint generation. Subterms and product closures. Well-defined protocols and constraint sequences. Ground derivability. Conservative solutions. Decision procedure for symbolic constraints.
Basic formulas of combinatorial analysis. Theorem of addition of probabilities of incompatible events. Theorem of multiplication of probabilities. Bayes’s formulas. Mathematical operations over random variables. Properties of a distribution function.
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.
Determination of diameter of a opening, corner of a opening and focal distance of an optical-type antenna. Calculation of a space directional diagram and determination of parameters of the parabolic antenna. Constructive calculation of the antenna.
Solving the Cauchy problem for the heat equation with random factors as a classical problem in mathematical physics. The main stochastic processes in the Orlicz space. Estimates of the distribution of the supremum of a solution of the heat equation.
Analysis of the improvement of piezoelectric transducers. A special place is occupied by piezoelectric transducers in electric, underwater acoustics, where they are intended for radiation and reception of acoustic vibrations in air or aquatic environment.
Methods of rapid information. Reduce time of realization of cryptographic RSA transformations. Application of the principle of ring shift in the module number system. Increasing the speed of realization of cryptographic transformations with the open key.
Proving of the theorem on a normal limit distribution of the normalized number of false solutions of a beforehand consistent system of nonlinear random equations over the field GF(2) with additional condition on the number of nonzero components.
Spatial relationships and examples of three-dimensional figures. The calculation of the surface area of three-dimensional figures and volume of cylinders and prisms. The ratio of the volume of the cone and the pyramid to the volume of cylinder and prism.
Tiling of the limit space under the action of a (self-similar) subgroup. Self-similar groups and their limit spaces. Subgroup tilings of limit spaces. Tilings of limit spaces of abelian and nilpotent groups. Functional analysis to nilpotent Lie groups.
Оценка различий между двумя выборками по уровню количественно измеренного признака. Назначение и описание критерия Манна-Уитни. Его графическое представление. Возможные варианты соотношений рядов значений в двух выборках. Ограничения и подсчет критерия.
