Complex numbers and functions
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.
Подобные документы
Arithmetic operations and properties of decimals, proportion and percents. Fundamental concepts of algebra, functions and graphs. The fundamental operations with complex numbers. Limits of function values, one-sided limits, infinitesimal functions.
учебное пособие, добавлен 11.10.2014The uniqueness problem of meromorphic functions having the same pole sharing of a nite set with the aid of weighted sharing of sets we. Meromorphic functions in whole complex plane. Standard notations of the Nevanlinna theory of meromorphic functions.
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статья, добавлен 27.06.2016Multidimensional 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.
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книга, добавлен 08.03.2014Analyzing 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.
статья, добавлен 08.02.2013Affine plane curves. A brief introduction to the p-adic numbers. Regular functions on projective curves. Plane projective cubic curves with a rational inflection point. Reduction of an elliptic curve. Cohomology of finite, infinite Galois groups.
учебное пособие, добавлен 03.07.2013Obtaining 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.
статья, добавлен 19.02.2016The Cartesian product of copies. The set of all nonnegative real numbers. The algebra of polar operators (poles). Definition of a binary operation. Polarized elements, extension of the algebra of poles to the whole plane. Classes of equivalence.
статья, добавлен 27.06.2016Role of Euler`s number in differential and integral calculus, in algebra. Consideration of a new limit for the number e and giving its rigorous proof using the apparatus of mathematical analysis. Combinatorial interpretation is given for Euler’s number.
статья, добавлен 28.08.2020Ways of representation of functions of two variables. Partial increment and derivatives of the first order. Application of the total differential to approximate calculations. Description of the largest and smallest values of a function of two variables.
учебное пособие, добавлен 11.10.2014Prime 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.
статья, добавлен 15.09.2012Sums, floors and recurrences. Finite and infinite calculus. Hypergeometric functions and transformations. Special, exponential generating functions. Euler’s summation formula. Domino theory and change. Partial hypergeometric sums. Stirling numbers.
учебное пособие, добавлен 25.11.2013The manual contains definitions, formulas, theorems of the differential calculus of functions of one variable. Derivative and its geometrical and physical meaning. Applying differential to approximate calculations. Extremum of function, the quotient rule.
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статья, добавлен 09.09.2012The 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.
статья, добавлен 19.02.2016- 18. Vectors spaces
The definition of real and complex vector spaces. The calculation of the reference type. Rules of addition and multiplication of scalars. The concept of subset. The direct sum of two subspaces. The calculation of the projection of the vector on the area.
презентация, добавлен 13.04.2016 - 19. 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.
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учебное пособие, добавлен 30.07.2016An 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.
статья, добавлен 27.06.2016Applications of the mathematics of harmony as a new interdisciplinary direction of modern science. Algorithmic measurement theory, number systems with irrational bases and their applications in computer science, the hyperbolic Fibonacci functions.
статья, добавлен 24.06.2016The quart formula - a tool for describing the composition of functions, the modification of which directly changes properties, which are easily detected by numerical modeling. A complete infinite power-factorial functional series of the exponent.
статья, добавлен 12.05.2018Using 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.
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