Results 291 to 300 of about 12,500,740 (339)
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On the complexity of numbering operators
Discrete Mathematics and Applications, 1996This is a paper in the classical style of the Russian school concentrated on the estimators of Shannon functions for different complexity measures and function classes. In this case the computing model is a Boolean circuit and the set of functions is the set of all enumeration functions for some subsets of \(\{0,1\}^n\) of restricted size.
I. A. Vikhlyantsev, A. E. Andreev
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On the Fourier transform of Bessel functions over complex numbers—I: the spherical case
, 2016In this note, we prove a formula for the Fourier transform of spherical Bessel functions over complex numbers, viewed as the complex analogue of the classical formulae of Hardy and Weber. The formula has strong representation theoretic motivations in the
Zhi Qi
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Distribution of the prime numbers
Bulletin of Applied Mathematics and Mathematics EducationThis research explores the distribution of prime numbers, which are a fundamental topic in number theory. The study originated from the author's fascination with mathematics and the desire to discover something novel.
Lolav Ahmed Khalil
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2010
Numbers of the form \( a + b\sqrt { - 1} \), where a and b are real numbers—what we call complex numbers.appeared as early as the 16th century. Cardan (1501–1576) worked with complex numbers in solving quadratic and cubic equations. In the 18th century, functions involving complex numberswere found by Euler to yield solutions to differential equations.
Donald J. Newman, Joseph Bak
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Numbers of the form \( a + b\sqrt { - 1} \), where a and b are real numbers—what we call complex numbers.appeared as early as the 16th century. Cardan (1501–1576) worked with complex numbers in solving quadratic and cubic equations. In the 18th century, functions involving complex numberswere found by Euler to yield solutions to differential equations.
Donald J. Newman, Joseph Bak
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Visualizing the Arithmetic of Complex Numbers
The International Journal for Technology in Mathematics Education, 2014The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential).
Hortensia Soto-Johnson
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New Sum-Product Estimates for Real and Complex Numbers
Discrete & Computational Geometry, 2014A variation on the sum-product problem seeks to show that a set which is defined by additive and multiplicative operations will always be large. In this paper, we prove new results of this type.
A. Balog, O. Roche-Newton
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1989
The fundamental theorem of algebra—that a polynomial of degree k has exactly k complex roots—enables us to get the “right” number of intersections between a curve of degree m and a curve of degree n. However, it is not enough to introduce complex coordinates: getting the right count of intersections also requires us to adjust our viewpoint in two other
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The fundamental theorem of algebra—that a polynomial of degree k has exactly k complex roots—enables us to get the “right” number of intersections between a curve of degree m and a curve of degree n. However, it is not enough to introduce complex coordinates: getting the right count of intersections also requires us to adjust our viewpoint in two other
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1989
The insight into algebraic curves afforded by complex coordinates—that a complex curve is topologically a surface—has important repercussions for functions defined as integrals of algebraic functions, such as the logarithm, exponential, and elliptic functions.
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The insight into algebraic curves afforded by complex coordinates—that a complex curve is topologically a surface—has important repercussions for functions defined as integrals of algebraic functions, such as the logarithm, exponential, and elliptic functions.
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Complex Numbers in Algebra [PDF]
, 1989 The next three chapters revisit the topics of algebra, curves, and functions, observing how they are simplified by the introduction of complex numbers. That’s right: the so-called “complex” numbers actually make things simpler. In the present chapter we see where complex numbers came from (not from quadratic equations, as you might expect, but from ...
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Fuzzy Sets and Systems, 1989
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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