Sentence examples for function of a complex from inspiring English sources
Like Euler, he had discovered a function of a complex variable, with u and v its real and imaginary parts, respectively.
The complex numbers can be viewed as a plane (as pointed out in the section Fluid flow), so a function of a complex variable can be viewed as a function on the plane.
Starting from the work on trigonometric series and on the function of a complex variable done by the German mathematician Bernhard Riemann in 1854, Cantor in 1870 showed that such a function can be represented in only one way by a trigonometric series.
where f w is the probability density function of a complex normal law centered and variance σ w 2, given by f w ( x ) = 1 π σ w 2 e - | x | 2 ∕ σ w 2, (10).
It is postulated that how fast a country actually becomes a core innovator is a function of a complex set of factors that form the national environment of innovation.
The performance function of a complex engineering structure is always highly nonlinear and implicit, and its reliability needs to be evaluated through a time-consuming computer codes, such as finite element analysis (FEA).
His A Course of Modern Analysis (1902) was the first book in English to present the theory of functions of a complex variable at an undergraduate level.
"Yet mappings in which a linear axis becomes curvilinear — functions of a complex variable such as w=ez, where a straight line in the z-plane maps to a circle in the w-plane," said Dr. Rao, "do suggest the possibility of linear time becoming circular, and so achieving eternal return as simply, or should I say complexly, as that"...
The work of Augustin-Louis Cauchy on functions of a complex variable, of Arthur Cayley and James Joseph Sylvester on matrix algebra, and of Bernhard Riemann on non-Euclidean geometry, to name but a few, were investigations undertaken with little or no thought for practical applications.
The G-function of a complex variable z is given by a Mellin-Barnes type integral: G p, q m, n ( z ) = G z a 1, …, a n, …, a p b 1, …, b m, …, b q = G z ( a p ) ( b q ) = 1 2 Πi ∫ L g ( s ) z − s ds, (41).
Functions of a Complex Variable.
