Results 251 to 260 of about 1,777,027 (265)
Some of the next articles are maybe not open access.
2012
The fundamental concept of holomorphic function is introduced via complex differentiability in section I.1. The relation between real and complex differentiability is then discussed, leading to the characterization of holomorphic functions by the Cauchy-Riemann differential equations (I.2).
Wolfgang Fischer, Ingo Lieb
openaire +2 more sources
The fundamental concept of holomorphic function is introduced via complex differentiability in section I.1. The relation between real and complex differentiability is then discussed, leading to the characterization of holomorphic functions by the Cauchy-Riemann differential equations (I.2).
Wolfgang Fischer, Ingo Lieb
openaire +2 more sources
2019
One of the primary goals in this book is to obtain analytical solutions for the equations of motion of fluids. In order that such solutions are found, fluid motion is often restricted to be stationary and two dimensional (2-D) in a plane. All fluid fields depend then on the x- and y-coordinates only, and the fluid velocity has no z-component, \(\vec {u}
openaire +2 more sources
One of the primary goals in this book is to obtain analytical solutions for the equations of motion of fluids. In order that such solutions are found, fluid motion is often restricted to be stationary and two dimensional (2-D) in a plane. All fluid fields depend then on the x- and y-coordinates only, and the fluid velocity has no z-component, \(\vec {u}
openaire +2 more sources
Integration in the Complex Plane
1997In order to evaluate the intractable integrals arising from Equation 4.53, we need to devote some space first to the theory of functions of a complex variable. We shall present with no proof, or very little, many results that deserve careful study and rigorous treatment.
openaire +2 more sources
Pyramids in the complex projective plane
Geometriae Dedicata, 1991For a metric space \(M\) and a natural number \(n\) the function \(\delta: M^ n\to\mathbb{R}\), \(\delta(x_ 1,\dots,x_ n)=\max_{ij}\hbox{dist}_ M(x_ i,x_ j)\) is called the diameter functional. In a previous paper the author constructed a suitable right inscribed pyramid on a \((2k+1)\)- gon whose set of vertices \(P_ k\) is a local minimum of \(\delta\
openaire +3 more sources
Integration in the Complex s-Plane
2018In the QCD FESR, Eq. 1.13, the integral around the circle of radius \(|s_0|\) can be performed in two ways, named Fixed Order Perturbation Theory (FOPT), and Contour Improved Perturbation Theory (CIPT). In FOPT the strong coupling is frozen on the circle, i.e.
openaire +2 more sources
On Some Semigroups on the Complex Plane
Semigroup Forum, 2004The author considers the sets \(C(\alpha) = \{z \in \mathbb{C} : | z \sin\;\alpha \pm i \cos\;\alpha | \leq 1\}\) and proves that these sets with \(\alpha \in (0, \pi/2)\) form multiplicative semigroups in the complex plane. The main result of the paper stands that the semigroups \(C(\alpha)\) and \(C(\beta)\) are not isomorphic for \(\alpha \not ...
openaire +2 more sources
CALCULUS ON ARCS IN THE COMPLEX PLANE
Analysis, 1998Let \(\Gamma\) be a Jordan are joining \(a\) to \(b\) in the complex plane \(\mathbb{C}\) and let \(f\) be a function continuous on \(\Gamma\). Assume that \(\int_\Gamma fdz\) is defined via Riemann sums. The author is concerned with the following questions (1) is the formula \(\int_\Gamma f(z)dz=F(b)-F(a)\), \(F\) being a primitive for \(f\) ``along \(
openaire +3 more sources