Search results for "Branch point"
showing 4 items of 4 documents
Introducing the Pietarinen expansion method into the single-channel pole extraction problem
2013
We present a new approach to quantifying pole parameters of single-channel processes based on a Laurent expansion of partial-wave T matrices in the vicinity of the real axis. Instead of using the conventional power-series description of the nonsingular part of the Laurent expansion, we represent this part by a convergent series of Pietarinen functions. As the analytic structure of the nonsingular part is usually very well known (physical cuts with branch points at inelastic thresholds, and unphysical cuts in the negative energy plane), we find that one Pietarinen series per cut represents the analytic structure fairly reliably. The number of terms in each Pietarinen series is determined by …
Hurwitz spaces of coverings with two special fibers and monodromy group a Weyl group of typeBd
2012
f! Y; where is a degree-two coverings with n1 branch points and branch locus D and f is a degree-d coverings with n2 points of simple branching and two special points whose local monodromy is given by e and q, respectively. Furthermore the covering f has monodromy group Sd and f. D /\ D fD? where D f denotes the branch locus of f . We prove that the corresponding Hurwitz spaces are irreducible under the hypothesis n2 s r dC 1.
Branch Points of Algebraic Functions and the Beginnings of Modern Knot Theory
1995
Many of the key ideas which formed modern topology grew out of “normal research” in one of the mainstream fields of 19th-century mathematical thinking, the theory of complex algebraic functions. These ideas were eventually divorced from their original context. The present study discusses an example illustrating this process. During the years 1895-1905, the Austrian mathematician, Wilhelm Wirtinger, tried to generalize Felix Klein's view of algebraic functions to the case of several variables. An investigation of the monodromy behavior of such functions in the neighborhood of singular points led to the first computation of a knot group. Modern knot theory was then formed after a shift in mat…
Algebraic Curves and Riemann Surfaces in Matlab
2010
In the previous chapter, a detailed description of the algorithms for the ‘algcurves’ package in Maple was presented. As discussed there, the package is able to handle general algebraic curves with coefficients given as exact arithmetic expressions, a restriction due to the use of exact integer arithmetic. Coefficients in terms of floating point numbers, i.e., the representation of decimal numbers of finite length on a computer, can in principle be handled, but the floating point numbers have to be converted to rational numbers. This can lead to technical difficulties in practice. One also faces limitations if one wants to study families of Riemann surfaces, where the coefficients in the al…