Connected Components of  H_(r,g)^A (G)

The Hurwitz space is the space of genus g covers of the Riemann sphere with branch points and the monodromy group . In this paper, we enumerate the connected components of the Hurwitz spaces for a finite primitive group of degree 7 and genus zero except . We achieve this with the aid of the computer algebra system GAP and the MAPCLASS package.

Download Full-text

Connected Components of the Hurwitz Space for the Symmetric Group of Degree 7

Sultan Qaboos University Journal for Science [SQUJS] ◽

10.24200/squjs.vol24iss2pp129-138 ◽

2020 ◽

Vol 24 (2) ◽

pp. 129

Author(s):

Haval M. Mohammed Salih

Keyword(s):

Symmetric Group ◽

Monodromy Group ◽

Riemann Sphere ◽

Complete Classification ◽

Connected Components ◽

Branch Points ◽

Genus Zero ◽

Computational Tools ◽

Hurwitz Space

The Hurwitz space is the space of genus covers of the Riemann sphere with branch points and the monodromy group . Let be the symmetric group . In this paper, we enumerate the connected components of . Our approach uses computational tools, relying on the computer algebra system GAP and the MAPCLASS package, to find the connected components of . This work gives us the complete classification of primitive genus zero symmetric group of degree seven.

Download Full-text

Hurwitz components of groups with socle PSL(3, q)

Extracta Mathematicae ◽

10.17398/2605-5686.36.1.51 ◽

2021 ◽

Vol 36 (1) ◽

pp. 51-62

Author(s):

H.M. Mohammed Salih

Keyword(s):

Finite Group ◽

Monodromy Group ◽

Riemann Sphere ◽

Complete List ◽

Simple Groups ◽

Connected Components ◽

Branch Points ◽

Almost Simple Groups ◽

Hurwitz Space ◽

A Finite Group

For a finite group G, the Hurwitz space Hinr,g(G) is the space of genus g covers of the Riemann sphere P1 with r branch points and the monodromy group G. In this paper, we give a complete list of some almost simple groups of Lie rank two. That is, we assume that G is a primitive almost simple groups of Lie rank two. Under this assumption we determine the braid orbits on the suitable Nielsen classes, which is equivalent to finding connected components in Hinr,g(G).

Download Full-text

One-Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2008/609425 ◽

2008 ◽

Vol 2008 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Antonio F. Costa ◽

Milagros Izquierdo ◽

Gonzalo Riera

Keyword(s):

Dihedral Group ◽

Meromorphic Functions ◽

Monodromy Group ◽

Elliptic Functions ◽

Hurwitz Spaces ◽

One Dimensional ◽

Hurwitz Space ◽

Upper Half Plane ◽

Triangular Group ◽

Real Forms

Hurwitz spaces are spaces of pairs(S,f)whereSis a Riemann surface andf:S→ℂ^a meromorphic function. In this work, we study1-dimensional Hurwitz spacesℋDpof meromorphicp-fold functions with four branched points, three of them fixed; the corresponding monodromy representation over each branched point is a product of(p−1)/2transpositions and the monodromy group is the dihedral groupDp. We prove that the completionℋDp¯of the Hurwitz spaceℋDpis uniformized by a non-nomal indexp+1subgroup of a triangular group with signature(0;[p,p,p]). We also establish the relation of the meromorphic covers with elliptic functions and show thatℋDpis a quotient of the upper half plane by the modular groupΓ(2)∩Γ0(p). Finally, we study the real forms of the Belyi projectionℋDp¯→ℂ^and show that there are two nonbicoformal equivalent such real forms which are topologically conjugated.

Download Full-text

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

Methods of Information in Medicine ◽

10.1055/s-0038-1634534 ◽

1998 ◽

Vol 37 (03) ◽

pp. 235-238 ◽

Cited By ~ 1

Author(s):

M. El-Taha ◽

D. E. Clark

Keyword(s):

Monte Carlo ◽

Decision Trees ◽

Computer Algebra ◽

Taylor Series ◽

Computer Algebra System ◽

Random Variable ◽

Monte Carlo Analysis ◽

Normal Random Variable ◽

Medical Decision ◽

Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Download Full-text