Search results for "MathematicsofComputing_GENERAL"
showing 10 items of 84 documents
Adaptive Function and Brain Evolution
2012
Comparing brains is not a mere intellectual exercise but also helps to understand how the brain enables adaptive behavioral strategies to cope with an ever-changing world and how this complex organ has evolved during the phylogeny. For instance, comparative neurobiology helps understanding the specific features of our species, an issue that attracted scientists since the time of Santiago Ramon y Cajal. Following this tradition, 20 years ago Hans ten Donkelaar and Gerhard Roth started the European Conferences on Comparative Neurobiology (ECCN). This e-book includes some of the contributions to the last meeting, the sixth ECCN (Valencia, Spain; April 22-24 2010), plus selected works by severa…
Convergence in discrete Cauchy problems and applications to circle patterns
2005
A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size ε \varepsilon tends to zero. The convergence is in C ∞ C^\infty and the approximation error for arbitrary derivatives is quadratic in ε \varepsilon . In application, C ∞ C^\infty -approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.
On groups having a p-constant character
2020
Let G G be a finite group, and p p a prime number; a character of G G is called p p -constant if it takes a constant value on all the elements of G G whose order is divisible by p p . This is a generalization of the very important concept of characters of p p -defect zero. In this paper, we characterize the finite p p -solvable groups having a faithful irreducible character that is p p -constant and not of p p -defect zero, and we will show that a non- p p -solvable group with this property is an almost-simple group.
Degrees of irreducible characters of the symmetric group and exponential growth
2015
We consider sequences of degrees of ordinary irreducible S n S_n - characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of n n with leading coefficient less than one. We show that any such sequence has at least exponential growth and we compute an explicit bound.
A lower bound for the Bloch radius of 𝐾-quasiregular mappings
2004
We give a quantitative proof to Eremenko’s theorem (2000), which extends Bloch’s classical theorem to the class of n n -dimensional K K -quasiregular mappings.
A musical reading of a contemporary installation and back: mathematical investigations of patterns in Qwalala
2021
Mathematical music theory helps us investigate musical compositions in mathematical terms. Some hints can be extended towards the visual arts. Mathematical approaches can also help formalize a "translation" from the visual domain to the auditory one and vice versa. Thus, a visual artwork can be mathematically investigated, then translated into music. The final, refined musical rendition can be compared to the initial visual idea. Can an artistic idea be preserved through these changes of media? Can a non-trivial pattern be envisaged in an artwork, and then still be identified after the change of medium? Here, we consider a contemporary installation and an ensemble musical piece derived from…
When is a 𝑝-block a 𝑞-block?
1997
Let p p and q q be distinct prime numbers and let G G be a finite group. If B p B_{p} is a p p -block of G G and B q B_{q} is a q q -block, we study when the set of ordinary irreducible characters in the blocks B p B_{p} and B q B_{q} coincide.
Group algebras whose units satisfy a group identity
1997
Let F G FG be the group algebra of a torsion group over an infinite field F F . Let U U be the group of units of F G FG . We prove that if U U satisfies a group identity, then F G FG satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.
Complex group algebras of finite groups: Brauer’s Problem 1
2005
Brauer’s Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m m of isomorphic summands, then its dimension is bounded in terms of m m . We prove that this is true for every finite group if it is true for the symmetric groups.
Computer code from Sex roles and the evolution of parental care specialization.
2019
Computer code for the mathematical model in Mathematica