Search results for "combinatoric"

Fractional master equations and fractal time random walks

1995

Fractional master equations containing fractional time derivatives of order 0\ensuremath{\le}1 are introduced on the basis of a recent classification of time generators in ergodic theory. It is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks. The corresponding waiting time density \ensuremath{\psi}(t) is obtained exactly as \ensuremath{\psi}(t)=(${\mathit{t}}^{\mathrm{\ensuremath{\omega}}\mathrm{\ensuremath{-}}1}$/C)${\mathit{E}}_{\mathrm{\ensuremath{\omega}},\mathrm{\ensuremath{\omega}}}$(-${\mathit{t}}^{\mathrm{\ensuremath{\omega}}}$/C), where ${\mathit{E}}_{\mathrm{\ensuremath{\omega}},\mathrm{\ensuremat…

Elementarteiler von Inzidenzmatrizen symmetrischer Blockpläne

1986

By a study of the integral code generated by the rows of the incidence matrix and its extention the following results are obtained: Let d 1,...,d V(d 1|d 2,d 2|d 3...) be the elementary divisors of the incidence matrix of a symmetric (v,n+λ, λ) design. Then d v=(n+λ)n/g.c.d. (n, λ). Moreover, if p is a prime such that p|n, p∤λ and if x p denotes the p-part of x, then (d idv+2−i) p =n p for 2≤i≤v. For projective planes it can be shown that d 1=···=d 3n−2=1, hence $$d_{n^2 - 2n{\text{ }} + {\text{ }}5} {\text{ }} = \cdots = d_{n^2 + n} = n$$ and $$d_{n^2 - n{\text{ }} + {\text{ }}1} = (n + 1)n$$ . The paper also contains some results about elementary divisors of incidence matrices G satisfyin…

Periodic Solutions of the Second Order Quadratic Rational Difference Equation $$x_{n+1}=\frac{\alpha }{(1+x_n)x_{n-1}} $$ x n + 1 = α ( 1 + x n ) x n…

2016

The aim of this article is to investigate the periodic nature of solutions of a rational difference equation $$x_{n+1}=\frac{\alpha }{(1+x_n)x_{n-1}}. {(*)} $$ We explore Open Problem 3.3 given in Amleh et al. (Int J Differ Equ 3(1):1–35, 2008, [2]) that requires to determine all periodic solutions of the equation (*). We conclude that for the equation (*) there are no periodic solution with prime period 3 and 4. Period 7 is first period for which exists nonnegative parameter \(\alpha \) and nonnegative initial conditions.

Covering and differentiation

1995

Poincaré Week in Göttingen, 22–28 April 1909

2018

When Paul Wolfskehl died in 1906, his will established a prize for the first mathematician who could supply a proof of Fermat’s Last Theorem, or give a counterexample refuting it. The interest from this prize money was later used to bring world-renowned mathematicians to Gottingen to deliver a series of lectures. Hilbert was apparently very pleased with this arrangement, and once jested that the only thing that kept him from proving Fermat’s famous conjecture was the thought of killing the goose that laid these golden eggs.

Hypergraph functor and attachment

2010

Using an arbitrary variety of algebras, the paper introduces a fuzzified version of the notion of attachment in a complete lattice of Guido, to provide a common framework for the concept of hypergraph functor considered by different authors in the literature. The new notion also gives rise to a category of variable-basis topological spaces which is a proper supercategory of the respective category of Rodabaugh.

Group-graded algebras with polynomial identity

1998

LetG be a finite group and letR=Σg∈GRg be any associative algebra over a field such that the subspacesRg satisfyRgRh⊆Rgh. We prove that ifR1 satisfies a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the order ofG. This result implies the following: ifH is a finite-dimensional semisimple commutative Hopfalgebra andR is anyH-module algebra withRH satisfying a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the dimension ofH.

On σ-subnormal closure

2020

Let σ={σi:i∈I} be a partition of the set P of all prime numbers. A subgroup A of a finite group G is called σ-subnormal in G if there is a chain of subgroups A=A0⊆A1⊆⋯⊆An=G with Ai−1 normal in Ai o...

The minimal number of characters over a normal p-subgroup

2007

Abstract If N is a normal p-subgroup of a finite group G and θ ∈ Irr ( N ) is a G-invariant irreducible character of N, then the number | Irr ( G | θ ) | of irreducible characters of G over θ is always greater than or equal to the number k p ′ ( G / N ) of conjugacy classes of G / N consisting of p ′ -elements. In this paper, we investigate when there is equality.

p-Parts of Brauer character degrees

2014

Abstract Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.