Search results for "combinatoric"
showing 10 items of 1776 documents
Metric Lie groups admitting dilations
2019
We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $ d(\delta_\lambda x,\delta_\lambda y) = \lambda d(x,y)$, for all $x,y\in G$ and all $\lambda>0$. First, we show that all such distances are admissible, that is, they induce the manifold topology. Second, we characterize multiplicative one-parameter groups of Lie automorphisms that are dilations for some left-invariant distance in terms of algebraic properties of their infinitesimal generator. Third, we show that an admissible left-invariant distance on a Lie …
On a class of generalised Schmidt groups
2015
In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A 5 -free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.
Some new Hadamard designs with 79 points admitting automorphisms of order 13 and 19
2001
Abstract We have proved that there exists at least 2091 mutually nonisomorphic symmetric (79,39,19)-designs. In particular, 1896 of them admit an action of the nonabelian group of order 57, and an additional 194 an action of the nonabelian group of order 39.
The probability that $x$ and $y$ commute in a compact group
2010
We show that a compact group $G$ has finite conjugacy classes, i.e., is an FC-group if and only if its center $Z(G)$ is open if and only if its commutator subgroup $G'$ is finite. Let $d(G)$ denote the Haar measure of the set of all pairs $(x,y)$ in $G \times G$ for which $[x,y] = 1$; this, formally, is the probability that two randomly picked elements commute. We prove that $d(G)$ is always rational and that it is positive if and only if $G$ is an extension of an FC-group by a finite group. This entails that $G$ is abelian by finite. The proofs involve measure theory, transformation groups, Lie theory of arbitrary compact groups, and representation theory of compact groups. Examples and re…
Evidence for the decays of and *
2019
Abstract We study the hadronic decays of to the final states and , using an annihilation data sample of 567 pb-1 taken at a center-of-mass energy of 4.6 GeV with the BESIII detector at the BEPCII collider. We find evidence for the decays and with statistical significance of and , respectively. Normalizing to the reference decays and , we obtain the ratios of the branching fractions and to be and , respectively. The upper limits at the 90% confidence level are set to be and . Using BESIII measurements of the branching fractions of the reference decays, we determine % (<0.68%) and % (<1.9%). Here, the first uncertainties are statistical and the second systematic. The obtained branching …
Hajłasz–Sobolev imbedding and extension
2011
Abstract The author establishes some geometric criteria for a Hajlasz–Sobolev M ˙ ball s , p -extension (resp. M ˙ ball s , p -imbedding) domain of R n with n ⩾ 2 , s ∈ ( 0 , 1 ] and p ∈ [ n / s , ∞ ] (resp. p ∈ ( n / s , ∞ ] ). In particular, the author proves that a bounded finitely connected planar domain Ω is a weak α -cigar domain with α ∈ ( 0 , 1 ) if and only if F ˙ p , ∞ s ( R 2 ) | Ω = M ˙ ball s , p ( Ω ) for some/all s ∈ [ α , 1 ) and p = ( 2 − α ) / ( s − α ) , where F ˙ p , ∞ s ( R 2 ) | Ω denotes the restriction of the Triebel–Lizorkin space F ˙ p , ∞ s ( R 2 ) on Ω .
Inverse eigenvalue problem for normal J-hamiltonian matrices
2015
[EN] A complex square matrix A is called J-hamiltonian if AT is hermitian where J is a normal real matrix such that J(2) = -I-n. In this paper we solve the problem of finding J-hamiltonian normal solutions for the inverse eigenvalue problem. (C) 2015 Elsevier Ltd. All rights reserved.
An optimal Poincaré-Wirtinger inequality in Gauss space
2013
International audience; Let $\Omega$ be a smooth, convex, unbounded domain of $\mathbb{R}^N$. Denote by $\mu_1(\Omega)$ the first nontrivial Neumann eigenvalue of the Hermite operator in $\Omega$; we prove that $\mu_1(\Omega) \ge 1$. The result is sharp since equality sign is achieved when $\Omega$ is a $N$-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincaré-Wirtinger inequality for functions belonging to the weighted Sobolev space $H^1(\Omega,d\gamma_N)$, where $\gamma_N$ is the $N$% -dimensional Gaussian measure.
Comparison results for Hessian equations via symmetrization
2007
where the λ’s are the eigenvalues of the Hessian matrix D2u of u and Sk is the kth elementary symmetric function. For example, for k = 1, S1(Du) = 1u, while, for k = n, Sn(D 2u) = detD2u. Equations involving these operators, and some more general equations of the form F(λ1, . . . , λn) = f in , (1.2) have been widely studied by many authors, who restrict their considerations to convenient cones of solutions with respect to which the operator in (1.2) is elliptic. Following [25] we define the cone 0k of ellipticity for (1.1) to be the connected component containing the positive cone 0 = {λ ∈ R : λi > 0 ∀i = 1, . . . , n} of the set where Sk is positive. Thus 0k is an open, convex, symmetric…
Avoiding Boundary Effects in Wang-Landau Sampling
2003
A simple modification of the ``Wang-Landau sampling'' algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm.