Search results for "group"
showing 10 items of 19225 documents
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
2020
This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic $L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic $1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that…
On asymptotic behavior of solutions to higher-order sublinear Emden–Fowler delay differential equations
2017
Abstract We study asymptotic behavior of solutions to a class of higher-order sublinear Emden–Fowler delay differential equations. Our theorems improve several results reported recently in the literature. Two examples are provided to illustrate the importance and advantages of new criteria.
On two classes of finite supersoluble groups
2017
ABSTRACTLet ℨ be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called ℨ-S-semipermutable if H permutes with every Sylow p-subgroup of G in ℨ for all p∉π(H); H is said to be ℨ-S-seminormal if it is normalized by every Sylow p-subgroup of G in ℨ for all p∉π(H). The main aim of this paper is to characterize the ℨ-MS-groups, or groups G in which the maximal subgroups of every Sylow subgroup in ℨ are ℨ-S-semipermutable in G and the ℨ-MSN-groups, or groups in which the maximal subgroups of every Sylow subgroup in ℨ are ℨ-S-seminormal in G.
Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research
2004
International audience; .This essay is intended to present a fruitful collaboration which has developed among a group of people whose names are listed above: entropy methods have proved over the last years to be an efficient tool for the understanding of the qualitative properties of physically sound models, for accurate numerics and for a more mathematical understanding of nonlinear PDEs. The goal of this essay is to sketch the historical development of the concept of entropy in connection with PDEs of continuum mechanics, to present recent results which have been obtained by the members of the group and to emphasize the most striking achievements of this research. The presentation is by n…
Defect zero characters predicted by local structure
2017
Let $G$ be a finite group and let $p$ be a prime. Assume that there exists a prime $q$ dividing $|G|$ which does not divide the order of any $p$-local subgroup of $G$. If $G$ is $p$-solvable or $q$ divides $p-1$, then $G$ has a $p$-block of defect zero. The case $q=2$ is a well-known result by Brauer and Fowler.
Existence of normal Hall subgroups by means of orders of products
2018
Let G be a finite group, let π be a set of primes and let p be a prime. We characterize the existence of a normal Hall π‐subgroup in G in terms of the order of products of certain elements of G. This theorem generalizes a characterization of A. Moretó and the second author by using the orders of products of elements for those groups having a normal Sylow p‐subgroup 6. As a consequence, we also give a π‐decomposability criterion for a finite group also by means of the orders of products.
Efficient generation of restricted growth words
2013
A length n restricted growth word is a word w=w"1w"2...w"n over the set of integers where w"1=0 and each w"i, i>1, lies between 0 and the value of a word statistics of the prefix w"1w"2...w"i"-"1 of w, plus one. Restricted growth words simultaneously generalize combinatorial objects as restricted growth functions, staircase words and ascent or binary sequences. Here we give a generic generating algorithm for restricted growth words. It produces a Gray code and runs in constant average time provided that the corresponding statistics has some local properties.
Constant sign and nodal solutions for nonlinear robin equations with locally defined source term
2020
We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).
Vertical versus horizontal Sobolev spaces
2020
Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…
A half-metallic half-Heusler alloy having the largest atomic-like magnetic moment at optimized lattice constant
2016
For half-Heusler alloys, the general formula is XYZ, where X can be a transition or alkali metal element, Y is another transition metal element, typically Mn or Cr, and Z is a group IV element or a pnicitide. The atomic arrangements within a unit-cell show three configurations. Before this study, most of the predictions of half-metallic properties of half-Heusler alloys at the lattice constants differing from their optimized lattice constant. Based on the electropositivity of X and electronegativity of Z for half-Heusler alloys, we found that one of the configurations of LiCrS exhibits half-metallic properties at its optimized lattice constant of 5.803Å, and has the maximum atomic-like magn…