Search results for "group theory"
showing 10 items of 703 documents
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.
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.
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.
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…
Efficiency of H center stabilization in alkali halide crystals at low-temperature uniaxial deformation
2020
The efficiency of stabilization of H centers as well as its dependence on the degree of uniaxial deformation are considered within the framework of the modified geometric model of alkali halides. It is shown that stabilization of H centers is difficult in KI and RbI crystals, while in other NaCl-type crystals it becomes quite probable. Under uniaxial deformation, the interstitial space, in which the defect will be located, decreases, and the efficiency decrease. In the case of cesium halides, the orientation of the H centers takes place predominantly in the direction; therefore, the criteria for their stabilization differ from the NaCl-type alkali halide crystals. According to calculations,…
The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules
2003
International audience; The MIRS spectroscopic software for the modeling of ro-vibrational spectra of polyatomic molecules is presented. It is designed for the global treatment of complex band systems of molecules to take full account of symmetry properties. It includes e cient algorithms based on the irreducible tensor formalism. Predictions and simultaneous data fi tting (positions and intensities) are implemented as well as advanced options related to group theory algebra. Illustrative examples on CH3D, CH4, CH3Cl and PH3 are reported and the present status of data available is given. It is written in C++ for standard PC computer operating under Windows. The full package including on-lin…
Constructing Antidictionaries of Long Texts in Output-Sensitive Space
2021
AbstractA wordxthat is absent from a wordyis calledminimalif all its proper factors occur iny. Given a collection ofkwordsy1, … ,ykover an alphabetΣ, we are asked to compute the set$\mathrm {M}^{\ell }_{\{y_1,\ldots ,y_k\}}$M{y1,…,yk}ℓof minimal absent words of length at mostℓof the collection {y1, … ,yk}. The set$\mathrm {M}^{\ell }_{\{y_1,\ldots ,y_k\}}$M{y1,…,yk}ℓcontains all the wordsxsuch thatxis absent from all the words of the collection while there existi,j, such that the maximal proper suffix ofxis a factor ofyiand the maximal proper prefix ofxis a factor ofyj. In data compression, this corresponds to computing the antidictionary ofkdocuments. In bioinformatics, it corresponds to c…
On finite groups with many supersoluble subgroups
2017
[EN] The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A5 or SL2 (5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A5 or SL2 (5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201 206, 2012).
Improved polyhedral descriptions and exact procedures for a broad class of uncapacitated p-hub median problems
2019
Abstract This work focuses on a broad class of uncapacitated p-hub median problems that includes non-stop services and setup costs for the network structures. In order to capture both the single and the multiple allocation patterns as well as any intermediate case of interest, we consider the so-called r-allocation pattern with r denoting the maximum number of hubs a terminal can be allocated to. We start by revisiting an optimization model recently proposed for the problem. For that model, we introduce several families of valid inequalities as well as optimality cuts. Moreover, we consider a relaxation of the model that contains several sets of set packing constraints. This motivates a pol…