Search results for "COMB"

showing 10 items of 7115 documents

Lie Algebras Generated by Extremal Elements

1999

We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.

17B05[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Non-associative algebraAdjoint representationGroup Theory (math.GR)01 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Graded Lie algebraCombinatoricsMathematics - Algebraic Geometry0103 physical sciences[MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA]FOS: Mathematics0101 mathematicsAlgebraic Geometry (math.AG)[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]MathematicsDiscrete mathematicsAlgebra and Number TheorySimple Lie group010102 general mathematics[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]20D06[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Rings and AlgebrasKilling formAffine Lie algebra[ MATH.MATH-RA ] Mathematics [math]/Rings and Algebras [math.RA]Lie conformal algebra[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Adjoint representation of a Lie algebraRings and Algebras (math.RA)17B05; 20D06010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Group TheoryJournal of Algebra
researchProduct

Efficacy and foliar absorption of flupyrsulfuron-methyl and prosulfocarb applied alone or in mixture on Lolium multiflorum and wheat

2001

Des melanges de flupyrsulfuron-methyle et de prosulfocarbe concus pour ameliorer la lutte contre Lolium multiflorum Lam. dans le ble (Triticum aestivum L.) ont ete etudies grâce a des essais biologiques sur plantes entieres et a des etudes de penetration foliaire. Dans les essais biologiques, le flupyrsulfuron-methyle et le prosulfocarbe etaient appliques a 6-7 doses, seuls ou en melange dans les rapports 1:400, 1:40 et 1:4 (p/p). Les courbes de reponse etaient ajustees au moyen de modeles logistiques et l'action conjuguee etait evaluee par la methode des isoboles. Dans les essais biologiques conduits en serre sur L. multiflorum, l'action conjuguee des melanges montrait une additivite de do…

2. Zero hunger[SDV.SA]Life Sciences [q-bio]/Agricultural sciences[SDV.SA] Life Sciences [q-bio]/Agricultural sciencesbiologyChemistryFLUPYRSULFURON-METHYL04 agricultural and veterinary sciencesLolium multiflorum010501 environmental sciencesbiology.organism_classification01 natural sciencesMolecular biologyJoint actionCombined treatmentFlupyrsulfuronBotany040103 agronomy & agriculture0401 agriculture forestry and fisheriesAgronomy and Crop ScienceProsulfocarbComputingMilieux_MISCELLANEOUS0105 earth and related environmental sciences
researchProduct

Computing the Original eBWT Faster, Simpler, and with Less Memory

2021

Mantaci et al. [TCS 2007] defined the \(\mathrm {eBWT}\) to extend the definition of the \(\mathrm {BWT}\) to a collection of strings. However, since this introduction, it has been used more generally to describe any \(\mathrm {BWT}\) of a collection of strings, and the fundamental property of the original definition (i.e., the independence from the input order) is frequently disregarded. In this paper, we propose a simple linear-time algorithm for the construction of the original \(\mathrm {eBWT}\), which does not require the preprocessing of Bannai et al. [CPM 2021]. As a byproduct, we obtain the first linear-time algorithm for computing the \(\mathrm {BWT}\) of a single string that uses …

2019-20 coronavirus outbreakSpeedupString collectionsBig BWTSettore INF/01 - InformaticaSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2)String (computer science)Suffix arrayOrder (ring theory)omega-orderQuantitative Biology::GenomicsBurrows-Wheeler-TransformBurrows-Wheeler-Transform String collections SAIS Big BWT prefix-free parsing extended BWTlaw.inventionCombinatoricsprefix-free parsingSimple (abstract algebra)lawSAISSAIS algorithmIndependence (probability theory)extended BWTMathematics
researchProduct

The average element order and the number of conjugacy classes of finite groups

2021

Abstract Let o ( G ) be the average order of the elements of G, where G is a finite group. We show that there is no polynomial lower bound for o ( G ) in terms of o ( N ) , where N ⊴ G , even when G is a prime-power order group and N is abelian. This gives a negative answer to a question of A. Jaikin-Zapirain.

20D15 20C15 20E45Finite groupPolynomialAlgebra and Number TheoryGroup (mathematics)010102 general mathematicsGroup Theory (math.GR)01 natural sciencesUpper and lower boundsElement OrderCombinatoricsConjugacy class0103 physical sciencesFOS: MathematicsOrder (group theory)010307 mathematical physics0101 mathematicsAbelian groupMathematics - Group TheoryG110 Pure MathematicsMathematics
researchProduct

The proof of Birman’s conjecture on singular braid monoids

2003

Let B_n be the Artin braid group on n strings with standard generators sigma_1, ..., sigma_{n-1}, and let SB_n be the singular braid monoid with generators sigma_1^{+-1}, ..., sigma_{n-1}^{+-1}, tau_1, ..., tau_{n-1}. The desingularization map is the multiplicative homomorphism eta: SB_n --> Z[B_n] defined by eta(sigma_i^{+-1}) =_i^{+-1} and eta(tau_i) = sigma_i - sigma_i^{-1}, for 1 <= i <= n-1. The purpose of the present paper is to prove Birman's conjecture, namely, that the desingularization map eta is injective.

20F36 57M25. 57M27[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Monoid[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Braid group20F36Group Theory (math.GR)01 natural sciencesBirman's conjecture[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsMathematics - Geometric TopologyMathematics::Group Theory57M25. 57M27Mathematics::Category Theory[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: MathematicsBraid0101 mathematics[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR][MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]MathematicsConjecturedesingularization010102 general mathematicsMultiplicative functionSigmaGeometric Topology (math.GT)singular braidsInjective function010101 applied mathematicsHomomorphismGeometry and TopologyMathematics - Group TheoryGeometry & Topology
researchProduct

Automorphisms of 2–dimensional right-angled Artin groups

2007

We study the outer automorphism group of a right-angled Artin group AA in the case where the defining graph A is connected and triangle-free. We give an algebraic description of Out.AA/ in terms of maximal join subgraphs in A and prove that the Tits’ alternative holds for Out.AA/. We construct an analogue of outer space for Out.AA/ and prove that it is finite dimensional, contractible, and has a proper action of Out.AA/. We show that Out.AA/ has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most general upper bound. 20F36; 20F65, 20F28

20F36outer spaceCohomological dimensionComputer Science::Digital LibrariesQuantitative Biology::Other01 natural sciencesContractible spaceUpper and lower boundsCombinatorics0103 physical sciences20F650101 mathematicsAlgebraic numberMathematics20F28Quantitative Biology::Biomolecules010102 general mathematicsAstrophysics::Instrumentation and Methods for AstrophysicsOuter automorphism groupAutomorphismGraphArtin groupright-angled Artin groups010307 mathematical physicsGeometry and Topologyouter automorphismsGeometry & Topology
researchProduct

Maximal subgroups and PST-groups

2013

A subgroup H of a group G is said r to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maxmial subgroups, Arch. Math. (Basel), 2011, 96(1), 19-25)] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions o…

20e2820d05General MathematicsCombinatoricsLocally finite groupPermutabilityQA1-939Permutable prime20d10Algebra over a fieldMathematicsDiscrete mathematicsTransitive relation20f16Group (mathematics)20e15Sylow theoremsGrups Teoria deSylow-permutabilitySupersolubilityFinite groupsNumber theoryMaximal subgroupsÀlgebraMATEMATICA APLICADAMathematics
researchProduct

Space-filling vs. Luzin's condition (N)

2013

Let us assume that we are given two metric spaces, where the Hausdorff dimension of the first space is strictly smaller than the one of the second space. Suppose further that the first space has sigma-finite measure with respect to the Hausdorff measure of the corresponding dimension. We show for quite general metric spaces that for any measurable surjection from the first onto the second space, there is a set of measure zero that is mapped to a set of positive measure (both measures are the Hausdorff measures corresponding to the Hausdorff dimension of the first space). We also study more general situations where the measures on the two metric spaces are not necessarily the same and not ne…

28A75 (Primary) 54C10 26B35 28A12 28A20 (Secondary)General Mathematicsta111Hausdorff spaceMathematics::General TopologySpace (mathematics)Functional Analysis (math.FA)Mathematics - Functional AnalysisSurjective functionCombinatoricsSet (abstract data type)Metric spaceMathematics - Classical Analysis and ODEsHausdorff dimensionClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematicsAnnales Academiae Scientiarum Fennicae Mathematica
researchProduct

Integrability of orthogonal projections, and applications to Furstenberg sets

2022

Let $\mathcal{G}(d,n)$ be the Grassmannian manifold of $n$-dimensional subspaces of $\mathbb{R}^{d}$, and let $\pi_{V} \colon \mathbb{R}^{d} \to V$ be the orthogonal projection. We prove that if $\mu$ is a compactly supported Radon measure on $\mathbb{R}^{d}$ satisfying the $s$-dimensional Frostman condition $\mu(B(x,r)) \leq Cr^{s}$ for all $x \in \mathbb{R}^{d}$ and $r > 0$, then $$\int_{\mathcal{G}(d,n)} \|\pi_{V}\mu\|_{L^{p}(V)}^{p} \, d\gamma_{d,n}(V) \tfrac{1}{2}$ and $t \geq 1 + \epsilon$ for a small absolute constant $\epsilon > 0$. We also prove a higher dimensional analogue of this estimate for codimension-1 Furstenberg sets in $\mathbb{R}^{d}$. As another corollary of our method,…

28A80 (primary) 28A78 44A12 (secondary)Mathematics - Metric GeometryMathematics - Classical Analysis and ODEsGeneral MathematicsFurstenberg setsIncidencesClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics - CombinatoricsMetric Geometry (math.MG)k-plane transformCombinatorics (math.CO)Projections
researchProduct

Asymmetric synthesis of 3,3′-pyrrolidinyl-dispirooxindoles via a one-pot organocatalytic Mannich/deprotection/aza-Michael sequence

2016

Chemical communications 52, 2249-2252 (2016). doi:10.1039/C5CC10057G

3'-pyrrolidinyl-spirooxindole3010405 organic chemistryChemistryMannich/deprotection/aza-Michael sequenceMetals and AlloysEnantioselective synthesisSequence (biology)General Chemistrychemistry010402 general chemistry54001 natural sciencesCombinatorial chemistryCatalysis0104 chemical sciencesSurfaces Coatings and FilmsElectronic Optical and Magnetic MaterialsCatalysisStereocenterddc:540Materials ChemistryCeramics and CompositesStereoselectivityta116
researchProduct