Search results for "bound"

showing 10 items of 2948 documents

On James Hyde's example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$

2020

In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of $\mathrm{Homeo}(D,\partial D)$, the group of homeomorphisms of the disk fixing the boundary. This implies that the group $\mathrm{Homeo}(D,\partial D)$ itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.

CombinatoricsGroup (mathematics)Primary 37C85. Secondary 37E05 37E10 37E20[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]FOS: MathematicsBoundary (topology)Finitely-generated abelian groupGroup Theory (math.GR)Dynamical Systems (math.DS)Mathematics - Dynamical SystemsMathematics - Group Theory[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Mathematics
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A bound on the p-length of p-solvable groups

2013

Let G be a finite p-solvable group and P a Sylow p-subgroup of G. Suppose that $\gamma_{l(p-1)}(P)\subseteq \gamma_r(P)^{p^s}$ for $l(p-1)<r+s(p-1)$, then the p-length is bounded by a function depending on l.

CombinatoricsGroup (mathematics)Solvable groupGeneral MathematicsBounded functionSylow theoremsFOS: Mathematics20D10Function (mathematics)Group Theory (math.GR)Mathematics - Group TheoryMathematics
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Hölder inequality for functions that are integrable with respect to bilinear maps

2008

Let $(\Omega, \Sigma, \mu)$ be a finite measure space, $1\le p&lt;\infty$, $X$ be a Banach space $X$ and $B:X\times Y \to Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p$-integrable with respect to $B$ whenever $\sup_{\|y\|=1} \int_\Omega \|B(f(w),y)\|^p\,d\mu&lt;\infty$. We get an analogue to Hölder's inequality in this setting.

CombinatoricsHölder's inequalityGeneral MathematicsBounded functionMathematical analysisBanach spaceFunction (mathematics)Bilinear mapSpace (mathematics)OmegaMeasure (mathematics)MathematicsMATHEMATICA SCANDINAVICA
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A Star-Variety With Almost Polynomial Growth

2000

Abstract Let F be a field of characteristic zero. In this paper we construct a finite dimensional F -algebra with involution M and we study its ∗ -polynomial identities; on one hand we determine a generator of the corresponding T -ideal of the free algebra with involution and on the other we give a complete description of the multilinear ∗ -identities through the representation theory of the hyperoctahedral group. As an outcome of this study we show that the ∗ -variety generated by M , var( M , ∗ ) has almost polynomial growth, i.e., the sequence of ∗ -codimensions of M cannot be bounded by any polynomial function but any proper ∗ -subvariety of var( M , ∗ ) has polynomial growth. If G 2 is…

CombinatoricsInvolution (mathematics)Multilinear mapAlgebra and Number TheorylawAlternating polynomialFree algebraBounded functionA* search algorithmHyperoctahedral groupRepresentation theorylaw.inventionMathematicsJournal of Algebra
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Operators on PIP-Spaces and Indexed PIP-Spaces

2009

As already mentioned, the basic idea of pip-spaces is that vectors should not be considered individually, but only in terms of the subspaces V r (r Є F), the building blocks of the structure. Correspondingly, an operator on a pipspace should be defined in terms of assaying subspaces only, with the proviso that only continuous or bounded operators are allowed. Thus an operator is a coherent collection of continuous operators. We recall that in a nondegenerate pip-space, every assaying subspace V r carries its Mackey topology \(\tau (V_r , V \bar{r})\) and thus its dual is \(V \bar{r}\). This applies in particular to \(V^{\#}\) and V itself. For simplicity, a continuous linear map between two…

CombinatoricsLinear mapsymbols.namesakeOperator (computer programming)Unitary representationBounded functionHilbert spacesymbolsProduct topologyLinear subspaceMathematicsMackey topology
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Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields

2003

Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ Ising lattices with nearest neighbor ferromagnetic exchange and four free $L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ surfaces, at which antisymmetric surface fields $\ifmmode\pm\else\textpm\fi{}{H}_{s}$ act, are studied for a wide range of linear dimensions $(4l~Ll~320,30l~{L}_{y}l~1000),$ in an attempt to clarify finite size effects on the wedge filling transition in this ``double-wedge'' geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a li…

CombinatoricsMagnetizationCondensed matter physicsFerromagnetismTransition temperatureLattice (order)Periodic boundary conditionsIsing modelInverse functionCubic crystal systemMathematicsPhysical Review E
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Topological lower bounds on the distance between area preserving diffeomorphisms

2000

Area preserving diffeomorphisms of the 2-disk which are Identity near the boundary form a group which can be equipped, using theL2-norm on its Lie algebra, with a right invariant metric. In this paper we give a lower bound on the distance between diffeomorphisms which is invariant under area preserving changes of coordinates and which improves the lower bound induced by the Calabi invariant. In the case of renormalizable and infinitely renormalizable maps, our estimate can be improved and computed.

CombinatoricsMathematics::Dynamical SystemsGeneral MathematicsLie algebraInvariant (mathematics)TopologyUpper and lower boundsMathematicsBoletim da Sociedade Brasileira de Matem�tica
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Browder's theorems through localized SVEP

2005

A bounded linear operator T ∈ L(X) on aBanach space X is said to satisfy “Browder’s theorem” if the Browder spectrum coincides with the Weyl spectrum. T ∈ L(X) is said to satisfy “a-Browder’s theorem” if the upper semi-Browder spectrum coincides with the approximate point Weyl spectrum. In this note we give several characterizations of operators satisfying these theorems. Most of these characterizations are obtained by using a localized version of the single-valued extension property of T. In the last part we shall give some characterizations of operators for which “Weyl’s theorem” holds.

CombinatoricsMathematics::Functional AnalysisOperator (computer programming)General MathematicsSpectrum (functional analysis)PropertyOperatorExtension (predicate logic)Space (mathematics)theorem holdsMathematics::Algebraic TopologyBounded operatorMathematics
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An algorithm for the solution of tree equations

1997

We consider the problem of solving equations over k-ary trees. Here an equation is a pair of labeled α-ary trees, where α is a function associating an arity to each label. A solution to an equation is a morphism from α-ary trees to k-ary trees that maps the left and right hand side of the equation to the same k-ary tree.

CombinatoricsMorphismBinary treeBranch and boundSearch algorithmTree (set theory)Function (mathematics)ArityComputer Science::Information TheoryMathematicsEquation solving
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Extension of a Schur theorem to groups with a central factor with a bounded section rank

2013

Abstract A well-known result reported by Schur states that the derived subgroup of a group is finite provided its central factor is finite. Here we show that if the p-section rank of the central factor of a locally generalized radical group is bounded, then so is the p-section rank of its derived subgroup. We also give an explicit expression for this bound.

CombinatoricsMultiplier (Fourier analysis)Algebra and Number TheoryBounded functionSchur's lemmaCommutator subgroupFocal subgroup theoremRank of an abelian groupSchur's theoremSchur multiplierMathematicsJournal of Algebra
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