Search results for "Bounded function"
showing 10 items of 508 documents
On the decision problem for the guarded fragment with transitivity
2002
The guarded fragment with transitive guards, [GF+TG], is an extension of GF in which certain relations are required to be transitive, transitive predicate letters appear only in guards of the quantifiers and the equality symbol may appear everywhere. We prove that the decision problem for [GF+TG] is decidable. This answers the question posed in (Ganzinger et al., 1999). Moreover, we show that the problem is 2EXPTIME-complete. This result is optimal since the satisfiability problem for GF is 2EXPTIME-complete (Gradel, 1999). We also show that the satisfiability problem for two-variable [GF+TG] is NEXPTIME-hard in contrast to GF with bounded number of variables for which the satisfiability pr…
k-Weakly almost convex groups and ? 1 ? $$\tilde M^3 $$
1993
We extend Cannon's notion ofk-almost convex groups which requires that for two pointsx, y on then-sphere in the Cayley graph which can be joined by a pathl1 of length ≤k, there is a second pathl2 in then-ball, joiningx andy, of bounded length ≤N(k). Ourk-weakly almost convexity relaxes this condition by requiring only thatl1 ∝l2 bounds a disk of area ≤C1(k)n1 - e(k) +C2(k). IfM3 is a closed 3-manifold with 3-weakly almost convex fundamental group, then π1∞\(\tilde M^3 = 0\).
Composition of quasiconformal mappings and functions in Triebel-Lizorkin spaces
2012
Let α > 0 and p ∈ [1, ∞) satisfy αp ≤ n. Suppose that f: Rn Rn is a K-quasiconformal mapping and let u ∈ Wα, p(Rn) have compact support. We find an optimal value of β = β(α, K, n) such that u○f ∈ Wβ, p(Rn). We also give an answer to the analogous problem where we moreover assume that u is bounded.
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.
Hölder inequality for functions that are integrable with respect to bilinear maps
2008
Let $(\Omega, \Sigma, \mu)$ be a finite measure space, $1\le p<\infty$, $X$ 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 $\sup_{\|y\|=1} \int_\Omega \|B(f(w),y)\|^p\,d\mu<\infty$. We get an analogue to Hölder's inequality in this setting.
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…
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…
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.
On the number of conjugacy classes of zeros of characters
2004
Letm be a fixed non-negative integer. In this work we try to answer the following question: What can be said about a (finite) groupG if all of its irreducible (complex) characters vanish on at mostm conjugacy classes? The classical result of Burnside about zeros of characters says thatG is abelian ifm=0, so it is reasonable to expect that the structure ofG will somehow reflect the fact that the irreducible characters vanish on a bounded number of classes. The same question can also be posed under the weaker hypothesis thatsome irreducible character ofG hasm classes of zeros. For nilpotent groups we shall prove that the order is bounded by a function ofm in the first case but only the derive…
The Neumann Problem for the Total Variation Flow
2004
This chapter is devoted to prove existence and uniqueness of solutions for the minimizing total variation flow with Neumann boundary conditions, namely $$ \left\{ \begin{gathered} \frac{{\partial u}} {{\partial t}} = div\left( {\frac{{Du}} {{\left| {Du} \right|}}} \right) in Q = (0,\infty ) \times \Omega , \hfill \\ \frac{{\partial u}} {{\partial \eta }} = 0 on S = (0,\infty ) \times \partial \Omega , \hfill \\ u(0,x) = u_0 (x) in x \in \Omega , \hfill \\ \end{gathered} \right. $$ (2.1) where Ω is a bounded set in ℝ N with Lipschitz continuous boundary ∂ Ω and u0 ∈ L1(Ω). As we saw in the previous chapter, this partial differential equation appears when one uses the steepest descent method …