Search results for "Applied Mathematics"

Self-normalizing Sylow subgroups

2003

Using the classification of finite simple groups we prove the following statement: Let p > 3 p>3 be a prime, Q Q a group of automorphisms of p p -power order of a finite group G G , and P P a Q Q -invariant Sylow p p -subgroup of G G . If C N G ( P ) / P ( Q ) \mathbf {C}_{\mathbf {N}_G(P)/P}(Q) is trivial, then G G is solvable. An equivalent formulation is that if G G has a self-normalizing Sylow p p -subgroup with p > 3 p >3 a prime, then G G is solvable. We also investigate the possibilities when p = 3 p=3 .

Squaring a conjugacy class and cosets of normal subgroups

2015

Lengths of radii under conformal maps of the unit disc

1999

If E f ( R ) E_{f}(R) is the set of endpoints of radii which have length greater than or equal to R > 0 R>0 under a conformal map f f of the unit disc, then cap ⁡ E f ( R ) = O ( R − 1 / 2 ) \operatorname {cap} E_{f}(R)=O(R^{-1/2}) as R → ∞ R\to \infty for the logarithmic capacity of E f ( R ) E_{f}(R) . The exponent − 1 / 2 -1/2 is sharp.

Braiding minimal sets of vector fields

2002

We extend a classical but fundamental theorem of knot and braid theories to describe the geometry of nonsingular minimal sets of 3-dimensional flows.

Doubly nonlinear equations with unbounded operators

2004

Abstract The solvability of the evolution system v′(t)+ B (t)u(t)∋ f (t),v(t)∈ A (t)u(t) , 0 A (t) are bounded, possibly degenerate, subdifferentials and B (t) are unbounded subdifferentials.

Asymptotics for the multiplicities in the cocharacters of some PI-algebras

2003

We consider associative PI-algebras over a field of characteristic zero. We study the asymptotic behavior of the sequence of multiplicities of the cocharacters for some significant classes of algebras. We also give a characterization of finitely generated algebras for which this behavior is linear or quadratic.

Type and Cotype in Vector-Valued Nakano Sequence Spaces

2001

AbstractGiven a sequence of Banach spaces {Xn}n and a sequence of real numbers {pn}n in [1,∞), the vector-valued Nakano sequence spaces ℓ({pn},{Xn}) consist of elements {xn}n in ∏nXn for which there is a constant λ>0 such that ∑n(‖xn‖/λ)pn<∞. In this paper we find the conditions on the Banach spaces Xn and on the sequence {pn}n for the spaces ℓ({pn},{Xn}) to have cotype q or type p.

Regular subclasses in the Sobolev space

2009

Abstract We study some slight modifications of the class α - A C n ( Ω , R m ) introduced in [D. Bongiorno, Absolutely continuous functions in R n , J. Math. Anal. and Appl. 303 (2005) 119–134]. In particular we prove that the classes α - A C λ n ( Ω , R m ) , 0 λ 1 , introduced in [C. Di Bari, C. Vetro, A remark on absolutely continuous functions in R n , Rend. Circ. Matem. Palermo 55 (2006) 296–304] are independent by λ and contain properly the class α - A C n ( Ω , R m ) . Moreover we prove that α - A C n ( Ω , R m ) = ( α - A C λ n ( Ω , R m ) ) ∩ ( α - A C n , λ ( Ω , R m ) ) , where α - A C n , λ ( Ω , R m ) is the symmetric class of α - A C λ n ( Ω , R m ) , 0 λ 1 .

The best constant for the Sobolev trace embedding from into

2004

Abstract In this paper we study the best constant, λ 1 ( Ω ) for the trace map from W 1 , 1 ( Ω ) into L 1 ( ∂ Ω ) . We show that this constant is attained in BV ( Ω ) when λ 1 ( Ω ) 1 . Moreover, we prove that this constant can be obtained as limit when p ↘ 1 of the best constant of W 1 , p ( Ω ) ↪ L p ( ∂ Ω ) . To perform the proofs we will look at Neumann problems involving the 1-Laplacian, Δ 1 ( u ) = div ( Du / | Du | ) .

Entropy, transverse entropy and partitions of unity

1994

AbstractThe topological entropy of a transformation is expressed in terms of partitions of unity. The transverse entropy of a flow tangential to a foliation is defined and expresed in a similar way. The geometric entropy of a foliation of a Riemannian manifold is compared with the transverse entropy of its geodesic flow.