In this paper we prove that if φ : C → C is a K-quasiconformal map, 0 < t < 2, and E ⊂ C is a compact set contained in a ball B, then H(E) diam(B) ≤ C(K) ( H ′ (φ(E)) diam(φ(B))t′ ) t tK

In this paper we show that the maximal solutions (φ , A ) in the Abelian Chern-Simons Higgs model on a ’t Hooft type periodic domain converges to (φ∗, A∗) and φ∗ is a harmonic map. We also study asymptotic behaviors of the energy density.

A commuting row contraction is a d-tuple of commuting operators T1, . . . , Td such that ∑d i=1 TiT ∗ i ≤ I. Such operators have a polynomial functional calculus which extends to a norm closed algebra of multipliers Ad on Drury-Arveson space. We characterize those row contractions which admit an extension of this map to a weak-∗ continuous functional calculus on the full multiplier algebra. In ...

Let {Xj , j ≥ 1} be a strictly stationary φ-mixing sequence of non-degenerate random variables with EX1 = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {Xj} under the condition that L(x) := EX2 1 I{|X1| ≤ x} is a slowly varying function at ∞, without any higher moment conditions.

The mixing between nonstrange and strange quark wavefunctions in the ω and φ mesons leads to a small predicted branching ratio B(D+ s → ωeνe) = O(10−4)(δ/3.34◦)2, where δ is the mixing angle. The value δ = −3.34◦ is obtained in a mass-independent analysis, while a mass-dependent analysis gives δ = −0.45◦ at m(ω) and −4.64◦ at m(φ). Measurement of this branching ratio thus can tell whether the d...

Let V = B(H) or S(H), where B(H) is the algebra of bounded linear operator acting on the Hilbert space H, and S(H) is the set of self-adjoint operators in B(H). Denote the numerical range of A ∈ B(H) by W (A) = {(Ax, x) : x ∈ H, (x, x) = 1}. It is shown that a surjective map φ : V→ V satisfies W (AB +BA) =W (φ(A)φ(B) + φ(B)φ(A)) for all A,B ∈ V if and only if there is a unitary operator U ∈ B(H...

We say that the quasi-norm Φ of a symmetric sequence space E has property P if, for all x, y ∈ E with 0 ≤ xn ≤ yn for all n, and xN < yN for some N , we have Φ (xn) < Φ (yn) . Simon [6] proved that if the Banach norm Φ has property P , then whenever An → A in the weak operator topology on the unitary matrix space CE and Φ(An)→ Φ(A), then An → A in the strong operator topology on CE . In this no...

We prove that if A and B are semisimple Banach algebras, then the separating subspace of every Lie isomorphism from A onto B is contained in the centre of B. Over the years, there has been considerable effort made and success in studying the structure of Lie isomorphisms of rings and Banach algebras [2–5, 7–15]. We are interested in investigating the continuity of Lie isomorphisms of Banach alg...