Let l be an oriented link of d components with nonzero Alexander polynomial ∆(u1, . . . , ud). Let Λ be a finite-index subgroup of H1(S− l) ∼= Z, and let MΛ be the corresponding abelian cover of S branched along l. The growth rate of the order of the torsion subgroup of H1(MΛ), as a suitable measure of Λ approaches infinity, is equal to the Mahler measure of ∆.

Let M be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace τ . Let d be an injective positive measurable operator with respect to (M, τ ) such that d is also measurable. Define Lp(d) = {x ∈ L0(M) : dx+ xd ∈ Lp(M)} and ‖x‖Lp(d) = ‖dx+ xd‖p . We show that for 1 6 p0 < p1 6 ∞, 0 < θ < 1 and α0 > 0, α1 > 0 the interpolation equality (Lp0(d 0), Lp1(d α))θ = Lp(d ) hol...

Our aim is to present constructions in which some of the cofinalities drop down, i.e. the generators of PCF structure are far a part. 1 Some Preliminary Settings Let λ0 < κ0 < λ1 < κ1 < ... < λn < κn < ...., n < ω be a sequence of cardinals such that for each n < ω • λn is λ +n+2 n +2 n strong as witnessed by an extender Eλn • κn is κ +n+2 n +2 n strong as witnessed by an extender Eκn Let κ = ⋃...

Let Γ0 ⊂ O(2, 1) be a Schottky group, and let Σ = H2/Γ0 be the corresponding hyperbolic surface. Let C(Σ) denote the space of geodesic currents on Σ. The cohomology group H1(Γ0, V) parametrizes equivalence classes of affine deformations Γu of Γ0 acting on an irreducible representation V of O(2, 1). We define a continuous biaffine map C(Σ)×H1(Γ0, V) Ψ −→ R which is linear on the vector space H1(...

We begin with three technical lemmas. Lemma 2 Let y ̸ = 0 and 0 < λ 1 ≤ ∥X T y∥ ∞. We have ⟨ y λ 1 − θ * 1 , θ * 1 ⟩ ≥ 0. Proof Since the Euclidean projection of y λ1 onto {θ : ∥X T θ∥ ∞ ≤ 1} is θ * 1 , it follows from Lemma 1 that ⟨θ * 1 − y λ 1 , θ − θ * 1 ⟩ ≥ 0, ∀θ : ∥X T θ∥ ∞ ≤ 1. (46) As 0 ∈ {θ : ∥X T θ∥ ∞ ≤ 1}, we have Eq. (45). Lemma 3 Let y ̸ = 0 and 0 < λ 1 ≤ ∥X T y∥ ∞. If θ * 1 parallel...

Interpolation theorem has an important role in classic predicate logic. Two prominent applications are Robinson’s joint consistency theorem and Beth’s definability theorem (though both were proved originally in different ways). It also have close relation to cut-elimination of sequent calculus. However, interpolation theorem fails in quantified modal logic S5 and related extensions. In this ter...

For each element u in a finite group G define map θ : → by ( g ) = [ − , ] and set Θ { ∈ | n for some > 0 } . Then induces permutation of ; let β be the number orbits apart from {1}. Building on work J.N. Bray, R.A. Wilson second author, we show that index soluble radical is bounded terms values 2-elements

Let M be a non-compact connected Riemann surface of finite type, and R ⊂⊂ M be a relatively compact domain such that H1(M,Z) = H1(R,Z). Let R̃ −→ R be a covering. We study the algebra H∞(U) of bounded holomorphic functions defined in some domains U ⊂ R̃. Our main result is a Forelli type theorem on projections in H∞(D).

We obtain the following characterization of Q-polynomial distance-regular graphs. Let Γ denote a distance-regular graph with diameter d ≥ 3. Let E denote a minimal idempotent of Γ which is not the trivial idempotent E0. Let {θ∗ i }i=0 denote the dual eigenvalue sequence for E. We show that E is Q-polynomial if and only if (i) the entry-wise product E ◦ E is a linear combination of E0, E, and at...

This article studies a locally optimal test φ for testing H0 : θ ≥ θ0 versus H1 : θ < θ0 for the lifetime parameter θ in an exponential distribution based on type-I censored data. Certain properties associated with φ are addressed. We compare the performance of φ with that of Spurrier and Wei’s [Spurrier, J.D., Wei, L.J., 1980. A test of the parameter of the exponential distribution in the type...