Let A, B ⊆ Z be finite, nonempty subsets such that maxB − minB ≤ maxA − minA, gcd(A+B−c) = 1, for some c ∈ A+B, and |A+B| ≤ |A|+2|B|−3−δ(A,B), where δ(A,B) is 1 if x + A ⊆ B for some x ∈ Z, and is 0 otherwise. Assume one of the following conditions holds true: • maxA−minA ≤ |A| + |B|− 3, • gcd(A− a) ≤ 2, for some a ∈ A, • |A + B| ≤ 2|A| + |B|− 3− δ(B,A). Then A+B contains a (|A|+ |B|−1)–term ar...

We prove a quantitative stability result for the Brunn-Minkowski inequality: if |A| = |B| = 1, t ∈ [τ, 1−τ ] with τ > 0, and |tA+(1−t)B| ≤ 1+δ for some small δ, then, up to a translation, both A and B are quantitatively close (in terms of δ) to a convex set K.

Let B H t be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). We study the regularity, in the sense of the Malliavin calculus, of the renormalized self-intersection local time ℓ = T 0 t 0 δ 0 (B H t − B H s)dsdt − E T 0 t 0 δ 0 (B H t − B H s)dsdt , where δ 0 is the Dirac delta function.

We study the surface quasi-geostrophic equation with an irregular spatial perturbation∂tθ+u⋅∇θ=−ν(−Δ)γ/2θ+ζ,u=∇⊥(−Δ)−1θ, on [0,∞)×T2, ν⩾0, γ∈[0,3/2) and ζ∈B∞,∞−2+κ(T2) for some κ>0. This covers case of ζ=(−Δ)α/2ξ α<1 ξ a white noise T2. Depending relation between γ α, our setting is subcritical, critical or supercritical in language Hairer's regularity structures [38]. Based purely analytical t...

Definition 1.1. A class of τ -structures, (K,≺K), is said to be an abstract elementary class (AEC) if both K and the binary relation ≺K are closed under isomorphism and satisfy the following conditions. • A1. IfM ≺K N thenM ⊆ N . • A2. ≺K is a partial order on K. • A3. If 〈Ai : i < δ〉 is continuous ≺K -increasing chain: (1) ⋃ i<δ Ai ∈K; (2) for each j < δ, Aj ≺K ⋃ i<δ Ai (3) if each Ai ≺K M ∈K ...

and Applied Analysis 3 2. The Difference Sequence Spaces c 0 B and c λ B of Non-Absolute Type The difference sequence spaces have been studied by several authors in different ways see e.g. 12, 16–21 . In the present section, we introduce the spaces c 0 Δ , and c λ Δ , and show that these spaces are BK-spaces of non-absolute type which are norm isomorphic to the spaces c0 and c, respectively. We...

Let Vn be a vectorspace of complex-valued functions defined on R of dimension n + 1 over C. We say that Vn is shift invariant (on R) if f ∈ Vn implies that fa ∈ Vn for every a ∈ R, where fa(x) := f(x− a) on R. In this note we prove the following. Theorem. Let Vn ⊂ C[a, b] be a shift invariant vectorspace of complex-valued functions defined on R of dimension n+ 1 over C. Let p ∈ (0, 2]. Then ‖f‖...

Let 0 < a < b < 1 and let T be the doubling map. Set J (a, b) := {x ∈ [0, 1] : Tx / ∈ (a, b), n ≥ 0}. In this paper we completely characterize the holes (a, b) for which any of the following scenarios holds: (i) J (a, b) contains a point x ∈ (0, 1); (ii) J (a, b) ∩ [δ, 1− δ] is infinite for any fixed δ > 0; (iii) J (a, b) is uncountable of zero Hausdorff dimension; (iv) J (a, b) is of positive ...

RZ Cas is an Algol-type partial eclipsing binary, the secondary component of which has filled its Roche lobe. Its visual magnitude is 6.18 and its period is 1.195 days. The most important characteristics of RZ Cas are period change (due to mass transfer) and anomalies in the primary minimum of its light curve (due to δ Scuti pulsations). In this paper, light curves of RZ Cas are obtained using ...

BACKGROUND Noninvasive techniques for the localization of the accessory pathways (APs) might help guide mapping procedures and ablation techniques. We sought to examine the diagnostic accuracy of strain imaging for the localization of the APs in Wolff-Parkinson-White syndrome. METHODS We prospectively studied 25 patients (mean age = 32 ± 17 years, 58.3% men) with evidence of pre-excitation on...