The time evolution of a neutral kaon state state is described by d dt Ψ = −iΛΨ , Λ ≡ M − i 2 Γ (1) where M and Γ are Hermitian 2 × 2 matrices known as the mass and decay matrices. The corresponding eigenvalues are λ L,S = m L,S − i 2 γ L,S. CPT invariance requires the diagonal elements of Λ to be equal. The CPT-violation complex parameter δ is defined as δ = Λ K 0 K 0 − Λ K 0 K 0 2(λ L − λ S) =...

Let {xn}n∈N be a sequence of [0, 1]d, {λn}n∈N a sequence of positive real numbers converging to 0, and δ > 1. The classical ubiquity results are concerned with the computation of the Hausdorff dimension of limsup-sets of the form S(δ) = T N∈N S n≥N B(xn, λ δ n). Let μ be a positive Borel measure on [0, 1]d, ρ ∈ (0, 1] and α > 0. Consider the finer limsup-set

2. (T) Let CPn be complex projective n-space. (a) Describe the cohomology ring H∗(CPn,Z) and, using the Kunneth formula, the cohomology ring H∗(CPn × CPn,Z). (b) Let ∆ ⊂ CPn×CPn be the diagonal, and δ = i∗[∆] ∈ H2n(CP×CP,Z) the image of the fundamental class of ∆ under the inclusion i : ∆ → CPn × CPn. In terms of your description of H∗(CPn × CPn,Z) above, find the Poincaré dual δ∗ ∈ H2n(CPn × C...

Proof. We apply Lemma 3.1 of (Jayram & Woodruff, 2013) with parameters α = 2, p = 1, b = 1, ε = δ, and δ = . This encodes inputs from a problem they prove is hard (augmented indexing on large domains) to inputs appropriate for Hamming estimation. In particular, for n′ = O( 1 δ2 log(1/ )) it gives a distribution on (a, b) ∈ {0, 1} n′ × {0, 1}n that are divided into “NO” and “YES” instances, such...

Electronic transition spectrum of cobalt monoboride (CoB) in the visible region between 495 and 560 nm has been observed and analyzed using laser-induced fluorescence spectroscopy. CoB molecule was produced by the reaction of laser-ablated cobalt atom and diborane (B(2)H(6)) seeded in argon. Fifteen vibrational bands with resolved rotational structure have been recorded, which included transiti...

A b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that is adjacent to a vertex of every other color. The b-chromatic number b(G) of a graph G is the largest k such that G admits a b-coloring with k colors. A graph G is b-chromatic edge critical if for any edge e of G, the b-chromatic number of G − e is less than the b-chromatic number of G. We ...

A conflict-avoiding code (CAC) C of length n and weight k is a collection of k-subsets of Zn such that Δ(x) ∩ Δ(y) = ∅ for any x, y ∈ C and x = y, where Δ(x) = {a − b : a, b ∈ x, a = b}. Let CAC(n, k) denote the class of all CACs of length n and weight k. A CAC C ∈ CAC(n, k) is said to be equi-difference if any codeword x ∈ C has the form {0, i, 2i, . . . , (k − 1)i}. A CAC with maximum size is...

PURPOSE To investigate whether diffusion time (Δ) affects the diffusion measurements in liver and their sensitivity in detecting fibrosis. METHODS Liver fibrosis was induced in Sprague-Dawley rats (n = 12) by carbon tetrachloride (CCl(4)) injections. Diffusion-weighted MRI was performed longitudinally during 8-week CCl(4) administration at 7 Tesla (T) using single-shot stimulated-echo EPI wit...

A time-dependent double-barrier option is a derivative security that delivers the terminal value φ(ST ) at expiry T if neither of the continuous time-dependent barriers b± : [0, T ]→R+ have been hit during the time interval [0, T ]. Using a probabilistic approach, we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a w...

We study Cesàro (C, δ) means for two-variable Jacobi polynomials on the parabolic biangle B = {(x1, x2) ∈ R2 : 0 ≤ x1 ≤ x2 ≤ 1}. Using the product formula derived by Koornwinder & Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C, δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ > ...