Let ε > 0 and consider ε2u′′(t; ε) + u′(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε)ds+ f(t; ε), t ≥ 0, u(0; ε) = u0(ε), u ′(0; ε) = u1(ε), and w′(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t), t ≥ 0, w(0) = w0, in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear operator for t ≥ 0. With some conv...

The turbulent pulsatile blood flow through stenosed arteries considering the elastic property of the wall is investigated numerically. During the numerical model validation both standard k-ε model and RNG K-ε model are used. Compared with the RNG K-ε model, the standard K-ε model shows better agreement with previous experimental results and is better able to show the reverse flow region. Also, ...

l k=0 (−1) m−k l k m − k n 2k k − 2l + m = l k=0 l k 2k n n − l m + n − 3k − l. On the basis of this identity, for d ∈ {0, 1, 2,. .. } and ε ∈ {0, ±1} we construct explicit f ε (d) and g ε (d) such that for any prime p > d we have p−1 k=1 k ε C k+d ≡ f ε (d) if p ≡ 1 (mod 3), g ε (d) if p ≡ 2 (mod 3), where C n denotes the Catalan number 1 n+1 2n n ; for example, if p 5 is a prime then 0<k<p−4 ...

COVID-19 reached its fourth year of pandemic since 2020. The repeated waves infections have been driven by multiple factors such as pathological traits variants, diagnostic accuracy, and vaccination conditions. This study revisits analyzes the dynamic processes viral transmission to generate new scientific knowledge. A cascade model from one case another was developed, theoretically analyzed ho...

In this work, we study the socially fair k-median/k-means problem. We are given a set of points P in metric space X with distance function d(.,.). There ℓ groups: P1,…,Pℓ⊆P. also F feasible centers X. The goal k-median problem is to find C⊆F k that minimizes maximum average cost over all groups. That is, C objective Φ(C,P)≡maxj⁡{∑x∈Pjd(C,x)/|Pj|}, where d(C,x) x closest center C. k-means define...

We quantify the important effect of strong final state interactions in the weak K → 2π amplitudes, using the measured π–π phase shifts with J = 0 and I = 0, 2. The final rescattering of the two pions provides a strong enhancement of the ∆I = 1/2 amplitude, which so far has been neglected in the theoretical predictions of ε′/ε. This correction increases the Standard Model prediction of ε′/ε to v...

We present a study of the Hausdorff Core problem on simple polygons. A polygon Q is a k-bounded Hausdorff Core of a polygon P if P contains Q, Q is convex, and the Hausdorff distance between P and Q is at most k. A Hausdorff Core of P is a k-bounded Hausdorff Core of P with the minimum possible value of k, which we denote kmin. Given any k and any ε > 0, we describe an algorithm for computing a...