In a seminal paper, Charikar et al. derive upper and lower bounds on the approximation ratios for several grammar-based compressors, but in all cases there is gap between bound. Here gaps LZ78 BISECTION are closed by showing that ratio of ?((n/log n) 2/3 ), whereas ?(?(n/log n)). addition, bound...

A trapped-ion-based quantum computer that fits in two boxes, each the size of a studio apartment’s shower, can create fully entangled 24-particle state.

A prime gap is the difference between two successive numbers. Two smallest possible primes. twin a that has of two. The conjecture states there are infinitely many This been one great open problems in number theory for years. In May 2013, popular Yitang Zhang's paper was accepted by journal Annals Mathematics where it announced some integer N less than 70 million, pairs primes differ N. few mon...

An L(2, 1)-labeling (or distance two labeling) of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that |f(x) − f(y)| ≥ 2 if d(x, y) = 1 and |f(x) − f(y)| ≥ 1 if d(x, y) = 2. The L(2, 1)-labeling number λ(G) of G is the smallest number k such that G has an L(2, 1)-labeling with max{f(v) : v ∈ V (G)} = k. In this paper we completely determine the λ-...

We consider models where one Majorana neutrino is massless at tree level (like the see saw with two right-handed neutrinos), and compute the contribution to its mass m generated by two-loop quantum corrections. The result is m ∼ 10 eV in the SM and m ∼ 10 eV · (tan β/10) in the MSSM, compatible with the restricted range suggested by Affleck-Dine baryogenesis.