We calculate the leading divergences at NNLO for the octet part of the nonleptonic weak sector of chiral perturbation theory, using renormalization group methods. The role of counterterms which vanish at the equation of motion and their use to simplify the calculation is shown explicitly. The obtained countertem Lagrangian can be employed to calculate the chiral double log contributions of quan...

We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.

In this paper, we study a generalization of z-ideals in the ring C(X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z-ideals in C(X).

We further examine Kummer's incorrect conjectured asymptotic estimate for the size of the rst factor of the class number of a cyclotomic eld, h 1 (p). Whereas Kummer had conjectured that h 1 (p) G(p) := 2p(p=4 2) p?1 4 we show, under certain plausible assumptions, that there exist constants a ; b such that h 1 (p) G(p) for a x= log b x primes p x whenever log is rational. On the other hand, the...

This paper presents an adaptive randomized algorithm for computing the butterfly factorization of $m\times n$ matrix with $m\approx provided that both and its transpose can be rapidly applied to arbitrary vectors. The resulting is composed $\mathcal{O}(\log n)$ sparse factors, each containing $\mathcal{O}(n)$ nonzero entries. attained using $\mathcal{O}(n^{3/2}\log computation $\mathcal{O}(n\lo...

The bit error rate (BER) expression and performance of free-space optical communication link in clear but turbulent atmosphere using subcarrier intensity modulation (SIM) with differential phase shift keying (DPSK) is presented. The practical linear combining technique suitable for differentially modulated data (selection combining) is considered and its performance evaluated under weak atmosph...

We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs dimension 4. As main ingredients, we verify 3-dimensional pairs, and show that which admit weak Zariski decompositions follows from in lower dimensions.

We prove that every globally F -regular variety is log Fano. In other words, if a prime characteristic variety X is globally F -regular, then it admits an effective Qdivisor ∆ such that −KX −∆ is ample and (X, ∆) has controlled (Kawamata log terminal, in fact globally F -regular) singularities. A weak form of this result can be viewed as a prime characteristic analog of de Fernex and Hacon’s ne...