We compute the imaginary part of the 2-loop vertex corrections in the QCD Factorization framework for hadronic two-body decays as B → ππ. This completes the NNLO calculation of the imaginary part of the topological tree amplitudes and represents an important step towards a NNLO prediction of direct CP asymmetries in QCD Factorization. Concerning the technical aspects, we find that soft and coll...

We experimentally demonstrate broadband waveguide crossing arrays showing ultralow loss of 0.0 4dB/crossing (0.9%) on average and converging to 0.033 dB/crossing (0.075%) matching theory and cross-talk suppression over 35 dB in a CMOS-compatible geometry. The principle of operation is the tailored excitation of a low-loss spatial Bloch wave formed by matching the periodicity of the crossing arr...

Partial transmit sequence (PTS) is an attractive technique for PAPR reduction without distortion, but to obtain preferable PAPR performance it needs many inverse fast Fourier transforms (IFFTs), which results in high computational complexity. In order to reduce the complexity, modified PTS technique, with real and imaginary parts, separately multiplied with phase factors is considered in this p...

Local phase equivalent interactions to the nonlocal Kerman, McManus, and Thaler multiple scattering nucleon —nucleus optical potentials are determined. Both firstand second-order contributions in the free nucleon-nucleon transition amplitude are included. The second order terms modify the derived potentials in a nontrivial way and reduce the strengths of the real and imaginary central potential...

I describe a modification to Shanks’ baby-step giant-step algorithm for computing the order n of an element g of a group G, assuming n is finite. My method has the advantage of being able to compute n quickly, which Shanks’ method fails to do when the order of G is infinite, unknown, or much larger than n. I describe the algorithm in detail. I also present the results of implementations of my a...

Complex-step differentiation is a recent popular method to compute a real valued function and its first derivative approximately with second order error using imaginary step size. We propose a generalization of complex-step method to compute a complex valued function and its derivatives up to order n – 1 with approximate error of order n, for any desired integer n. For this, we use a hypercompl...

The present study compares prosodic features of child-directed speech (CDS) and foreigner-directed speech (FDS), to examine whether FDS is a derivative of CDS as suggested in sociolinguistic studies. Twelve female speakers completed a simple referential communication task addressed to an imaginary adult, an imaginary foreigner, and an imaginary child. The results showed that, compared to the ad...