Result on the Mobius Function over Shifted Primes

This article provides new asymptotic results for the summatory Mobius function $\sum_{p \leq x} \mu(p+a) =O \left (x(\log x)^{-c} \right )$ and the summatory Liouville function $\sum_{p \leq x} \lambda(p+a) =O \left (x(\log x)^{-c} \right )$ over the shifted primes, where $a\ne0$ is a fixed parameter, and $c>1$ is an arbitrary constant. These results improve the current estimates $\sum_{p \leq x} \mu(p+a)=(1-\delta)\pi(x)$, and $\sum_{p \leq x} \lambda(p+a)=(1-\delta)\pi(x)$ for $\delta>0$, respectively. Furthermore, a conditional proof for the autocorrelation function $\sum_{p \leq x} \mu(p+a)\mu(p+b) =O \left (x(\log x)^{-c} \right )$, and an unconditional proof for the autocorrelation function $\sum_{p \leq x} \lambda(p+a)\lambda(p+b) =O \left (x(\log x)^{-c} \right )$ over the shifted primes, where $a\ne b$, are also included.Comment: Fifty Three Pages. Keywords: Shifted prime; Arithmetic function; Mobius function; Liouville function; vonMangoldt function; Correlation; Autocorrelation; Chowla conjecture; Sarnak conjectur

QCD Physics with ZEUS and H1 at HERA

A review is presented of recent results in QCD from the H1 and ZEUS experiments at HERA, emphasizing the use of higher order calculations to describe the data.Comment: 12 pages, 15 figures, invited review paper for Mod. Phys. Lett

Effect of alirocumab on lipids and lipoproteins in individuals with metabolic syndrome without diabetes: Pooled data from 10 phase 3 trials.

AimsThis analysis assessed the efficacy and safety of alirocumab, a proprotein convertase subtilisin/kexin type 9 inhibitor, in patients with or without metabolic syndrome (MetS) using pooled data from 10 phase 3 ODYSSEY trials.Materials and methodsData from 4983 randomized patients (1940 with MetS; 1642 with diabetes excluded) were assessed in subgroups by MetS status. Efficacy data were analysed in 4 pools per study design: 2 placebo-controlled pools (1 using alirocumab 150 mg every 2 weeks [Q2W], 1 using 75/150 mg Q2W) with background statin, and 2 ezetimibe-controlled pools (both alirocumab 75/150 mg Q2W), 1 with and 1 without background statin. Alirocumab 75/150 mg indicates possible dose increase from 75 to 150 mg at Week 12 based on Week 8 LDL-C.ResultsLDL-C percentage reduction from baseline at Week 24 with alirocumab was 63.9% (MetS) and 56.8% (non-MetS) in the pool of alirocumab 150 mg Q2W, and 42.2% to 52.2% (MetS) and 45.0% to 52.6% (non-MetS) in 3 pools using 75/150 mg Q2W. Levels of other lipid and lipoprotein parameters were also improved with alirocumab treatment, including apolipoprotein B, non-high-density lipoprotein cholesterol (non-HDL-C), lipoprotein(a) and HDL-C. Overall, the percentage change at Week 24 in LDL-C and other lipids and lipoproteins did not vary by MetS status. Adverse event rates were generally similar between treatment groups, regardless of MetS status; injection-site reactions occurred more frequently in alirocumab vs control groups.ConclusionsAcross study pools, alirocumab-associated reductions in LDL-C, apolipoprotein B, and non-HDL-C were significant vs control, and did not vary by MetS status

High-E_T dijet photoproduction at HERA

The cross section for high-E_T dijet production in photoproduction has been measured with the ZEUS detector at HERA using an integrated luminosity of 81.8 pb-1. The events were required to have a virtuality of the incoming photon, Q^2, of less than 1 GeV^2 and a photon-proton centre-of-mass energy in the range 142 < W < 293 GeV. Events were selected if at least two jets satisfied the transverse-energy requirements of E_T(jet1) > 20 GeV and E_T(jet2) > 15 GeV and pseudorapidity requirements of -1 < eta(jet1,2) < 3, with at least one of the jets satisfying -1 < eta(jet) < 2.5. The measurements show sensitivity to the parton distributions in the photon and proton and effects beyond next-to-leading order in QCD. Hence these data can be used to constrain further the parton densities in the proton and photon.Comment: 36 pages, 13 figures, 20 tables, including minor revisions from referees. Accepted by Phys. Rev.

A probability-conserving cross-section biasing mechanism for variance reduction in Monte Carlo particle transport calculations

In Monte Carlo particle transport codes, it is often important to adjust reaction cross sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analogous Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross section change. This makes it possible to increase the cross section of nuclear reactions by factors exceeding 10^4 (in appropriate cases), without distorting the results of energy deposition calculations or coincidence rates. The procedure is also valid for bias factors less than unity, which is useful, for example, in problems that involve computation of particle penetration deep into a target, such as occurs in atmospheric showers or in shielding