Recent measurements of the ratio of the elastic electromagnetic form factors of the proton, GEp/GMp, using the polarization transfer technique at Jefferson Lab show that this ratio decreases dramatically with increasing Q 2 , in contradiction to previous measurements using the Rosenbluth separation technique. Using this new high quality data as a constraint, we have reanalyzed most of the world ep elastic cross section data. In this paper, we present a new empirical fit to the reanalyzed data for the proton elastic magnetic form factor in the region 0 < Q 2 < 30 GeV 2 . As well, we present an empirical fit to the proton electromagnetic form factor ratio, GEp/GMp, which is valid in the region 0.1 < Q 2 < 6 GeV 2 .The elastic electromagnetic form factors are crucial to our understanding of the proton's internal structure. Indeed, the differential cross section for elastic ep → ep scattering is described completely in terms of the Dirac and Pauli form factors, F 1 and F 2 , respectively, based solely on fundamental symmetry arguments. Further, the Sachs form factors, G Ep and G Mp , which are simply derived from F 1 and F 2 , reflect the distributions of charge and magnetization current within the proton.Until recently, the form factors of the proton have been determined experimentally using the Rosenbluth separation method [3], in which one measures elastic ep cross sections at constant Q 2 , and varies both the beam energy and scattering angle to separate the electric and magnetic contributions. In terms of the Sachs form factors, the differential cross section for elastic ep scattering has traditionally been written as, θ e is the in-plane electron scattering angle. For elastic ep scattering, the so-called nonstructure cross section, σ ns is given bywhere α em is the electromagnetic coupling constant, and E ′ (E) is the energy of the scattered (incident) electron. From the measured differential cross section, one typically derives a "reduced cross section", defined according towhere ǫ = {1 + 2(1 + τ ) tan 2 (θ e /2)} −1 is a measure of the virtual photon polarization. Equation 3 is known as the Rosenbluth formula, and shows that fits to reduced cross section measurements made at constant Q 2 but varying ǫ values may be used to extract both form factors independently.With increasing Q 2 , the reduced cross sections are increasingly dominated by the magnetic term G Mp ; at Q 2 ≈ 3 GeV 2 , the electric term contributes only a few percent of the cross section. Furthermore, referring to the open data points in the left panel of Fig. 1, one can see that the various Rosenbluth separation data sets [4][5][6][7][8][9] for the ratio µ p G Ep /G Mp , where µ p = 2.79 is the magnetic moment of the proton, are not consistent with one another for Q 2 > 1 GeV 2 . It is clear that a tremendous effort has gone into the analysis of these difficult experiments, however, one is forced to speculate that some of the experiments have underestimated the systematic errors. For example, the Rosenbluth experiments apply radiative correcti...
Background: Nivolumab has a survival benefit for heavily pretreated patients with advanced or recurrent G/GEJ cancer. ATTRACTION-4 is a randomized, multicenter, phase 2/3 study to evaluate the efficacy and safety of nivolumab plus chemotherapy vs. chemotherapy as first-line treatment in patients with HER2-negative, advanced or recurrent G/GEJ cancer. Here we report the results of the double-blind phase III part.Methods: Patients were randomized 1:1 to receive nivolumab plus chemotherapy (N+C, S-1 plus oxaliplatin or capecitabine plus oxaliplatin) or placebo plus chemotherapy (C). Nivolumab or placebo was intravenously administered every 3 weeks until disease progression or unacceptable toxicity. Tumor assessment was performed every 6 weeks through week 54, then repeated every 12 weeks. The co-primary endpoints were centrally-assessed PFS and OS, and it was prespecified that the primary objective is deemed to be achieved if at least one of the null hypotheses of the primary endpoints is rejected.Results: A total of 724 Asian patients were randomized to N+C (n¼362) or C (n¼362) between Mar 7, 2017, and May 10, 2018. At the interim analysis primary for PFS with the median follow-up period of 11.6 mo, PFS was significantly improved in N+C vs. C (HR 0.68; 98.51% CI 0.51-0.90; p¼0.0007; median PFS, 10.5 vs. 8.3 mo), meeting the primary endpoint. At the final analysis primary for OS with the median follow-up period of 26.6 mo, there was no statistically significant difference (HR 0.90; 95% CI 0.75-1.08; p¼0.257; median OS, 17.5 vs. 17.2 mo), while PFS was continuously longer in N+C than in C. ORR was higher in N+C than in C (57.5 vs. 47.8%; p¼0.0088). The incidences of grade 3 to 5 treatment-related adverse events were 57.9% in N+C and 49.2% in C.Conclusions: PFS was significantly improved in N+C vs. C, achieving the primary objective. The combination of nivolumab and chemotherapy, which demonstrated clinically meaningful efficacy in PFS and ORR with a manageable safety profile but not statistically significant improvement in OS, can be considered a new first-line treatment option in advanced or recurrent G/GEJ cancer.
Stochastic analyses of groundwater flow and transport are frequently based on partial differential equations which have random coefficients or forcing terms. Analytical methods for solving these equations rely on restrictive assumptions which may not hold in some practical applications. Numerically oriented alternatives are computationally demanding and generally not able to deal with large three‐dimensional problems. In this paper we describe a hybrid solution approach which combines classical Fourier transform concepts with numerical solution techniques. Our approach is based on a nonstationary generalization of the spectral representation theorem commonly used in time series analysis. The generalized spectral representation is expressed in terms of an unknown transfer function which depends on space, time, and wave number. The transfer function is found by solving a linearized deterministic partial differential equation which has the same form as the original stochastic flow or transport equation. This approach can accomodate boundary conditions, spatially variable mean gradients, measurement conditioning, and other sources of nonstationarity which cannot be included in classical spectral methods. Here we introduce the nonstationary spectral method and show how it can be used to derive unconditional statistics of interest in groundwater flow and transport applications.
This paper describes a nonstationary spectral theory for analyzing flow in a heterogeneous porous medium with a systematic trend in log hydraulic conductivity. This theory relies on a linearization of the groundwater flow equation but does not require the stationarity assumptions used in classical spectral theories. The nonstationary theory is illustrated with a two‐dimensional analysis of a linear trend aligned with the mean flow direction. In this case, closed‐form solutions can be obtained for the effective hydraulic conductivity, head covariance, and log conductivity‐head cross covariance. The effective hydraulic conductivity decreases from the geometrical mean as the mean slope of the log conductivity increases. Trending leads to a reduction of head variance and a structural change in the head covariance and the log conductivity‐head cross covariance. Such changes have important implications for measurement conditioning (or cokriging) methods which rely on the head covariance and log conductivity‐head covariance. The nonstationary spectral analysis is also compared with classical spectral analysis. This comparison indicates that the classical spectral method correctly predicts the normalized head covariance in a linear trending media. The stationary spectral method fails to capture the qualitative influence of trends on the effective hydraulic conductivity and the log conductivity‐head cross covariance, although the magnitude of the error is relatively small for realistic values of the mean log conductivity slope. The stationary and nonstationary results are the same when there is no trend in log conductivity. The trending conductivity example illustrates that the nonstationary spectral method has all the capabilities of the classical spectral approach while not requiring as many restrictive assumptions.
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