No abstract

No abstract

We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas’ multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, we observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension D. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as ∼ 100. We observe that our algorithm also works well for settings without a UT basis.

The thermal stability of multilayer films has been studied by use of small-angle x-ray diffraction. The temperatures at which the periodicities of Pt/Si, W/Si, Mo/Si, and W/C multilayers begin to be worse are 200, 300, 400, 900 °C, respectively. The temperatures of total mixing of Pt/Si, W/Si, Mo/Si, and W/C are 600, 600, 700, and >900 °C, respectively. The periods of Mo/Si and W/Si decrease about 5%, 10%, respectively, after annealing at 400 °C for 0.5 h. The period of W/C increases continuously with the increasing temperatures. After annealing at 1000 °C for 0.5 h the increment of the period of W/C is about 20%. The former may be mainly due to the interfacial reaction between metal and Si and the latter may be due to the expansion of C films in W/C.

The crystallization behavior of a-Si:H/Ag/a-Si:H sandwich films has been studied in detail. Fractals of Si caused by metal enhanced crystallization appear after annealing at 350–600 °C. The fractal dimension decreases (the Si fractals become more open) with the increasing annealing temperature. The number density of fractals increases at 350–450 °C and turns to decrease at 500–600 °C. The average fractal size increases from 350 to 550 °C and shows a decreasing tendency at 600 °C. The formation of fractals can be explained by a random successive nucleation and growth model. The x-ray energy dispersive spectroscopy (EDS) microanalysis indicates that although there is lateral interdiffusion of Ag and Si atoms, the thicknesses of the fractal region and the matrix remain nearly the same. At the same time, EDS shows that there are also Ag aggregates extending out of the films. It is suggested that besides the preferred nucleation at the Ag/Si interface the break of Si—H bonds may also stimulate the crystallization of a-Si:H so that the crystallization temperature of an a-Si:H/Ag system is much lower than that of an a-Si/Ag system.

Soybean is an important cash crop in the world, and drought is the main reason for the loss of soybean plants productivity, with drought stress during the most water-sensitive flowering period of soybeans. In this article, drought-tolerant variety Heinong 44 (HN44) and drought-sensitive variety Heinong 65 (HN65) were used as experimental materials. Drought treatment was carried out at the early flowering stage. The method of controlling soil moisture content was used to simulate different degrees of drought, and the physiological changes of these two varieties of soybean under different soil moisture contents were studied. The results showed that with a decrease in soil moisture content, the content of malondialdehyde (MDA) in soybean leaves increased significantly; the activities of peroxidase (POD), catalase (CAT), and ascorbic acid peroxidase (APX) increased first and then decreased; the content of proline, soluble sugar, and soluble protein increased; and the total antioxidant capacity (T-AOC) increased significantly. When the soil moisture content was 15.5%, the degree of membrane lipid peroxidation, osmotic regulatory substances, antioxidant enzyme activity, and T-AOC increased the most, and the decrease in drought-tolerant variety HN44 was significantly less than that of drought-sensitive variety HN65. Our research reveals the response law of soybean crops to physiological characteristics under water deficit and provides theoretical basis and guiding significance for drought-resistant cultivation and breeding of soybean.

Cross-sectional transmission electron microscopy, selected area electron diffraction, and small-angle x-ray diffraction have been used to observe the systematic deviations of period in W/Si and W/C multilayers. The mean periods decreased gradually as the detected regions were located farther away from the substrate. To avoid destroying the multilayer, a method is suggested to measure the systematic deviation of period by using soft x rays with wavelengths below and above an absorption edge and hard x rays such as Cu Kα1.

Dynamical optical dispersion theory is employed to analyze the variations of the positions and intensities of x-ray diffraction peaks from the W/C multilayer. It is confirmed that the thickness of the C layer expands with the annealing temperature and the multilayer remains undamaged until 800 °C. There is an obvious drop of interfacial root mean square (rms) roughness at 600–800 °C.