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In this paper, we derive general monotone quantities and geometric inequalities associated with $p$-capacitary functions in asymptotically flat $3$-manifolds with simple topology and nonnegative scalar curvature. The inequalities become equalities on the spatial Schwarzschild manifolds outside rotationally symmetric spheres. This generalizes Miao's result \cite{M} from $p=2$ to $p\in (1, 3)$. As applications, we recover mass-to-$p$-capacity and $p$-capacity-to-area inequalities due to Bray-Miao \cite{BM} and Xiao \cite{Xiao}., 30 pages. Any comments are welcome!

Supplementary Material 2

The plant-based refers to plant-based raw materials or products that are available as the source of protein and fat. Utilization and development of walnuts as a plant-based, resulting in a high-quality protein-rich walnut plant-based product: walnut protein powder and walnut peptides. Progress in research on the application of walnuts as a plant-based has been advanced, solving the problem of wasted resources and environmental pollution caused by the fact that walnut residue, a product of walnuts after oil extraction, is often thrown away as waste, or becomes animal feed or compost. This paper reviews and summarizes the research and reports on walnut plant-based at home and abroad, focusing on the application of walnut plant-based in the preparation process (enzymatic and fermentation methods) and the biological activity of the walnut protein and walnut peptide, to provide a theoretical basis for the further processing of walnuts as a walnut plant-based. It can make full use of walnut resources and play its nutritional and health care value, develop and build a series of walnut plant-based products, improve the competitiveness of walnut peptide products, turn them into treasure, and provide more powerful guidance for the development of food and medicine health industry in Yunnan.

Additional file 1.

This study was conducted to determine the DE, ME, and apparent (AID) and standardized ileal digestibility (SID) of AA in different wheat cultivars fed to growing pigs. In Exp. 1, twelve crossbred growing barrows were allotted to a replicated 6 × 6 Latin square design to determine the DE and ME contents of 12 different wheat cultivars. In Exp. 2, twelve growing barrows with a simple T-cannula were used to determine the AID and SID of AA in 10 different wheat cultivars. Pigs were randomly allotted to a replicated 6 × 6 Latin square design and fed one nitrogen-free diet and 10 different cultivars of wheat diets. Among different wheat cultivars, the concentrations of GE, CP, NDF, ADF, and starch ranged from 4,385 to 4,458 kcal/kg, 12.95% to 18.14%, 9.16% to 13.89%, 1.93% to 2.92% and 60.81% to 70.77%, respectively (DM basis). There were significant differences (P < 0.05) in the DE, ME values, and the ATTD of GE in 12 different cultivars of wheat in Exp. 1. The DE and ME contents and the ATTD of GE ranged (P < 0.05) from 3,922 to 4,067 kcal/kg DM, 3,759 to 3,941 kcal/kg DM and 88.14% to 90.31%, respectively. The best prediction equations of DE and ME for different cultivars of wheat cultivars were DE = −2,738 – (40.8 × % ADF) + (1.7 × GE) – (51.5 × % Xylans) – (95.7 × % Ash) + (22.3 × % EE), R(2) = 0.98, and ME = −2,990 + (1.7 × GE) – (50.2 × % Xylans) – (87.6 × % Ash), R(2) = 0.88, respectively. There were also differences (P < 0.05) in the AID and SID of CP and indispensable AA, expect for His, in 10 wheat cultivars in Exp. 2. The AID and SID of CP, Lys, and Met ranged (P < 0.05) from 82.02% to 89.46%, 74.13% to 84.73%, 87.35% to 92.49% and 87.56% to 94.04%, 80.56% to 89.89%, 89.56% to 94.45%, respectively. In conclusion, the chemical composition, energy contents, and most AA digestibility in different cultivars of wheat varied widely.

In this article, a design of bipolar nonsalient pole (BNSP) transmitter, which originates from motor theory, for high-power EV dynamic wireless power transfer (DWPT) system is proposed. To analyze and evaluate BNSP transmitter in aspect of principle, characteristic, and performance, the existing I-type, S-type, and N-type transmitters in DWPT application are classified as bipolar salient pole (BSP) transmitter, which establishes a reference for comparing. The design parameters and other contrast conditions of BNSP and BSP transmitters are given. Coupling flux and leakage flux of BNSP transmitter are analyzed by comparing the magnetic models and the finite-element models of BNSP and BSP transmitters. Based on the modular design in practical application, the sensitivity of coupling performance to the module gap in BNSP and BSP transmitters is analyzed and compared in simulation. All theoretical results are verified by contrast experiments. The maximum effective mutual inductance of BNSP transmitter is about 31.0% larger than that of BSP transmitter, and the efficiency of the system with output power of 10 kW is 93.5% with BNSP transmitter, about 2.4% higher than that with BSP transmitter. Besides, BNSP transmitter needs 5.9% shorter Litz wire and 53.1% smaller volume of cores, which makes it smaller in size.