Degenerate complex Hessian equations on compact K\"ahler manifolds

Let $(X,\omega)$ be a compact K\"ahler manifold of dimension $n$ and fix $m\in \mathbb{N}$ such that $1\leq m \leq n$. We prove that any $(\omega,m)$-sh function can be approximated from above by smooth $(\omega,m)$-sh functions. A potential theory for the complex Hessian equation is also developed which generalizes the classical pluripotential theory on compact K\"ahler manifolds. We then use novel variational tools due to Berman, Boucksom, Guedj and Zeriahi to study degenerate complex Hessian equations

Effects of using Water Hyacinth (Eichhornia crassipes L.) in the Diet of Swamp Buffaloes on Nutrient Digestibility, Rumen Environment, Purine Derivatives, and Nitrogen Retention

The present experiment aims to evaluate the effects of incremental levels of water hyacinth (WH) in Para grass (Brachiaria mutica) based on the diet on nutrient intake, digestibility, and nitrogen retention of growing swamp buffaloes. Four male buffaloes of 305 ± 8.40 kg were allocated in a 4x4 Latin square design. The treatments were 25, 50, 75, and 100% WH (DM basis), replacing the Para grass (PG) corresponding to WH25, WH50, WH75, and WH100 treatment. Urea-molasses cake was used to supply the dietary crude protein intake so that this was 210 g/100 kg live weight per day for all the treatments (DM basis). The results showed that although the dry matter (DM), neutral detergent fiber (NDF), and metabolizable energy (ME) intake were not significantly different (P>0.05) among the treatments, these were numerically higher for the WH50 treatment. Especially in the daily ME intake (MJ/k g LW) was 39.1, 43.4, 41.7, and 39.9 for the WH25, WH50, WH75, and WH100 treatments, respectively. With 50% WH replacing PG in the diet, it gave potential for better nutrient digestibility, nitrogen retention, and daily weight gain in the present study. In conclusion, WH could be used to replace PG in buffalo diet up to 100%. At a level of 50% replacement of WH to PG in the buffalo, the diet was optimum based on the utilization of nutrients and energy of WH, lower feed cost, and environmental improvement

A multi-criteria decision-making in relieving grinding process of surface of gear milling tooth based on the archimedean spiral using taguchi-ahp-topsis method

In this study, in order to optimize the quality criteria of the machined surface based on the Archimedean spiral, the relieving grinding process (RGP) was performed to machine the material of HSS P18 in a 1Б811 machine with four input parameters including graininess of grinding wheel (G), grinding wheel hardness (Hd), velocity of grinding wheel (V), and feed rate (s) and with three quality criteria including surface roughness (Ra), hardening of surface layer (∆HRC), and hardened layer thickness (∆L). Taguchi-AHP-Topsis method was successfully applied to solve the Multi-Criteria Decision Making (MCDM) problem in this case. The optimized results of the output parameters are surface roughness of 0.21 µm, surface hardening of 1.45 HRC, and hardened layer thickness of 34.18 µm. These results were determined at the set of the input parameters includes G, V, s with their values of 120, 24 m/s, 2.08 m/min, respectively, and Hd at level 1. The optimal results were verified through the comparison between the calculated and the experimental results using this set of optimal parameters. The differences between the calculated results and the experimental results were quite small (maximum different value was 4.8 %) Thus, the results of this study can be applied to solve the multi-objective optimization problems in RGP of the GMT surface based on the Archimedean spira