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

The correlation between learning styles and self–directed learning of fifth graders

Vietnam education has been directed into a learner-centered approach and fostering competencies for students, especially self-directed learning. Thus, understanding how students’ learning styles impact self-directed learning are crucial for the new direction of Vietnam education. This research employed the survey method by questionnaire and presents the results of practical research on the correlation between styles of learning and self–directed learning of fifth-grade students at elementary schools in District 10, Ho Chi Minh City, Vietnam. The sample was 364 fifth graders voluntarily participating in the survey with the consent of parents. The results indicated that learning styles are strongly correlated with self–directed learning competency of fifth graders. The data revealed that students at District 10 not only attained high self-directed learning levels but also their learning styles attributing impactfully on their self-directed learning competency

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

Estimation of forest Carbon Stocks in Ba Be National Park, Bac Kan province, Vietnam

Climate change and an increase in the greenhouse effect are a matter of global concern. One of reasons for this phenomenon is the increase in greenhouse gases, especially CO2. Therefore, the authors investigated CO2 absorption from forests of 45 plots in Ba Be National Park, characterized by 3 forest states as rich, medium and poor forest, rehabilitated forest after exploitation to estimate carbon sequestration of the forest. In which, the carbon stock of rich forest reaches 273.17 tones/ha, the medium forest is 136.23 tones/ha and the poor forest, rehabilitated forest is 42.06 tones/ha. With a forest growth rate of 1.8% per year, the carbon sequestration in Ba Be National Park for 3 forest states is about 16,499 tones per year. This will contribute to improve environmental quality, reducing greenhouse gas emissions and creating a scientific basis for managers to develop a payment mechanism of forest carbon sequestration services

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