Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

What is the optimal cutoff surface for ore bodies with more than one mineral?

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in n dimensions it is a hyperplane.     

The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.     

Cyberbullying: Effect of emergency perception on the helping tendencies of bystanders

The effect of the emergency perception of bystanders of cyberbullying victims on helping behaviors is often neglected in research on cyberbullying. In this study, we explored the influence of this cognitive factor on cyber-bystanders’ helping tendencies as well as elucidated possible underlying processes. The results of two studies were reported. In Study 1, 150 undergraduates read a true case of a girl experiencing cyberbullying. The results indicated that when the participants perceived the victim’s situation to be more critical (i.e., higher emergency perception), their helping tendencies were stronger, partly through increased state empathy followed by feelings of responsibility to help. In Study 2, we randomly assigned 300 undergraduates to two groups. The low emergency group read the same cyberbullying case as Study 1, whereas the cyberbullying case read by the high emergency group contained additional emergency information of the victim. The results indicated that the high emergency group expressed stronger helping tendencies than did the low emergency group. This effect was caused by a stronger perception that the victim was in an emergency situation, which not only strengthened the participants’ helping tendencies directly but also indirectly through increasing their state empathy and feelings of responsibility to help.     

Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

Determinants of the intention to use non-medical insertable digital devices: The case of Chile and Colombia

In the past, thinking of carrying electronic devices inside our bodies was only posed by non-real scenarios. The emergence of insertable devices has changed this. Since this technology is still in its initial development stages, few studies have investigated factors that influence its acceptance. This paper analyzes the predictors of the intention to use non-medical insertable devices in two Latin American contexts. We used partial least squares structural equation modeling to examine whether six constructs predicted intention to use insertable devices. A questionnaire was administered to undergraduate students located in Colombia and Chile (n = 672). We also examined whether these predictors influenced intention differently for both of them. Four common constructs significantly and positively influenced both Chilean and Colombian respondents to use insertable devices (hedonic motivation, habit, performance expectancy, and social influence). Also, the habit has a complementary mediating effect on the relationship between social influence and behavioral intention. By contrast, effort expectations were a positive and significant predictor, but only among Chilean respondents. Findings suggest that when technologies are emerging, well-known predictors of intention (e.g., performance and effort expectations) are less influential than predictors related to self-efficacy (e.g., habit and hedonic motivation). The use of insertable devices has a significant impact on society. Thus, a better understanding of what motivates their use has implications for both academia and industry.     

Dark Energy with Phantom Crossing and the H0 Tension

We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (H0), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint H0=71.0−3.8+2.9 km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtained the constraint H0=70.25±0.78 km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor am=0.851−0.031+0.048 at a 68% confidence level.     

基于GA_XGBoost模型的大学生科研能力预测问题研究

科学评价大学生科研创新能力对我国科研水平的提高具有重要意义.采用机器学习模型来预测大学生科研能力可以起到良好的效果,提出一种GAXGBoost模型来实现对大学生的科研能力预测.此模型是以Xgboost算法为基础,然后充分利用遗传算法的全局搜索能力自动搜索Xgboost最优超参数,避免了人为经验调参不准确的缺陷,最后采用精英选择策略以此确保每一轮都是最佳的进化结果.通过分析表明,所采用的GAXGBoost模型在大学生科研能力预测的结果中具有很高的精度,将此模型与Logistic Regression、Random Forest、SVM等模型进行对比,GAXGBoost模型的预测精度最高.