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 $d^{⁎}\in \{5,6,7\}$.     

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.     

2.3–21 GHz broadband and high linearity distributed low noise amplifier

This paper focuses on the design of a 2.3–21 GHz Distributed Low Noise Amplifier (LNA) with low noise figure (NF), high gain (S₂₁), and high linearity (IIP3) for broadband applications. This distributed amplifier (DA) includes S/C/X/Ku/K-band, which makes it very suitable for heterodyne receivers. The proposed DA uses a 0.18 μm GaAs pHEMT process (OMMIC ED02AH) in cascade architecture with lines adaptation and equalization of phase velocity techniques, to absorb their parasitic capacitances into the gate and drain transmission lines in order to achieve wide bandwidth and to enhance gain and linearity. The proposed broadband DA achieved an excellent gain in the flatness of 13.5 ± 0.2 dB, a low noise figure of 3.44 ± 1.12 dB, and a small group delay variation of ±19.721 ps over the range of 2.3–21 GHz. The input and output reflection coefficients S₁₁ and S₂₂ are less than −10 dB. The input compression point (P_1dB) and input third-order intercept point (IIP3) are −1.5 dBm and 11.5 dBm, respectively at 13 GHz. The dissipated power is 282 mW and the core layout size is 2.2 × 0.8 mm².