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.     

An efficient edge based data structure for the compressible Reynolds-averaged Navier–Stokes equations on hybrid unstructured meshes

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.     

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.     

Ultrahigh Loading Copper Single Atom Catalyst for Palladium-free Wacker Oxidation

Wacker oxidation is an industry-adopted process to transform olefins into value-added epoxides and carbonyls. However, traditional Wacker oxidation involves the use of homogeneous palladium and copper catalysts for the olefin addition and reductive elimination. Here, we demonstrated an ultrahigh loading Cu single atom catalyst(14% Cu, mass fraction) for the palladium-free Wacker oxidation of 4-vinylanisole into the corresponding ketone with N-methylhydroxylamine hydrochloride as an additive under mild conditions. Mechanistic studies by ¹⁸O and deuterium isotope labelling revealed a hydrogen shift mechanism in this palladium-free process using N-methylhydroxylamine hydrochloride as the oxygen source. The reaction scope can be further extended to Kucherov oxidation. Our study paves the way to replace noble metal catalysts in the traditional homogeneous processes with single atom catalysts.     

Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.