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.     

截断调和Bergman空间上Toeplitz算子的代数性质

本文首先讨论调截断和Bergman空间 $b_{n}^{2}$ 上拟齐次函数为符号的Toeplitz算子的有限秩乘积问题,其次考察两个以拟齐次函数为符号的Toeplitz算子的换位子与半换位子的有限秩问题.     

截断调和Bergman空间上的Toeplitz算子

截断调和Bergman空间b_n~2=L_a~2{w,w~2,…,w~n}~v是Hilbert空间L~2的闭子空间.研究了单位圆盘上的截断调和Bergman空间上的Toeplitz算子的乘积问题,完整地刻画了具有有界调和符号的两个Toeplitz算子的有限秩与紧的半换位子或换位子.     

High order shear horizontal modes for minimum remnant thickness

Thickness mapping in aging structures suffering from corrosion is challenging especially when the structure is only partially accessible. In plates the high order shear horizontal guided wave modes all have a cutoff frequency thickness product below which they cannot propagate. This property is potentially attractive to estimate the minimum remnant thickness between two transducers. When using a source and a sensor array it is possible to control the number of modes being excited and the size of the region interrogated by the technique. Finite element simulations were used to show that by exciting multiple guided wave modes simultaneously and identifying which modes are received by a sensor array it is possible to estimate the minimum remaining thickness along the propagation path. Initial experimental results showed excellent agreement with the finite element simulations when the plate is uniform and with a thickness reduction between the source and the sensor arrays the minimum remnant thickness was underestimated by approximately 20%.     

An electrostatic model of the cutoff probe

Although a circuit model of the previously developed cutoff probe for plasma diagnostics elucidates the basic physics and contributes to the development of the cutoff probe, a theoretical validation of the circuit model has yet to be accomplished. For theoretical validation, this paper proposes a one-dimensional electrostatic model, or 1dESM, of the cutoff probe, which is based on electrostatic field analysis in a finite two-wire approximation. The transmission spectrum S₂₁ calculated by the 1dESM shows a good agreement with that from a three-dimensional full electromagnetic wave simulation for various electron densities and pressures. Based on the 1dESM, the formation mechanism of the S₂₁ of the cutoff probe was analyzed. Theoretical validation of the circuit model was then achieved by comparing the circuit model with the 1dESM. This paper is believed to contribute to a better understanding of the cutoff probe and to the development of cutoff probe models.     

十三陵蓄能电站下库河床粘土层渗透特征及其成因模式研究

为解决十三陵抽水蓄能电站下库库尾渗漏问题, 拟在库尾半壁山附近做一防渗墙。由于河床覆盖层内存在着一厚约20m的粘性土层, 如做一悬挂式防渗墙, 把粘性土层做为防渗墙下界, 可比以下部基岩做为下界节约资金约三分之二以上。本文在以往勘探资料的基础上, 通过钻孔、物探、水文地质特征等方面的资料, 分析论证了粘土层在库盆内的连续性, 然后给出了十三陵盆地粘土层的成因及分布模式。     

Nonlinear stability of boundary layers for the Boltzmann equation with cutoff soft potentials

The study on the boundary layer is important in both mathematics and physics. This paper considers the nonlinear stability of boundary layer solutions for the Boltzmann equation with cutoff soft potentials when the Mach number of the far field is less than −1. Unlike the collision frequency is strictly positive in the hard potential or hard sphere model, the collision frequency has no positive lower bound for the cutoff soft potentials, so the decay in time cannot be expected. Instead, the present paper proves that the solution will always be in a small region around the boundary layer by noticing the decay property of collision operator in velocity.     

Development and application of consumer credit scoring models using profit-based classification measures

This paper presents a new approach for consumer credit scoring, by tailoring a profit-based classification performance measure to credit risk modeling. This performance measure takes into account the expected profits and losses of credit granting and thereby better aligns the model developers’ objectives with those of the lending company. It is based on the Expected Maximum Profit (EMP) measure and is used to find a trade-off between the expected losses – driven by the exposure of the loan and the loss given default – and the operational income given by the loan. Additionally, one of the major advantages of using the proposed measure is that it permits to calculate the optimal cutoff value, which is necessary for model implementation. To test the proposed approach, we use a dataset of loans granted by a government institution, and benchmarked the accuracy and monetary gain of using EMP, accuracy, and the area under the ROC curve as measures for selecting model parameters, and for determining the respective cutoff values. The results show that our proposed profit-based classification measure outperforms the alternative approaches in terms of both accuracy and monetary value in the test set, and that it facilitates model deployment.