A branch-and-bound method for the minimum k−enclosing ball problem

The minimum k-enclosing ball problem seeks the ball with smallest radius that contains at least k of m given points. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of k points to solve this problem. Our method is able to solve the problem exactly in a short amount of time for small and medium sized datasets.     

Fine Dry Grinding of Zeolite in a Laboratory Ball Mill

This paper presents the importance and usage of natural zeolites, which was recently recognized in the industry. Therefore, the grinding properties of natural zeolite were studied with the emphasis on a kinetic study in a ball mill. The experimental mill employed was laboratory sized, 200 mm diameter, 191 mm length, providing a total mill volume of 6000 cm³, with a total mass of 5.62 kg of steel balls of 25 mm diameter with a charge of 20% of the mill volume and with a rotation speed of 76 rpm. The breakage parameters were determined by using single sized feed fractions of ?850+600 μm, ?600+425 μm, and ?425+300 μm for the zeolite samples. The S_i (specific rate of breakage) and B_{i, j} (primary breakage distribution) values were obtained for those feed size fractions in order to predict the product size distributions by simulation for comparison to the experimental data. From the experimental results, S_i values increased as the feed sizes became coarser, i.e., the highest S_i value was 0.85 min^?1 for ?850+600 μm, while the lowest S_i value was 0.65 min^?1 for ?425+300 μm feed ground in the mill. The B_{i, j} values obtained for the zeolite sample were γ=0.84, ?=0.61, and β=4.25. The breakage parameters obtained showed that the zeolite is broken faster than quartz and slower than calcite and barite in terms of the a_T values reported previously at the same experimental conditions. The simulations of the product size distributions of zeolite were in good agreement with the experimental data using a standard ball mill simulation program. The slowing‐down effect was also seen in the mill after 4 min. of grinding.     

Measuring Light Field of Light Source with High Directional Resolution Using Mirrored Ball and Pinhole Camera

This paper presents a method of measuring a light field of a light source with high directional resolution using a mirrored ball and a pinhole camera. The light field describes a spatial and directional distribution of radiances from the light source. The directional distribution is expanded by a reflection on the mirrored ball, and the radiances are measured by a charge-coupled device (CCD) camera with a pinhole lens. The light source is laterally moved by a robot arm to measure the directionally expanded light field, and each pixel on a CCD can obtain the radiances from the light source through the pinhole lens with high directional resolution. The light field is estimated from the pixel value and the position of each pixel using a ray tracing technique. The light field of a krypton lamp was experimentally measured by the proposed method, and the accuracy of the measurement was evaluated against the irradiances measured by a spectro-radiometer at sample points.     

热连轧精轧机组温度模型的改进

从实际生产数据入手,研究了温度模型设定精度的现状及设定精度与各影响因素之间的关系,同时还消化了原来的温度模型程序并将其移植到微机上.经大量的离线统计回归分析,提出了一个行之有效的温度模型改进方案.该改进方案的思路同样适合其他热轧生产线.     

Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems

The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by ＂smooth＂ operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results.     

SQJ-Ⅰ型大型石球圆筒刀具对心加工设备的研制与应用

阐述了球面与圆筒刀具对心加工原理。介绍了应用该原理研制的SQJ—I型大型石球加工设备的结构特点、加工过程和性能特点。     

运动处方对三大球运动伤病的监测与分析

三大球运动是对抗性、竞争性、趣味性很浓的运动项目,在运动过程中,由于多种原因,会出现多样性伤病.本文就体育专业学生三大球运动伤病状况作调查统计分析,开设制定相应的运动处方,尽量减少或预防伤病的产生,以期更好地完成教学、训练任务.     

实空间上的闭子集与相似包含关系

Paul Frdos曾提出如下关于实直线R的问题：是否对R的每一个无限子集X，都存在一个具有正测度（Lebesgue测度）的闭子集E，使得E的任何子集都不相似于X（E的任何子集都不与X线性同胚）。1984年，Falconer证明了如下结论：对于一个满足limxn=0和linxn 1/xn＝1的单调递减的正实数列{xn}，Erdos问题有一个部分肯定的解答。本文将证明：上述关于数列的条件可以替换为更一般的（弱一些的）条件。最后把本文的相应结论推广到有限维欧氏空间R^n中。     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.