Minimum norm solution to the positive semidefinite linear complementarity problem

In this article, we present an algorithm to compute the minimum norm solution of the positive semidefinite linear complementarity problem. We show that its solution can be obtained using the alternative theorems and a convenient characterization of the solution set of a convex quadratic programming problem. This problem reduces to an unconstrained minimization problem with once differentiable convex objective function. We propose an extension of Newton's method for solving the unconstrained optimization problem. Computational results show that convergence to high accuracy often occurs in just a few iterations.     

G-凸空间的择一原理和极大极小不等式

Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.     

一个择一定理及对广义凸规划的应用

本文在实线性空间中得出了广义凸函数的择一定理 ,利用这一定理 ,我们获得广义凸规划的最优性条件     

Preliminary Evaluation of Supercritical Carbon Dioxide Extracted Dabai Pulp Oleoresin as a New Alternative Fat

There has been growing interest among food scientists in producing a toxin-free fat as an end product with varying physical or nutritional properties of interest to the food industry. Oleoresin is a rich source of bioactive compounds which consumers can easily add to a large variety of food. Dabai (Canarium odontophyllum) pulp oleoresin (DPL) was extracted using supercritical carbon dioxide (SC-CO₂) extraction, a green extraction technology. This study investigates the quality of SC-CO₂ extracted DPL in discovering its potential as a new alternative fat. The extraction experiment was carried out at a pressure of 40 MPa and a temperature of 40 °C. DPL is a saturated fatty acid (SFA)-rich fat due to its high SFA composition (47.72 ± 0.01%). In addition, the low content of peroxide value (PV) (5.60 ± 0.09 mEq/kg) and free fatty acids (FFA) (3.40 ± 0.03%) indicate the quality and stability of DPL for various applications besides food consumption. DPL also has a low slip melting point (SMP) (20.20 ± 0.03 °C), and HPLC-FID revealed that DPL contained 0.13 ± 0.02 mg/100 g of vitamin E (α-tocopherol), indicating its potential application as a solid fat with a bioactive compound. This present work demonstrates the possible prospect of DPL in the formulation of end products for food industries.     

集值映射向量最优化的最优性条件

本文在序线性拓扑空间中,证明了广义Y+一次似凸集值映射的一个择一性定理,利用此定理,我们得到集值映射向量最优化问题的最优性条件.     

Weighted Kaplan-Meier Tests for Umbrella Alternatives

The problem of testing for umbrella alternatives in a one-way layout with right-censored survival data is considered. Testing procedures based on the two-sample weighted Kaplan-Meier statistics suggested by Pepe and Fleming (1989, Biometrics, 45, 497–507; 1991, J. Roy. Statist. Soc. Ser. B, 53, 341–352) are suggested for both cases when the peak of the umbrella is known or unknown. The asymptotic relative efficiency of the weighted Kaplan-Meier test and the weighted logrank test proposed by Chen and Wolfe (2000, Statist. Sinica, 10, 595–612) is computed for the umbrella peak-known setting where the piecewise exponential survival distributions have the proportional or crossing hazards, or the related hazards differ at early or late times. Moreover, the results of a Monte Carlo study are presented to investigate the level and power performances of the umbrella tests. Finally, application of the proposed procedures to an appropriated data set is illustrated.     

About a Gap between Multiobjective Optimization and Scalar Optimization

We explain the reason for the existence of a gap between multiobjective and scalar optimization proposed in Ref. 1, giving a characterization of this gap.     

Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions

A new class of generalized convex set-valued functions, termed nearly-subconvexlike functions, is introduced. This class is a generalization of cone-subconvexlike maps, nearly-convexlike set-valued functions, and preinvex set-valued functions. Properties for the nearly-subconvexlike functions are derived and a theorem of the alternative is proved. A Lagrangian multiplier theorem is established and two scalarization theorems are obtained for vector optimization.     

一类交错级数的收敛定理

讨论和分析了一类交错级数的收敛问题,给出了异于莱布尼兹判别法的关于交错级数的一个收敛定理.我们的结论还推广了正项级数的拉阿伯判别法的使用范围.     

化学学习中记忆的7种缺陷

记忆是学生进行其他认知活动的基础,因记忆容量以及保持时间等限制具有一些缺陷,表现为分心、暗示、健忘、纠缠、空白、错认、偏颇等7种类型。记忆缺陷影响着学生的化学学习,了解化学学习中学生记忆的7种缺陷,可以精准地把握学生化学学习产生困难的原因,并采取一定的教学方法改进教学。