A new two‐phase structure‐preserving doubling algorithm for critically singular M‐matrix algebraic Riccati equations

Among numerous iterative methods for solving the minimal nonnegative solution of an M‐matrix algebraic Riccati equation, the structure‐preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1/2. In this paper, we first undertake a delineatory convergence analysis that reveals that the approximations by SDA can be decomposed into two components: the stable component that converges quadratically and the rank‐one component that converges linearly with the linear rate 1/2. Our analysis also shows that as soon as the stable component is fully converged, the rank‐one component can be accurately recovered. We then propose an efficient hybrid method, called the two‐phase SDA, for which the SDA iteration is stopped as soon as it is determined that the stable component is fully converged. Therefore, this two‐phase SDA saves those SDA iterative steps that previously have to have for the rank‐one component to be computed accurately, and thus essentially, it can be regarded as a quadratically convergent method. Numerical results confirm our analysis and demonstrate the efficiency of the new two‐phase SDA. Copyright © 2015 John Wiley & Sons, Ltd.     

A nonconvex approach to low‐rank matrix completion using convex optimization

This paper deals with the problem of recovering an unknown low‐rank matrix from a sampling of its entries. For its solution, we consider a nonconvex approach based on the minimization of a nonconvex functional that is the sum of a convex fidelity term and a nonconvex, nonsmooth relaxation of the rank function. We show that by a suitable choice of this nonconvex penalty, it is possible, under mild assumptions, to use also in this matrix setting the iterative forward–backward splitting method. Specifically, we propose the use of certain parameter dependent nonconvex penalties that with a good choice of the parameter value allow us to solve in the backward step a convex minimization problem, and we exploit this result to prove the convergence of the iterative forward–backward splitting algorithm. Based on the theoretical results, we develop for the solution of the matrix completion problem the efficient iterative improved matrix completion forward–backward algorithm, which exhibits lower computing times and improved recovery performance when compared with the best state‐of‐the‐art algorithms for matrix completion. Copyright © 2016 John Wiley & Sons, Ltd.     

问题式教学和案例教学在普通化学教学中的综合应用——自发热贴发热原理中的基础化学

In this article, the topic of "chemical principles in warmer pad" is used as an example to illustrate how problem-based learning (PBL) and case learning (CL) are used in the teaching of general chemistry. We take the advantages of PBL to arouse the studying interests of students in the casing learning atmosphere. Moreover, the teacher leads the discussion. By using these two teaching methods properly, students' active learning ability, the skills of analyzing and solving problems, as well as the comprehensive practical ability can be improved.     

Periodic solutions of nonlinear functional difference equations at nonresonance case

Sufficient conditions for the existence of at least one T-periodic solution of nonlinear functional difference equation

Δx(n)+a(n)x(n)=f(n,u(n)),     

Economic Cycles of Carnot Type

Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The first aim of this paper is to introduce and study the economic Carnot cycles concerning Roegenian economics, using our thermodynamic–economic dictionary. These cycles are described in both a Q−P diagram and a E−I diagram. An economic Carnot cycle has a maximum efficiency for a reversible economic “engine”. Three problems together with their solutions clarify the meaning of the economic Carnot cycle, in our context. Then we transform the ideal gas theory into the ideal income theory. The second aim is to analyze the economic Van der Waals equation, showing that the diffeomorphic-invariant information about the Van der Waals surface can be obtained by examining a cuspidal potential.     

Approximate counting via random optimization

Let ℱ_n be a family of subsets of {1,…,n}. We propose a simple randomized algorithm to estimate the cardinality of ℱ_n from the maximum weight of a subset X∈ℱ_n in a random weighting of {1,…,n}. The examples include enumeration of perfect matchings in graphs, bases in matroids, and Hamiltonian cycles in graphs. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 187–198 (1997)     

中美无机化学课程比较与探讨*——以美国康奈尔大学与河北工业大学无机化学课程为例

以河北工业大学和美国康奈尔大学的无机化学课程为例,从教材设置、教学方法和课程考核评价方式等方面对该课程教学进行了对比探讨,以期构建一套符合我国国情且具有国际视野的无机化学新的课程体系,能为国内高校本科无机化学课程的教学改革提供参考,提高其教育教学质量,促进本科人才培养。     

冻融循环作用下再生混凝土砖砌体通缝受剪试验研究

本文报导了对冻融循环作用下96个再生混凝土砖砌体抗剪试件进行的沿通缝抗剪试验。研究涉及冻融循环对再生混凝土砖砌体抗剪力学性能的影响,对比分析不同胶结材料试件的破坏形态及其抗剪强度,揭示冻融损伤对再生混凝土砖砌体抗剪强度的影响规律,并从微观角度探讨砂浆孔隙变化对砖砌体抗剪承载力的影响,建立再生混凝土砖砌体抗剪强度冻融损伤衰减模型。结果表明:砖砌体抗剪强度受冻融环境影响非常明显,其抗剪强度随冻融循环次数的增加而降低,降低的速度呈现出先慢后快的趋势;粉煤灰的加入有助于改善冻融环境下砖砌体的抗剪能力;对于石灰砂浆抗剪试件,初期的抗剪能力及冻融后的抗剪能力均下降;建立了考虑冻融损伤影响的砖砌体抗剪强度衰减模型,试验数据与计算结果吻合较好。     

An Evaluation of Primer Preseating in Small Caliber Cartridge Production

This work presents the findings of a study to quantify the relative effectiveness of the primer preseating operation in small caliber cartridge production. In theory, primer preseating would enable cartridge stamping tools to achieve deeper stamping penetration depths and subsequently, greater primer retention forces. This is because, with preseating incorporated in the existing small caliber cartridge production process, a cartridge stamping tool would be fully dedicated to performing the case stamping operation (rather than the simultaneous primer seating and case stamping operations it currently performs). The findings presented in this work include measured percentages of total stamping tool force dedicated to primer seating, stamping tool penetration depths with and without primer preseating and primer retention forces with and without primer preseating. These findings and their underlying principles were produced through a static force equilibrium analysis and finite element modeling and simulation studies.