Invariant fibrations for some birational maps of ℂ2

Abstract

In this article, we extract and study the zero entropy subfamilies of a certain family of birational maps of the plane. We find these zero entropy mappings and give the invariant fibrations associated to them.     

Enthalpically and Entropically Favorable Self-Assembly: Synthesis of C4h-Symmetric Tetraazatetrathia[8]circulenes by Regioselective Introduction of Pyridine Rings

Self-assembly of π-conjugated molecules in solution generally occurs owing to either an enthalpic or an entropic gain; however, designing π-conjugated systems that simultaneously exhibit enthalpically and entropically favorable self-assembly behavior is challenging. Herein, the self-assembly behavior of tetraazatetrathia[8]circulenes is disclosed, which is driven by both enthalpy and entropy. Single-crystal X-ray diffraction analysis demonstrated that molecules of these tetraazatetrathia[8]circulenes form face-to-face stacked dimers with a 1D columnar structure owing to the circularly arranged dipole moments. Importantly, concentration- and temperature-dependent ¹H NMR spectra revealed that the formation of self-assemblies of tetraazatetrathia[8]circulenes in chloroform and methanol is favored by both enthalpic and entropic factors. The unique association behavior is due to the presence of sp²-hybridized nitrogen atoms, which weakly coordinate to the hydrogen atoms of these solvents and reduce the π-electron density of the circulene cores.     

A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment

The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method.     

Phase-controlled atom-photon entanglement in a three-level Λ-type closed-loop atomic system

We study the entanglement of dressed atom and its spontaneous emission in a three-level Λ-type closed-loop atomic system in a multi-photon resonance condition and beyond it.It is shown that the von Neumann entropy in such a system is phase-dependent,and it can be controlled by either the intensity or relative phase of applied fields.It is demonstrated that for the special case of the Rabi frequency of applied fields,the system is disentangled.In addition,we take into account the effect of Doppler broadening on the entanglement and it is found that a suitable choice of laser propagation direction allows us to obtain the steady state degree of entanglement(DEM) even in the presence of the Doppler effect.     

A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.     

基于模糊神经元PID算法的注塑机注射速度控制算法研究

基于一款市场较为畅销的注塑机, 设计出一种能精确控制注射速度的模糊神经元PID控制器. 首先, 设计出具有自学能力的神经元PID控制器, 利用模糊算法对其进行优化; 其次, 在原有注射速度线性数学模型的基础上, 构建注塑机注射速度的非线性模型; 最后, 利用MATLAB在所建数学模型的基础上对模糊神经元PID控制器进行仿真实验. 实验结果表明, 所设计控制器具有响应迅速、无超调量、控制精度高、控制稳定等优点.     

突出矿井瓦斯抽放限制影响因素的AHP-熵权法评价模型

为提高煤与瓦斯突出矿井瓦斯抽放效果,建立了3个一级指标、14个二级指标的突出矿井瓦斯抽放限制影响因素评价指标体系,利用AHP和熵权法分别确定指标因子主、客观权重.通过实地调研分析和反馈验证了AHP-熵权法的可行性和正确性,利用加权平均法确定评价模型的综合权重.研究表明:封孔方式、钻孔半径、抽放时间、煤体裂隙发育程度和抽放负压是目前影响煤矿瓦斯抽放效果的主控因素.     

基于模糊综合评判的大学数学考核方式改革

独立高校数学课程的开设旨在让学生掌握数学知识的基础上,提高数学应用能力.然而现行的考核方式存在重考试结果,轻学习过程等问题.从传统考核方式入手,指出其不足之处,基于模糊综合评判法建立新型评价体系和数学模型,通过试点运行验证了新的考核方式的可行性、客观性、合理性和科学性.     

缩短单点作业时间影响因素的排序研究

提出国家电网公司在实施设备的检修作业时尽量减少停电时间,以实现电缆线路状态的有效监控的重要意义.分析缩短单点作业时间的末端影响因素.提出三角模糊集、指数模糊集用于权重设置的具体途径,应用OWA算子于因素排序评价数值的加权,并拓展其基本原理和方法,使其对极端评分值有所抑制对中间评分值有所提升.以上海市电力公司检修公司为研究背景,应用直觉模糊集及其IFHA集成方法于缩短单点作业时间的末端影响因素评价指标排序,并得出u_≥u_≥u_1u_4u_6≥u_2u_3的结论.