复合振冲碎石桩加固机理及施工过程数值模拟

采用振动荷载作用下超孔隙水压力产生的能量模型,考虑耗散能量和孔径扩张的影响及相互作用,并进行合理的简化,对复合振冲碎石桩施工过程做了数值模拟。采用有限差分离散求解复合振冲碎石桩边值问题,编制相应的数值程序,基于模拟结果详细讨论了排水井的存在对复合振冲碎石桩孔隙水压力发展变化的影响。最后对普通碎石桩和复合碎石桩的地基加固效果进行对比分析。数值模拟结果表明,复合振冲碎石桩由于排水井的存在,使地基加固范围明显增大,并且可以应用于渗透系数较小的粉土和砂质粉土地基中。     

非均质地基弹性薄板分析的Green函数法

本文对非均质地基弹性薄板的静力、自由振动和动态响应进行了详细的研究。在静力和动力分析中统一应用薄板静力弯曲的奇性控制方程的基本解作为其 Green 函数,避免应用复杂的动力问题基本解,使动力分析大为简化。本方法是一种特殊的边界元法。它不须计算奇异积分,能分析具有任意边界形状和任意边界条件的非均质地基弹性薄板,还能方便地分析单点或多点支承板以及连续板。算例表明本方法兼具计算量小而精度高等优点。     

Complete Hamiltonian Description of Wave-Like Features in Classical and Quantum Physics

The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system describing in terms of ray trajectories, for a stationary refractive medium, a very wide family of wave-like phenomena (including diffraction and interference) going much beyond the limits of the geometrical optics (“eikonal”) approximation, which is contained as a simple limiting case. Due to the fact, moreover, that the time independent Schrödinger equation is itself a Helmholtz-like equation, the same mathematics holding for a classical optical beam turns out to apply to a quantum particle beam moving in a stationary force field, and leads to a system of Hamiltonian equations providing exact and deterministic particle trajectories and dynamical laws, and containing the laws of Classical Mechanics in the eikonal limit.     

介于经典型和乘积型的奇异积分算子

 经典单参数奇异积分算子与多参数乘积型奇异积分算子既有联系也有区别。文中建立一套介于两者之间的奇异积分算子理论,给出该类算子的L^p(p>1)有界性。其中L²有界性是利用傅里叶变换与分部积分等方法得到的。一般的L^p (p>1)有界性是利用经典的Littlewood-Paley-Stein理论和方法得到的。     

Systems thinking and mathematical problem solving

Problem solving lies at the core of engineering and remains central in school mathematics. Word problems are a traditional instructional mechanism for learning how to apply mathematics to solving problems. Word problems are formulated so that a student can identify data relevant to the question asked and choose a set of mathematical operations that leads to the answer. However, the complexity and interconnectedness of contemporary problems demands that problem‐solving methods be shaped by systems thinking. This article presents results from three clinical interviews that aimed at understanding the effects that traditional word problems have on a student’s ability to use systems thinking. In particular, the interviews examined how children parse word problems and how they update their answers when contextual information is provided. Results show that traditional word problems create unintended dispositions that limit systems thinking.     

Twenty years of quantum contextuality at USTC

Quantum contextuality is one of the most perplexing and peculiar features of quantum mechanics. Concisely, it refers to the observation that the result of a single measurement in quantum mechanics depends on the set of joint measurements actually performed. The study of contextuality has a long history at the University of Science and Technology of China (USTC). Here we review the theoretical and experimental advances in this direction achieved at USTC over the last twenty years. We start by introducing the renowned simplest proof of state-independent contextuality. We then present several experimental tests of quantum versus noncontextual theories with photons. Finally, we discuss the investigation of the role of contextuality in general quantum information science and its application in quantum computation.     

新冠肺炎疫情前后大学生道德观比较

 道德基础理论认为,人类至少进化出了5种道德基础：公正、关爱、忠诚、权威和圣洁。人们对各道德基础的看重程度不同,表现出不同的道德观。在新冠肺炎疫情暴发的背景下,本研究采用道德基础问卷,分别于新冠肺炎疫情暴发前（2017年11月26日-12月7日）、暴发期间（2020年2月29日-4月30日）和暴发后（2020年7月14-16日）多次收集中国大学生的道德观数据,旨在考察疫情前后大学生道德观的变化趋势。研究发现：疫情暴发期间,大学生对个体性（公正和关爱）和群体性道德基础（忠诚、权威和圣洁）的看重程度均显著高于疫情暴发前;疫情基本得到控制后,大学生对个体性和群体性道德基础的总体看重程度并未立即出现明显回落或进一步上升。研究结果说明,与2017年相比,大学生的道德重视程度在疫情发生后有明显上升,其背后的原因需进一步探究。     

Why Do the Quantum Observables Form a Jordan Operator Algebra?

The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive nonassociative multiplication operation is hard to justify from a physical or statistical point of view. Considering the non-Boolean extension of classical probabilities, presented in a recent paper, it is shown in this paper that such a multiplication operation can be derived from certain properties of the conditional probabilities and the observables, i.e., from postulates with a clear statistical interpretation. The well-known close relation between Jordan operator algebras and C*-algebras then provides the connection to the quantum-mechanical Hilbert space formalism, thus resulting in a novel axiomatic approach to general quantum mechanics that includes the types II and III von Neumann algebras.     

Where and why the generalized Hamilton-Jacobi representation describes microstates of the Schrödinger wave function

A generalized Hamilton-Jacobi representation describes microstates of the Schrödinger wave function for bound states. At the very points that boundary values are applied to the bound state Schrödinger wave function, the generalized Hamilton-Jacobi equation for quantum mechanics exhibits a nodal singularity. For initial value problems, the two representations are equivalent.     

The End of a Classical Ontology for Quantum Mechanics?

In this paper, I argue that the Shrapnel–Costa no-go theorem undermines the last remaining viability of the view that the fundamental ontology of quantum mechanics is essentially classical: that is, the view that physical reality is underpinned by objectively real, counterfactually definite, uniquely spatiotemporally defined, local, dynamical entities with determinate valued properties, and where typically ‘quantum’ behaviour emerges as a function of our own in-principle ignorance of such entities. Call this view Einstein–Bell realism. One can show that the causally symmetric local hidden variable approach to interpreting quantum theory is the most natural interpretation that follows from Einstein–Bell realism, where causal symmetry plays a significant role in circumventing the nonclassical consequences of the traditional no-go theorems. However, Shrapnel and Costa argue that exotic causal structures, such as causal symmetry, are incapable of explaining quantum behaviour as arising as a result of noncontextual ontological properties of the world. This is particularly worrying for Einstein–Bell realism and classical ontology. In the first instance, the obvious consequence of the theorem is a straightforward rejection of Einstein–Bell realism. However, more than this, I argue that, even where there looks to be a possibility of accounting for contextual ontic variables within a causally symmetric framework, the cost of such an account undermines a key advantage of causal symmetry: that accepting causal symmetry is more economical than rejecting a classical ontology. Either way, it looks like we should give up on classical ontology.