With the Measuring Rod against the Floods: Ferdinand Verbiest and His Forgotten Introduction of Benedetto Castelli’s River Hydraulics to China

The monumental Studies to Fathom Principles(Qiongli xue窮理學;1683)by Ferdinand Verbiest S.J.(Nan Huairen南懷仁,1623–1688)was never printed,and its exact content is not known.A section of the only extant,though incomplete,manuscript deals with fluvial flood prevention and river control measures,a subject that until then had not cropped up in any Chinese-language work of the Jesuits.In this section,Verbiest not only described the already well-known Aristotelian theory of the origin of rivers,but also introduced to China new scientific propositions,concepts,and numerical examples originating from the seminal Renaissance work Della misura dell’acque correnti(Of the Mensuration of Running Waters;1628)by Benedetto Castelli(1578–1643).In addition,Verbiest presented to his readers some noteworthy examples of pertinent Western achievements such as the pound-lock with miter gate,and he provided them with a simple economic analysis of flood control options.The significance and possible influence of Verbiest’s text on further developments in Chinese approaches to water engineering are discussed,highlighting a hitherto largely disregarded facet of Western science and technology transfer in the field of river hydraulics and flood management.

The Number of Representations of an Integer as a Sum of Eight Triangular Numbers

An infinite product is expanded to Laurent series by residue theorem.Applying this expansion, the formula for the number of representations of an integer as a sum of eight triangular numbers is easily obtained.

Approximate Symmetries and Infinite Series Symmetry Reduction Solutions to Perturbed Kuramoto-Sivashinsky Equation

Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.

浅析朱熹的“存天理灭人欲”

朱熹的"存天理,灭人欲"的思想主要强调要将仁义礼智四德及人伦五常作为天理来约束行为,遏制个人欲望的膨胀及对个人利益的无限追求。进而说明了通过"居敬"、"穷理","行为重"来消灭欲望,明白天理,形成理想人格。这对我国形成清正廉洁的社会风气和社会主义和谐发展具有重要借鉴意义。

The Extension of Infinitesimal Prolongation Theorem and Its Application

Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much simpler than it was, meanwhile the nonstandard characteristics of convergence with respect to u.c. topology is given.

Existence of Positive Periodic Solutions of Competitor-Competitor-Mutualist Lotka-Volterra Systems with Infinite Delays

In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results.

SOME FUNCTIONAL LIMIT THEOREMS FOR THE INFINITE SERIES OF OU PROCESSES

This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of this process respectively.

Geographical patterns and anti-poverty targeting post-2020 in China

Poverty has been a focus of Chinese government for a long time. It is therefore of great significance to investigate both the mechanisms and spatial patterns of regional impoverishment in order to adequately target Chinese anti-poverty goals. Based on the human-environment relationship and multidimensional poverty theory, this study initially develops a three-dimensional model encompassing human, society, and environmental factors to investigate the mechanisms of rural impoverishment as well as to construct an indicator system to evaluate the comprehensive poverty level(CPL) in rural areas. A back propagation neural network model was then applied to measure CPL, and standard deviation classification was used to identify counties that still require national policy-support(CRNPSs) subsequent to 2020. The results of this study suggest that CPL values conform to a decreasing trend from the southeast coast towards the inland northwest of China. Data also show that 716 CRNPSs will be present after 2020, mainly distributed in high-arid areas of the Tibetan Plateau, the transitional zones of the three-gradient terrain, as well as karst areas of southwest China. Furthermore, CRNPSs can be divided into four types, that is, key aiding counties restricted by multidimensional factors, aiding counties restricted by human development ability, aiding counties restricted by both natural resource endowment and socioeconomic development level, and aiding counties restricted by both human development ability and socioeconomic development level. We therefore propose that China should develop and adopt scientific and targeted strategies to relieve the relative poverty that still exist subsequent to 2020.

“买东西”,为什么不说“买南北”

南宋理学大家朱熹在出仕前。家乡有个叫盛温和的好友，此人亦是博学多才的人。一天，两人相遇于巷子内。盛温和手中拿着一个竹篮子，朱熹问他：“你去哪里？”盛温和回答说：“我要去买点东西。”

A Set-Theoretical Lemma That Implies an Abstract Form of Gdel's Theorem

We propose a simple set-theoretical lemma that implies Godel＇s Incompleteness Theorem. Also mentioned are some related consequences.

Fidelity of states in infinite-dimensional quantum systems

We discuss the fidelity of states in the infinite-dimensional systems and give an elementary proof of the infinite-dimensional version of Uhlmann's theorem.This theorem is used to generalize several properties of the fidelity of the finite-dimensional case to the infinite-dimensional case.These are somewhat different from those for the finite-dimensional case.

SOLVABILITY OF VECTOR KY FAN INEQUALITIES WITH APPLICATIONS

This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.

KAM theorems and open problems for infinite-dimensional Hamiltonian with short range

We introduce several KAM theorems for infinite-dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori.Especially,we introduce a KAM theorem by Yuan published in CMP(2002),which shows that there are rich KAM tori for a class of Hamiltonian with short range and with linearized operator of pure point spectra.We also present several open problems.