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Reinvigorating the Wiener-Hopf technique in the pursuit of understanding processes and materials

National Science Review 2021年第2期8卷 11-13页

作者： David Abrahams Xun Huang Anastasia Kisil Gennady Mishuris Michael Nieves Sergei Rogosin Ilya Spitkovsky IsaacNewtonInstituteforMathematicalSciences CollegeofEngineering PekingUniversity DepartmentofMathematics UniversityofManchester DepartmentofMathematics AberystwythUniversity SchoolofComputingandMathematics KeeleUniversity facultyofeconomics BelarusianStateUniversity ScienceandMathematics NewYorkUniversityAbuDhabi

The Wiener-Hopf(WH) method was created in 1931, by Norbert Wiener and Eberhard Hopf, to deliver exact solutions to integral equations with convolutiontype kernels on a half-line. It appears that this problem is closely related to that posed by Riemann in 1857 on the problem concerning the construction of a Fuchsian system of differential equations with given singular points and a prescribed monodromy group. This later became known as the 21 st Hilbert problem. The WH method is a powerful and long-standing tool that served as a catalyst in broadening the applicability of Fourier analysis, owing to the essential characteristics of analytic functions. Employing the Fourier transform(FT) to the integral equation leads to a RiemannHilbert(RH) problem on the real axis:

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Towards a New Strategic Understanding Between Egypt and PRC in the Twenty -First Century

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外交评论（外交学院学报） 2000年第S1期20卷 35-43页

作者： Mohmmad El-Sayed Selim CenterforAsianStudies FacultyofEconomics&PoliticalScienceCairoUniversit

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The Road Traffic Analysis Based on an Urban Traffic Model of the Circular Working Field

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Acta Mathematicae Applicatae Sinica 2004年第1期20卷 77-84页

作者： Ming-zheLi facultyofeconomics.FukuokaUniversity.8-19-1Nanakuma.Jonan-ku.Vukuoka814-0140 Japan

Under a relatively realistic model, this paper theoretically analyzes the road traffic status inside an urban working field, including its radial roads and circular ones. Concretely, the radial and the circular average traveling distances of a car commuter in a tiny ring with wide dx are first derived, and then the necessary road area, road area rate distributions, the proportion between the radial and the circular roads to be needed are also calculated. The results presented here and the properties shown through the numerical analysis are considered to be significant at the very beginning stage of designing an urban city.

关键词： Average traveling distance Road area Commutation Working field

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Rethinking Pension Reform in China

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China & World Economy 2005年第2期13卷 39-53页

作者： ZhigangYuan JinFeng professor FacultyofEconomicsFudanUniversity. post-doctorialresearcher EmploymentandSocialSecurityResearchCenterFudanUniversity.

In linewith advicefrom internationalfinancial institutions, China introduced a three-pillar pension system in 1997. However, it performs badly, with high contribution levels, the ‘funded’ contributionsbeing used forcurrent expenditures,and delaysinpension payments. The problemsareoften ascribed tothe remaining elements of pay-as-you-go (PAYG) present in thesystem. Thispaper, however, arguesthat the advantagesofa fully-funded system (FF) havebeen exaggerated. The higher relative return of the PAYG system in China justifies a PAYG pension system forChina. It is arguedthat theproblemsoftheChinesepension system are not caused by the use of PAYG butbytheneed to finance transition costs and conditions particularto the pension system in China, notablyincomplete contribution coverage, a low pension age, and a high replacement rate. Itisthesefactors, and therateofgrowth ofoutput, which determine the viabilityof theChinese pension system.

关键词： pay-as-you-go pension reform productivity

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