Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction*

This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of type A or a. Under suitable scaling, the local proportion functions of A particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wrig...     

Structure,trend and prospect of operational research: a scientific analysis for publications from 1952 to 2020 included in Web of Science database

As an important research direction, operational research (OR) has always attracted scholars worldwide. We study the structure, trend and prospect in the OR field by conducting a bibliometric analysis of publications in the period of 1952–2020, which are included in the Web of Science (WoS) database. Using three effective bibliometric tools, namely, VOS viewer, CiteSpace, and Bibliometrix, a total of 5,353 publications were retrieved to show clear visual results using a series of scientific analyses. First, a performance analysis revealed the basic characteristics of publications considering the type distribution, annual trend, quantity and quality. Then, a cooperation analysis presented the influential countries/regions and showed the relationships among countries/regions, institutions and authors during different periods based on bibliometric indicators and co-authorship networks. Moreover, a keyword analysis was conducted to investigate the hot topics and development of the OR field, using co-occurrence analysis, timeline view analysis and evolution analysis. Finally, we discussed the implications and limitations, and summarized the main findings. This study hopes to provide important and valuable references for future research on the OR field.

     

An identification of the connections of Quillen and Beilinson-Schechtman

Given a family of Riemann surfaces and a holomorphic vector bundle Beilinson and Schechtman construct a canonical connection on the associated determinant bundle. We prove the conjecture which states that their connection coincides with the Quillen connection. This is done by reducing to the case where along fibers are invertible. Both connection forms become more accessible in this case.Supported in part by N.S.F. Grant No. DMS-9201022Supported in part by National Science Council of Republic of China Grant No. NSC 82-0208-M-002-125-T, and NSERC of Canada Grant No. OGP 0121883     

Mechanism of lamellar spacing adjustment in directionally frozen agar gels

A theory is presented for predicting the size of ice crystals which result from steady-state, unidirectional growth within aqueous agar gels. Cellular arrays of adjacent ice crystals were separated by an amorphous water-agar membrane at a composition near the vitrification point. Using this vitrification composition and both a steady-state condition and a minimum free energy criterion, the size of ice crystals was predicted for a given solidification velocity and diffusion condition. It was found, however, that this simple model could not predict the trend towards larger crystal sizes that was observed when the initial agar concentration in the gels increased from 3% to 10% by weight agar.     

Facile Total Synthesis of (±)‐Nimbiol

A facile total synthesis of (±)‐nimbiol 1 has been achieved. In order to decrease the dioxo byproduct 2a , an improved oxidation system of CrO₃/H₂O/HOAc/NaOAc was used.     

Studies on Chemical Constituents of Polygonum Ciliinerve Ohwi

Three new apianen lactones Maomailiaoine I ( 1 ), Maomailiaoine II ( 2 ) and Maoimaliaoine III ( 3 ), together with one known apianen lactone, five known flavonoids and three other known compounds were isolated from Polgonum ciliinerve Ohwi. Their structures were deduced from spectroscopic methods and 2D NMR techniques.