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.

     

Numerical computations of integrals over paths on Riemann surfaces of genusN

This paper is a continuation of work by Forest and Lee [1,2]. In [1,2] it was proved that the function theory of periodic soliton solutions occurs on the Riemann surfaces ? of genusN, where the integrals over paths on ? play the most fundamental role. In this paper a numerical method is developed to evaluate these integrals. Predisely, the aim is to develop a computational code for integrals of the form $$\int\limits_\gamma {f(z)\frac{{dz}}{{R(z)}}, or} \int\limits_\gamma {f(z)R(z)dz,} $$ wheref(z) is any single-valued analytic function on the complex planeC, andR(z) is a two-valued function onC of the form $$R^2 (z) = \prod\limits_{k = 1}^{2N + \delta } {(z - z_0 (k)), \delta = 0 or 1,} $$ where {z ₀(k),1≤k≤2N+δ} are distinct complex numbers which play the role of the branch points of the Riemann surface ? = {(z, R(z))} of genusN?1+δ. The integral path γ is continuous on ?. The numerical code is developed in “Mathematica” [3].