In this paper, the author computes canonical connections and KobayashiNomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifies algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure. 相似文献
Czechoslovak Mathematical Journal - During the last decade, several research groups have published results on sufficient conditions for the hamiltonicity of graphs by using some topological... 相似文献
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.
We consider quantum unbounded spin systems (lattice boson systems) in -dimensional lattice space Z. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly -dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case. 相似文献
G. Grätzer, H. Lakser, and E. T. Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a small lattice L, that is, a lattice L with O(n2) elements. G. Grätzer, I. Rival, and N. Zaguia proved that, for any <2, O(n2) can not be improved to O(n). In this note we show that the theorem about small representation can be improved further to get a more delicate result. 相似文献