Excited state geometry optimization with the density matrix renormalization group as applied to polyenes

We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al (J. Chem. Theor.Comput. 9, 4462 (2013)). We introduce a DMRG wavefunction maximum overlap following technique to facilitate state-specific DMRG excited state optimization. Using DMRG configuration interaction (DMRG-CI) gradients we relax the low-lying singlet states of a series of trans-polyenes up to C20H22. Using the relaxed excited state geometries as well as correlation functions, we elucidate the exciton, soliton, and bimagnon ("single-fission") character of the excited states, and find evidence for a planar conical intersection

Positive radial solutions for a class of quasilinear Schrödinger equations in R3

This paper is concerned with the following quasilinear Schrödinger equations of the form: −∆u − u∆(u 2 ) + u = |u| p−2u, x ∈ R 3 where p ∈ (2, 12). By making use of the constrained minimization method on a special manifold, we prove that the existence of positive radial solutions of the above problem for any p ∈ (2, 12)

On Legal English Translation from the Perspective of Legal Linguistics

With the deepening trend of globalization and the development of economy and society, the demand for international exchange talents is increasing. Especially with the increasing number of transnational corporations, almost every company should have professional legal translation employees to guarantee their legitimacy of transnational trade and effectively prevent the infringement of related rights and interests. Therefore, to improve the quality in transnational translation business and optimize legal English translation skills from the perspective of legal language can not only offer a reference for the industry, but also provide evidence for the problems arising from the actual legal translation process. Based on the perspective of legal linguistics, this paper tries to puts forward appropriate legal English translation measures mainly by analyzing the skills of legal English translation, with a view to providing some references for relevant scholars

Spatiotemporal Analysis of Urban Road Congestion during and Post COVID-19 Pandemic in Shanghai, China

Coronavirus Disease 2019 (COVID-19) has become one of the most serious global health crises in decades and tremendously influence the human mobility. Many residents changed their travel behavior during and after the pandemic, especially for a certain percentage of public transport users who chose to drive their owned vehicles. Thus, urban roadway congestion has been getting worse, and the spatiotemporal congestion patterns has changed significantly. Understanding spatiotemporal heterogeneity of urban roadway congestion during and post the pandemic is essential for mobility management. In this study, an analytical framework was proposed to investigate the spatiotemporal heterogeneity of urban roadway congestion in Shanghai, China. First, the matrix of average speed in each traffic analysis zones (TAZs) was calculated to extract spatiotemporal heterogeneity variation features. Second, the heterogenous component of each TAZ was extracted from the overall traffic characteristics using robust principal component analysis (RPCA). Third, clustering analysis was employed to explain the spatiotemporal distribution of heterogeneous traffic characteristics. Finally, fluctuation features of these characteristics were analyzed by iterated cumulative sums of squares (ICSS). The case study results suggested that the urban road traffic state evolution was complicated and varied significantly in different zones and periods during the long-term pandemic. Compared with suburban areas, traffic conditions in city central areas are more susceptible to the pandemic and other events. In some areas, the heterogeneous component shows opposite characteristics on working days and holidays with others. The key time nodes of state change for different areas have commonness and individuality. The proposed analytical framework and empirical results contribute to the policy decision-making of urban road transportation system during and post the COVID-19 pandemic