Modified hierarchy basis for solving singular boundary value problems

AbstractIn this paper, we develop an efficient preconditioning method on the basis of the modified hierarchy basis for solving the singular boundary value problem by the Galerkin method. After applying the preconditioning method, we show that the condition number of the linear system arising from the Galerkin method is uniformly bounded. In particular, the condition number of the preconditioned system will be bounded by 2 for the case q(x)=0 (see Eq. (1) in the paper). Numerical results are presented to confirm our theoretical results

Expanding Protection and Value Promotion of Cultural Routes to Promote Rural Revitalization—A Case Study of Ya’ an Section of the Sichuan-Tibet Ancient Tea-Horse Road

As a new theory of cultural heritage protection and research, cultural routes emphasize the integrity of culture and pay more attention to the interaction and integration between cultural communities along the route. The Ancient Tea-Horse Road is an important cultural, economic and religious exchange link between the various ethnic groups in the Han and Tibetan two places. As the starting point of the line, Ya ‘an section plays an extremely important role in history. Under the concept and connotation of cultural routes, this paper explores the cultural value of the Ya’an section of the Sichuan-Tibet Tea Horse Ancient Road with the idea of cultural integrity along the line, integrates the cultural elements along the line to form an integrated cultural industry cluster along the line, establishes the tea-horse ancient road cultural route heritage system and the management system of overall coordination and overall protection, deeply excavates the multiple values of the cultural industry along the line, promotes the coordinated development of the line, and empowers the rural revitalization along the line

Ds1∗(2860)D_{s1}^*(2860) and Ds3∗(2860)D_{s3}^*(2860): Candidates for 1D1D charmed-strange mesons

Newly observed two charmed-strange resonances, $D_{s1}^*(2860)$ and $D_{s3}^*(2860)$, are investigated by calculating their Okubo-Zweig-Iizuka allowed strong decays, which shows that they are suitable candidates for the $1^3D_1$ and $1^3D_3$ states in the charmed-strange meson family. Our study also predicts other main decay modes of $D_{s1}^*(2860)$ and $D_{s3}^*(2860)$, which can be accessible at the future experiment. In addition, the decay behaviors of the spin partners of $D_{s1}^*(2860)$ and $D_{s3}^*(2860)$, i.e., $1D(2^-)$ and $1D^\prime(2^-)$, are predicted in this work, which are still missing at present. Experimental search for the missing $1D(2^-)$ and $1D^\prime(2^-)$ charmed-strange mesons is an intriguing and challenging task for further experiment.Comment: 8 pages, 3 figures and 4 tables. More discussions added and typos corrected. Accepted by Eur. Phys. J.