一类带有交叉扩散的捕食-食饵模型的正解

该文研究了一类在齐次Dirichlet边界条件下的带有交叉扩散的捕食-食饵模型.首先,根据Leray-Schauder度理论,建立了系统的正解的存在性;其次,当参数m=且充分大时,分别研究了正则扰动方程和奇异扰动方程的正解的存在性,和借助分歧理论说明奇异系统的正解在a~*处爆破;最后,建立了系统正解的多解性.     

一类具有修正的Leslie-Gower项的捕食-食饵模型的正解

主要研究一类具有修正的Leslie-Gower型的捕食-食饵模型正解的动力学行为.首先,利用不动点指数理论给出了正解存在的充分条件;其次,讨论了当m充分大时模型正解的唯一性和稳定性;最后,以a为分歧参数,利用局部分歧理论研究了正解的分支结构,以及在适当条件下正解的多解性和局部分歧解的稳定性.结果 表明:在适当条件下两物...     

LAMOST medium-resolution spectroscopic survey of binarity and exotic star (LAMOST-MRS-B): Observation strategy and target selection

LAMOST-MRS-B is one of the sub-surveys of LAMOST medium-resolution ($R\sim7500$) spectroscopic survey. It aims at studying the statistical properties (e.g., binary fraction, orbital period distribution, mass ratio distribution) of binary stars and exotic stars. We intend to observe about 30000 stars ($10 {\rm mag}\leq G < 14.5$ mag) with at least 10 visits in five years. We first planned to observe 25 plates around the galactic plane in 2018. Then the plates were reduced to 12 in 2019 because of the limitation of observation. At the same time, two new plates located at the high galactic latitude were added to explore binary properties influenced by the different environments. In this survey project, we set the identified exotic and low-metallicity stars with the highest observation priorities. For the rest of the selected stars, we gave the higher priority to the relatively brighter stars in order to obtain high quality spectra as many as possible. Spectra of 49129 stars have been obtained in LAMOST-MRS-B field and released in DR8, of which 28828 and 3375 stars have been visited more than twice and ten times with $\rm SNR \geq 10$, respectively. Most of the sources are B-, A-, and F-type stars with $\rm -0.6< [Fe/H] < 0.4 $ dex. We also obtain 347 identified variable and exotic stars and about 250 stars with $\rm [Fe/H] <-1$ dex. We measure radial velocities (RVs) by using 892233 spectra of the stars. The uncertainties of RV achieve about $1$ ${\rm km \cdot s^{-1}}$and $10$ ${\rm km \cdot s^{-1}}$ for 95% of late- and early-type stars, respectively. The datasets presented in this paper are available at http://www.doi.org/10.57760/sciencedb.j00113.00035.