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Despite their impressive capabilities, large language models (LLMs) often face challenges such as temporal misalignment and generating hallucinatory content. Enhancing LLMs with retrieval mechanisms to fetch relevant information from external sources offers a promising solution. Inspired by the proverb "Think twice before you act," we propose a dual-angle evaluated retrieval-augmented generation framework \textit{Think-then-Act}. Unlike previous approaches that indiscriminately rewrite queries or perform retrieval regardless of necessity, or generate temporary responses before deciding on additional retrieval, which increases model generation costs, our framework employs a two-phase process: (i) assessing the input query for clarity and completeness to determine if rewriting is necessary; and (ii) evaluating the model's capability to answer the query and deciding if additional retrieval is needed. Experimental results on five datasets show that the \textit{Think-then-Act} framework significantly improves performance. Our framework demonstrates notable improvements in accuracy and efficiency compared to existing baselines and performs well in both English and non-English contexts. Ablation studies validate the optimal model confidence threshold, highlighting the resource optimization benefits of our approach., Comment: 12 pages, 8 figures

In this paper, we are mainly concerned with the well-posed problem of the fractional Keller--Segel system in the framework of variable Lebesgue spaces. Based on carefully examining the algebraical structure of the system, we reduced the fractional Keller--Segel system into the generalized nonlinear heat equation to overcome the difficulties caused by the boundedness of the Riesz potential in a variable Lebesgue spaces, then by mixing some structural properties of the variable Lebesgue spaces with the optimal decay estimates of the fractional heat kernel, we were able to establish two well-posedness results of the fractional Keller--Segel system in this functional setting., Comment: arXiv admin note: substantial text overlap with arXiv:2404.05127

In this paper, we are mainly concerned with the well-posedness of the dissipative surface quasi-geostrophic equation in the framework of variable Lebesgue spaces. Based on some analytical results developed in the variable Lebesgue spaces and the $L^{p}$-$L^{q}$ decay estimates of the fractional heat kernel, we establish the local existence and regularity of solutions to the 2D dissipative surface quasi-geostrophic equation in the variable Lebesgue space., Comment: 11 pages