equation

"为了使火星之旅只需数周而不是数月，并实现前往木星、土星和星际先驱任务，需要使用聚变。"

"我的问题是，为什么每个人总是假设持续的、不可阻挡的指数增长？"

"每个注意力头只有 3 个可学习的物理参数（频率、阻尼、相位）。"

"在更长的序列中，节省会增加：在2K个标记处节省31倍，在8K处节省107倍，在32K处节省367倍。"

"When combined with recent work on machine learning theory, our results provide guarantees on the generalization ability of transformer-based neural networks for in-context learning of Schr"odinger equations."

"The context mentions that the article is from ArXiv, indicating a pre-print research paper."

"An application to a system of $(k,ρ)$-fractional Hilfer integral equations via a measure of noncompactness."

"The study concerns the limit from Inverse Power Potential to Hard Sphere Boltzmann Equation."

"The context mentions the analysis focuses on qualitative properties of positive solutions."

"$x(1-t(x + x^{-1})) F(x;t) = x - t F(0;t)$"

"GaDE leverages GPU acceleration for the time-dependent Dirac equation."

"Local well-posedness of the skew mean curvature flow for large data."

"The source is ArXiv."

"The study focuses on the Fokas-Lenells equation and its solutions."

"The article's subject matter involves discrete equations and auto-traveling kinks of the φ⁶ model."

"The article's source is ArXiv."

"The paper focuses on Asymptotically Euclidean Solutions of the Constraint Equations."

"The paper investigates the long-time existence and behavior of solutions."

"The research is based on ArXiv, implying a peer-reviewed scientific investigation."

"The article's context focuses on the application of integrable perturbation theory to the defocusing nonlinear Schrödinger equation."

"The context indicates the source is an ArXiv paper."

"A Pick function approach for designing energy-decay preserving schemes."

"The article's topic involves parameter-dependent inhomogeneous boundary-value problems in Sobolev spaces."

"The study concerns the equation of state of strongly interacting matter."

"The article's focus is on the Navier-Stokes equation: $\bu_t+(\bu\cdot\nabla)\bu=\mu\Delta{\bf u}$."

"The research focuses on mixed $3-$ and $4-$wave kinetic equations."

"The article's context provides the title: 'The Semiclassical Limit of the 2D Dirac--Hartree Equation with Periodic Potentials.'"

"The paper studies dispersive decay for the Inter-critical nonlinear Schrödinger equation in $\mathbb{R}^3$."

"The article is sourced from ArXiv."

"The article focuses on Bohmian quantum cosmology within the framework of the Wheeler-DeWitt equation."