equation

"火星への旅を数ヶ月ではなく数週間で済ませ、木星、土星、恒星間前駆ミッションを可能にするには、核融合が必要である。"

"私の質問は、なぜ誰もが常に継続的で容赦のない指数関数的成長を想定するのかということです。"

"各アテンションヘッドには、学習可能な物理パラメータがわずか3つ（周波数、減衰、位相）あります。"

"より長いシーケンスでは、節約は増加します：2Kトークンで31倍、8Kで107倍、32Kで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."