equation

"はい、これは典型的な「隠れ2次（hidden quadratic）」として処理できます。"

"Extensive empirical results show that our model consistently outperforms conventional SDE-BNNs across various tasks, including image classification and sequence modeling, achieving lower NFEs and improved predictive accuracy."

"Despite operating in a purely zero-shot setting, JointFM reduces the energy loss by 14.2% relative to the strongest baseline when recovering oracle joint distributions generated by unseen synthetic SDEs."

"To make the journey to Mars a matter of weeks, not months, and to enable missions to Jupiter, Saturn, and interstellar precursor missions, fusion is required."

"My question is why does everyone always assume a continued, inexorable exponential growth?"

"Each attention head has just 3 learnable physics parameters (frequency, damping, phase)."

"At longer sequences the savings grow: 31x at 2K tokens, 107x at 8K, 367x at 32K."

"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.'"