“The article uses the term 'people weak at verbalization' not as a put-down, but as a label for those who find it challenging to articulate thoughts and intentions clearly from the start.”

“Our approach relies on a unified formulation of the distance from a point to a hyperplane on the considered spaces.”

“The paper identifies physical theories as least fixed points of admissibility constraints derived from Galois connections.”

“The best solution approach for a practical path-based model reduces the IP gap by an average of 26.5% and 22.5% for the two largest instance groups, compared to solving the reformulation alone.”

“The paper revisits the process of eigenvalue approximation from the perspective of computational spectral geometry.”

“The paper develops a general convergence analysis based on a reformulation of the operators by means of a fixed-point equation, providing a list of hypotheses related to the regularization properties of the equation and the convergence of the chosen approximation techniques on suitable subspaces.”

“The paper introduces an explicit formulation of object arrangement preferences along four interpretable constructs: spatial practicality, habitual convenience, semantic coherence, and commonsense appropriateness.”

“ConfigTuner demonstrates up to a 1.36x increase in throughput compared to Megatron-LM.”

“The paper focuses on modifying the damping and shifting schemes used in the original CFFT formulation to reduce boundary errors and improve accuracy and convergence.”

“The resulting formulation is based on a 4D Hodge-Laplacian operator with a spatiotemporal diffusion tensor and convection field, augmented by a small temporal perturbation to ensure nondegeneracy.”

“Late time levels are enhanced for the coated particles, implying a reduced effective interfacial diffusivity and a broadened release-time distribution.”

“The paper shows that there exists a unique minimal strong solution to the given particle system up until a certain maximal stopping time, which is stated explicitly in terms of the dual formulation of a linear programming problem.”

“The results showcase the real-world feasibility and superior performance of nonlinear MPC for 3D path-following guidance at ground speeds up to 36 meters per second.”

“The paper discusses the use of VQE as a novel SAT-solver and the importance of qubit efficiency in the Noisy Intermediate Scale Quantum-era.”

“The Zakharov-Shabat equations themselves recover the Lax operators under suitable change of independent variables in the case of the KP hierarchy and the modified KP hierarchy (in the matrix formulation).”

“The novelty of this work is two-fold: extending the catalogue of known optimal RMRAs and formulating a sub-optimal RMRA that abides by CFEs.”

“The paper validates the numerical approaches by successfully reproducing standard vacuum test cases and achieving long-term stable evolutions of stationary black holes, including Kerr black holes with extreme spin.”

“The charm production rate decreases monotonically across all medium formulations.”

“Online methods can achieve an average success rate of 45/19/77% with just a few thousand queries over three tasks where static methods from existing multi-turn conversation benchmarks find few or even no failure cases.”

“NashOpt is an open-source Python library for computing and designing generalized Nash equilibria (GNEs) in noncooperative games with shared constraints and real-valued decision variables.”

“MERINDA delivers substantial gains over GPU implementations: 114x lower energy, 28x smaller memory footprint, and 1.68x faster training, while matching state-of-the-art model-recovery accuracy.”

“The Dense Gradient admits a closed-form logit-level formula, enabling efficient GPU implementation.”

“MUSIC accurately learns solutions to complex coupled systems under data-scarce and noisy conditions, consistently outperforming non-sparse formulations.”

“The proposed model achieves convergence on large test systems (e.g., IEEE 118 bus) in seconds and is validated against exact AC solutions.”

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“The article likely details the mathematical formulation of P-FABRIK, its implementation, and experimental validation. It would probably compare its performance with existing methods in terms of accuracy, speed, and robustness.”

“The paper proposes integrable space discretizations of the sine-Gordon equation in three distinct cases of non-characteristic coordinates.”

“Resilient systems must anticipate disruption, maintain critical functions under attack, recover efficiently, and learn continuously.”

“The paper validates the new 3-crossed module structure by proving that the induced simplicial set forms a quasi-category and that the Moore complex of length 3 associated with a simplicial group naturally admits the structure of the proposed 3-crossed module.”

“The paper demonstrates that as few as three qubits per plaquette is sufficient to reach per-mille level precision on predictions for observables.”

“The paper constructs a covariant formulation for self-dual Yang-Mills and self-dual gravity, and subsequently extends this construction to the full Chiral Higher Spin Gravity.”

“The paper argues that the traditional opposition between determinism and indeterminism in physics is representational rather than ontological.”

“The proposed method significantly outperforms the typical phase-angle formulation with a 14-times faster computation speed on average.”

“The conformable derivative is not a fractional operator but a useful computational tool for systems with power-law time scaling, equivalent to classical differentiation under a nonlinear time reparametrization.”

“TrGLUE comprises Turkish-native corpora curated to mirror the domains and task formulations of GLUE-style evaluations, with labels obtained through a semi-automated pipeline that combines strong LLM-based annotation, cross-model agreement checks, and subsequent human validation.”

“The article is sourced from ArXiv.”

“The paper proposes statistical channel state information (sCSI)-based optimization of satellite clustering, beam selection, and transmit precoding, using a sum-rate upper-bound approximation.”

“The paper establishes a correspondence between the auxiliary field model of Russo and Townsend and the Ivanov--Zupnik formalism in four-dimensional electrodynamics.”

“The method is linear by construction, each time step requires only one linear solve. Across the benchmark suite, this reduces wall-clock time by $2$--$4\times$ relative to fully implicit nonlinear formulations while maintaining comparable accuracy.”

“The paper introduces a Biorthogonal Graph Fourier Transform (BGFT) adapted to directed diffusion.”

“The optimal antenna placement is in principle an electrostatic equilibrium problem.”

“The research focuses on a first-principles formulation within QED.”

“...a novel framework that leverages a hybrid view-transformation branch with 3D Gaussian and edge priors to enhance both geometric consistency and boundary awareness in 3D panoptic occupancy prediction.”

“KAN-AFT effectively models complex nonlinear relationships within the AFT framework.”

“Formulation of Relativistic Dissipative Spin Hydrodynamics”

“The research focuses on the streamfunction-vorticity formulation for incompressible viscid and inviscid flows on general surfaces.”

“The article's content would likely include detailed mathematical formulations, computational results, and comparisons with experimental data or other theoretical approaches.”

“The paper focuses on a sparsity-inducing formulation and a convergent decomposition training algorithm.”

“Without the actual article content, a specific quote cannot be provided. However, a relevant quote might discuss the information paradox, the holographic principle, or specific calculations within the AdS/CFT framework.”

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