“Each such variety is irreducible and admits a rational parametrization. The assignment is functorial: algebra quotients correspond to monomial maps among the varieties.”

“The paper finds that the entanglement entropy of Hawking radiation before the Page time increases with time, with the slope determined by the central charge. After the Page time, the unitarity of black hole evaporation is restored, and the entanglement entropy includes a logarithmic correction related to the central charge.”

“The resulting thermodynamic pressure increases with temperature but exhibits an approximately logarithmic dependence.”

“The paper finds that the dust mass depends linearly on gas metallicity and that destruction efficiency is higher in low-metallicity environments.”

“The spectrum of the system's response -- captured by the so-called logarithmic susceptibility (LS) -- enables a direct observation of characteristic features of real-time instantons.”

“The paper proves that the family of Bethe subspaces extends regularly to the minimal wonderful model of the toric arrangement.”

“The entanglement entropy grows logarithmically with effective central charge c=5.2. We find evidence for thermalization at infinite temperature.”

“The corner entanglement entropy grows linearly with the logarithm of imaginary time, dictated solely by the universality class of the quantum critical point.”

“The paper introduces a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices.”

“The paper finds that in (3+1) dimensions the scalar Love number is generically nonzero, while the Fermionic Love numbers follow a universal power-law. In (2+1) dimensions, the scalar field exhibits a logarithmic structure, and the Fermionic Love number retains a simple power-law form.”

“Thermodynamics becomes the study of how these shells deform with energy: the entropy is the logarithm of a geometric area, and its derivatives satisfy a deterministic hierarchy of entropy flow equations driven by microcanonical averages of curvature invariants.”

“The error of approximation of the $2π$-periodic sawtooth function $(π-x)/2$, $0\leq x<2π$, by its $n$-th Fourier polynomial is shown to be bounded by arccot$((2n+1)\sin(x/2))$.”

“The model achieves logarithmic depth and linear total complexity, enabling efficient inference across large and variable user sets without retraining or architectural changes.”

“The paper achieves explicitly computable constants that improve upon all previously known bounds, with a 14% improvement over the previous best constant for dimension 3.”

“All logarithms arising in the loop expansion of the single soft current can be reabsorbed in the scale choices for the $d$-dimensional coupling, casting some doubt on the need for a logarithmic celestial theory.”

“The paper argues that the coset graph $A \otimes G/\mathbb{Z}_2$ encodes not only the coset graph fusion algebra, but also boundary g-factors, defect g-factors, and relative symmetry resolved entanglement entropy.”

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“The context mentions Bose-Einstein Condensate dark matter with logarithmic nonlinearity.”

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