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

“The paper derives bilinear tau forms of the canonically quantized Painlevé equations, relating them to those previously obtained from the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations.”

“The paper derives sufficient conditions on a compact self adjoint perturbation to guarantee that the perturbed system stays exactly observable.”

“The paper derives explicit expressions for the joint Laplace-Stieltjes transform, probability density function, and governing differential equations of the multivariate gamma subordinator.”

“The paper derives the counting DRM, the effective area, and the flash effective area from the counting DRF.”

“The paper derives the graphicality of infinite sequences for double power-laws, uncovering a rich phase-diagram and pointing out the existence of five qualitatively distinct ways graphicality can be violated.”

“The paper derives fundamental estimation limits for a wide-band near-field sensing systems employing orthogonal frequency-division multiplexing signaling over a coherent processing interval.”

“The paper derives closed-form Cram'er--Rao bounds (CRBs) for joint estimation of target position, velocity, and radar cross-section (RCS).”

“The paper proves a fully nonlinear, saturable lower bound valid for arbitrary current vectors Δq: D_bath ≥ B(Δq,V,V'), where the bound depends only on the transported-charge signal Δq and the pre/post collision covariance matrices V and V'.”

“The paper derives a Pontryagin maximum principle on the belief space, providing necessary conditions for optimality in this hybrid setting.”

“The paper derives an exact identity for overdamped Langevin dynamics that equates the total EP rate to the mutual-information rate.”

“The paper shows that its restricted holonomy group is SU(2), implying universal single-qubit control by closed loops in shape space.”

“The paper establishes the consistency of the QMLE and derives its asymptotic distribution, and proposes a bias-corrected estimator.”

“The paper obtains mean-field analogues of momentum distribution formulas for electron gas in high density and metallic density limits, and applies to a general class of singular potentials.”

“The paper establishes error bounds for the reconstructed solution and the source term without requiring classical source conditions, and derives an expected convergence rate for the source error in a weaker topology.”

“The paper derives a third-order linear differential equation for the partition function, a key result.”

“The paper derives a symmetry that relates expectation values of Pauli strings, allowing for the reduction in the number of measurements needed when simulating fermionic systems.”

“The paper derives closed-form BF structures and develops an efficient first-order algorithm to achieve high-quality local solutions.”

“The paper derives explicit conditions that determine when certain values of N are valid for the encryption scheme.”

“The paper derives a novel recursion relationship across depth which extends the eligibility traces of E-prop to deeper layers.”

“The paper derives necessary and sufficient conditions for the existence of such residual generators and provides explicit design formulas.”

“The dispersive shift and vacuum Rabi splitting emerge from the transcendental eigenvalue equation, with the residues determined by matching to the splitting: $δ_{ge} = 2Lg^2ω_q^2/v^4$, where $g$ is the vacuum Rabi coupling.”

“The paper derives a generalized Heisenberg-Robertson uncertainty inequality valid across all spectral regimes.”

“The resulting equations take the form of Regge-Wheeler equations modified by expectation values of the quantum black hole geometry, providing a clear characterization of quantum corrections to the classical description of the black hole interior.”

“Necessary and sufficient conditions for complete positivity and trace preservation are derived and the canonical decomposition describing DU-covariant superchannels is provided.”

“The paper provides an expression of the optimal terminal wealth for complete markets using max-plus decomposition and derives explicit forms for the Black-Scholes-Merton model.”

“The paper derives the polynomial rate of decay of ruin probabilities in insurance portfolios where insolvency is driven by a single extreme claim.”

“The paper constructs a general class of unique solutions to certain matrix equations and derives several equivalent properties of W-weighted DMP and MPD inverses.”

“The paper reveals the structure of superconducting Berry curvatures and derives the superconducting Berry curvature induced thermal Edelstein effect and spin Nernst effect.”

“The paper proposes to use broad and narrow line emission and CGM nebulae as calorimeters of the ionising SED to trace different accretion "states".”

“The specific symmetry of 2D materials can induce a significant linear exciton Hall (Nernst) effect even without Berry curvature.”

“Random multiplexing achieves statistical fading-channel ergodicity for transmitted signals by constructing an equivalent input-isotropic channel matrix in the random transform domain.”

“The paper derives an exact semidefinite characterization of nonnegative APS and introduces a derivative-based regularizer that promotes smoothly varying APS profiles while preserving transitions of clusters.”

“The paper identifies an anomalous decay pattern where excited modes decay slower than the fundamental mode when the charge coupling is large.”

“The paper derives least squares estimators for the drift, diffusion, and jump-diffusion coefficients and establishes their asymptotic rate of convergence.”

“The paper derives generators and relations of the Coulomb branch operator algebra for specific SU(2) theories and analyzes theories with a specific Coulomb branch structure.”

“The paper defines squeezed cobosons as eigenstates of a Bogoliubov transformed coboson operator and derives explicit expressions for the associated quadrature variances.”

“The study derives a metallicity of $12+\log(\mathrm{O/H})=7.29\pm0.06$ dex, placing Leo A in the low-mass end of the Mass-Metallicity Relation (MZR).”

“The adder property is preserved despite changes in growth dynamics, emphasizing that the reduction in size variability is a consequence of the growth law rather than simple scaling with mean size.”

“The paper derives a fundamental identity that connects the (path-) derivative of a (possibly) non-Euclidean energy score to the score of the noisy marginal.”

“The phenomenology of the resulting correlators presents some novel features, such as oscillations with an envelope controlled by the anomalous dimension, rather than the usual value of 3/2.”

“The paper derives precise masses and the complete set of its fundamental parameters for the three components, and introduces a new orbital solution, and a new dynamical parallax.”

“The paper derives geodesic equations, analyzes the radial photon orbital equation, and explores the relationship between photon ring width and the Lyapunov exponent.”

“The paper derives WKB connection formulas that relate Kerr quasinormal frequencies to grey-body transmission coefficients.”

“The paper likely contributes to the understanding of supersymmetric quantum field theories.”

“DDSPO directly derives per-timestep supervision from winning and losing policies when such policies are available. In practice, we avoid reliance on labeled data by automatically generating preference signals using a pretrained reference model: we contrast its outputs when conditioned on original prompts versus semantically degraded variants.”

“The paper derives constraints on the coupling parameters using data from the LZ, XENON, and Borexino experiments, covering mediator mass from $10^{-6}$ to $1$ GeV.”

“The paper derives constraints on dimension-six operators that affect four-fermion interactions between leptons and bottom quarks, as well as Z-fermion couplings.”

“InSPO derives a globally optimal policy conditioning on both context and alternative responses, proving superior to DPO/RLHF while guaranteeing invariance to scalarization and reference choices.”

“The rotation parameter 'a' is more relevantly affecting the optical shadow radius (through a right shift), while the acoustic shadow retains its circular shape.”