Research
Research
Research
Research
184,527+ open-access research outputs.
Denote by $p(k)$ the limit, as $n \rightarrow \infty$, of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$. We give an asymptotic formula for $p(k)$, sho…
This paper investigates the existence and uniqueness of solutions for a nonlinear evolution equation governed by an m-accretive operator A in a Banach space, presenting a perturbation term that does n…
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
Fast radio bursts (FRBs), thought to originate from magnetars, exhibit diverse polarization properties that constrain their emission physics and local magneto-ionic environments. The polarization posi…
Type Ia supernova (SN Ia) standardisation parameters exhibit evidence for systematic variation across the host galaxy star-formation rate - stellar mass (SFR$-M_\star$) plane, motivating the incorpora…
Let $M$ be a smooth manifold without boundary and let $\mathcal{T}$ be a countable collection of manifolds with corners, each equipped with a smooth map to $M$. We show that the singular simplicial se…
We study the Liouville equation $\triangle u+e^{2u} =0$ in a Riemannian surface $(M, g)$ with nonnegative $Ricci$ curvature. Under some asymptotic lower bound assumptions, we classify all the soluti…
In this paper, we study the $L^p$-boundedness of Stein's square function $\mathfrak{S}^{\alpha}(\mathcal{L})$ associated with the sub-Laplacian $\mathcal{L}$ on M\'etivier group $G$. A key aspect of o…
The rapidly expanding artificial intelligence (AI) industry has produced diverse yet powerful prediction tools, each with its own network architecture, training strategy, data-processing pipeline, and…
Degenerate spinor Bose gases with repulsive density-density interaction and anti-ferromagnetic spin-spin coupling in one spatial dimension are shown to be described by a quantum integrable matrix exte…
Negatively charged boron vacancy (VB-) defects in hexagonal boron nitride (hBN) are promising for nanoscale-proximity quantum sensing. To evaluate their performance, it is important to characterize th…
The 'Species Scale' has proved to be an important concept when studying consistent effective actions in Quantum Gravity. This is a short summary of my contribution to the Corfu Summer Institute in Sep…
We study hypergeometric functions of nilpotent operators in finite-dimensional settings, motivated by the algebraic structure of exceptional points in non-Hermitian quantum mechanics. Our starting poi…
Open clusters are fundamental laboratories for investigating stellar and Galactic evolution, and serve as important benchmarks for asteroseismic analyses. Using a boutique method to analyze TESS photo…
We give a self-contained, modern exposition of \'Edouard Goursat's 1887 theorem on pseudo-elliptic integrals -- those integrals of the form $\int F(t)\,\d t/\sqrt{R(t)}$ with $R$ a cubic or quartic po…
The excitation of plasma wakefields driven by chirped laser pulses is investigated using a reduced relativistic fluid Poisson model supported by fully relativistic particle in cell (PIC) simulations. …
The main theorem of the paper provides an existence criterion of holomorphic discs for higher $A_\infty$ operations. The key step is to show that if a minimal disc in a K\"ahler manifold with boundary…
This work studies numerical integration by the M\"obius-transformed trapezoidal rule, which combines the classical trapezoidal rule with a change of variables induced by a M\"obius transformation that…
We have developed a novel BEDT-TTF-based organic conductor, $\kappa$-(BEDT-TTF)$_2 m$-HOOCC$_6$H$_4$SO$_3$ ($\kappa$-$m$-SBA), and propose it as a candidate for altermagnet. Tight-binding band calcula…
We develop a geometric and information-theoretic framework for encoder-decoder learning built on the Information Bottleneck (IB) principle. Recasting IB as a rate-distortion problem with Kullback-Leib…
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