Research
Research
Research
Research
245,541+ open-access research outputs.
We advance Matkovi\v{c} ideas, originally applied to complete the classification of tight structures on small Seifert fibred $L$-spaces, to show the existence of contact structures on Brieskorn sphere…
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…
In 1967 Hajnal and Juh{\'a}sz showed that the cardinality of a first-countable Hausdorff space with the countable chain condition has cardinality at most $\mathfrak{c}$, the cardinality of the real li…
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…
Computer architecture simulation is essential for evaluating new designs without the need for costly tapeout. The community has developed dozens of valuable simulators that have enabled significant ar…
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…
We prove a transfer theorem for hereditary classes of $(r+1)$-uniform hypergraphs. Let $\mathcal G$ be such a class, and for $H\in\mathcal G$ write $\Delta(H)$ and $d(H)$ for the maximum degree and av…
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…
Traditional Shot Boundary Detection (SBD) inherently struggles with complex transitions by formulating the task around isolated cut points, frequently yielding corrupted video shots. We address this f…
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…
Primates exhibit a robust deviation from canonical allometric scaling: at fixed body mass, their lifespans exceed those of non-primate mammals by factors of two to three. A rhesus macaque (8 kg) lives…
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…
We consider a quasi-static nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle …
Existing talking avatar methods typically adopt an image-to-video pipeline conditioned on a static reference image within the same scene as the target generation. This restricted, single-view perspect…
The toughness of a graph $G$, denoted by $\tau(G)$, is defined by $\tau(G)=$min $\{\frac{|S|}{c(G-S)}:S\subseteq V(G)$ and $c(G-S)\geq2\}$. A graph $G$ is said to be $\tau$-tough if $\tau(G)\geq \tau$…
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…
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…
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