Research
Research
Research
Research
125,100+ open-access research outputs.
We introduce the weighted prime sum $S(x) = \sum_{p \le x} \sqrt{(\log p)/p}$ and the derived quantity $E(x) = S(x)^2 - M(x)$, where $M(x) = \sum_{p \le x} (\log p)/p$. We prove that the order-of-magn…
This paper provides a new class of examples for the Koszul dualities established in~\cite{5}. We study quadratic monomial algebras from the perspective of Koszul duality, with particular emphasis on f…
We investigate the properties of dense quark matter and strange quark stars within a nonperturbative, Poincar\'e-covariant framework. Employing a symmetry-preserving vector$\,\otimes\,$vector contact …
Multimodal representation is crucial for E-commerce tasks such as identical product retrieval. Large representation models (e.g., VLM2Vec) demonstrate strong multimodal understanding capabilities, yet…
Compressible multiphase and multicomponent solvers require accurate interface representation without spurious pressure oscillations. At material interfaces, pressure and velocity are continuous while …
We develop a resurgent approach to the problem of unique continuation of mock theta functions across their natural boundary. The starting point is the representation of the associated Mordell-Appell i…
We present principles of algebraic diversity (AD), a group-theoretic approach to signal processing exploiting signal symmetry to extract more information per observation, complementing classical metho…
The deflection angle of a light ray passing the Schwarzschild (spherically symmetric vacuum) black hole was calculated by Charles Galton Darwin in 1959 in terms of the elliptic integral of the first k…
The Evans function is an analytic function that encodes information about the intersection of certain subspaces in ODE boundary value problems. As such it is a useful tool for computing the spectrum o…
We study twisted bilayer WSe$_2$ within a continuum moir\'e model and introduce a method for treating finite geometries directly in the continuum framework, overcoming limitations associated with mome…
We elaborate on the relation between the generalized Schur index of $N=2$ SCFTs in four dimensions and the non-relativistic limit of the elliptic Ruijsenaars-Schneider model. In particular we discuss …
It is generally believed that quantum fluctuations collaborate with thermal fluctuations, effectively reducing transition temperatures (e.g. for melting of charge order). We show that this is not alwa…
Disks (Keplerian or otherwise, particulate or fluid) are often assumed to have densities that drop off vertically as Gaussians. Recent mm-wave imaging of circumstellar debris disks contradicts this as…
We present Wan-Image, a unified visual generation system explicitly engineered to paradigm-shift image generation models from casual synthesizers into professional-grade productivity tools. While cont…
We analyze greedy routing in a random graph G_n constructed on the vertex set V = {1, 2, ..., n} embedded in Z. Vertices are inserted according to a uniform random permutation pi, and each newly inser…
In quadratic gravity, with a positive Weyl squared coefficient, the extra spin-2 sector is shown to correspond to a dual inverted harmonic oscillator, instead of a ghost. Using the Wightman spectrum c…
We study null controllability for the parabolic equation on $\mathbb{S}^{2}$ endowed with its canonical almost-Riemannian structure. For a spherical crown $\omega=\{\alpha<x_3<\beta\}$, where $0\le \a…
For the fixed-size Brualdi--Hoffman--Turan problem forbidding the fish graph $H(4,3)$, Zheng and Zhang proved that every $H(4,3)$-free graph of even size $m \ge 38$ without isolated vertices satisfies…
Synthesizing human--object interaction (HOI) videos has broad practical value in e-commerce, digital advertising, and virtual marketing. However, current diffusion models, despite their photorealistic…
Chemical sensing in real-world environments requires resolving rapidly fluctuating and spatially heterogeneous concentration fields. However, these dynamics are strongly distorted by widely used, low-…
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