Research
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Research
Research
11,922+ open-access research outputs.
In this paper, we prove that if the Frobenius traces agree at all but finitely many places, then two $l$-adic Galois representations, associated to rank-$2$ non-CM Drinfeld modules of generic characte…
We prove the $\frac{2d}{d+1}$-Sidon inequality for a system of functions representing the most general extension of the Rademacher $d$-chaos to the $p$-ary case.…
We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) …
We show that the associativity condition of the universal symmetric 2-algebraic 2-valued group defined by the Buchstaber polynomial admits several mutually equivalent interpretations from the viewpoin…
Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$. Early work by Friedland and Stanley addressed so…
This paper presents a method for incorporating control analysis into design optimization for highly-maneuverable aircraft. By studying reachable sets for aircraft dynamics, we ensure that the optimize…
We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-nor…
We showed a positive energy theorem for asymptotically flat initial data sets with the concept of spectral PSC by He-Shi-Yu, Bi-Hao-He-Shi-Zhu and Brendle-Wang. Then, we proved a quantitative shieldin…
A finite set $S \subset \mathbb{Z}$ is a \emph{Sidon set} if its pairwise differences are distinct. A \emph{perfect difference set} (PDS) of order $n$ is a set $B \subset \mathbb{Z}_v$ ($v = n^2 - n +…
This paper studies the error between the exact solution and it's Euler-Maruyama approximation in temporal-spatial H\"older-norms for L\'evy-driven stochastic differential equations.…
We construct string backgrounds in dimension 2 which connect the Hamilton cigar to the round sphere. Specifically, we construct a 1-parameter family of rotationally symmetric steady gradient Ricci-Yan…
Using the recent work of Brendle--Wang on the Riemannian positive mass theorem, we prove the spacetime positive mass theorem for asymptotically flat and asymptotically hyperboloidal initial data sets …
We study the temporal-spatial regularity properties of tamed Euler approximations for L\'evy-driven SDEs with superlinearly growing drift and diffusion coefficients. We first introduce a novel tamed E…
We study a parametrized family of strong maximal fractional operators. We prove their $L^p$ to $L^q$ boundedness for $1<p\le q<\infty$.…
Suppose that $M$ is a closed manifold of dimension greater than two and $r\geq 2$. We show that there exists a $C^r$-diffeomorphism $f:M\longrightarrow M$ with a wild affine blender-horseshoe $\Lambda…
Since the pioneering work of Korteweg (1901) and the subsequent refinement of capillary fluid models by Dunn and Serrin (1985), the global existence of strong solutions to the multi-dimensional compre…
Let $A:=\mathbb{C}[z_+,z_-]\otimes \Lambda(\theta_1,\theta_2,\theta_3)$, with $z_\pm$ even and $\theta_1,\theta_2,\theta_3$ odd. For a reductive Lie algebra $\mathfrak g$, let $\mathfrak g[A]:=\mathfr…
We establish regularity results for viscosity solutions to a class of quasilinear parabolic equations exhibiting nonhomogeneous degeneracy or singularity (a double phase regime) of the form \[ u_t - \…
The authors previously formulated the hybrid conjecture, unifying Andr\'e-Pink-Zannier and Andr\'e-Oort conjectures, and proved it in Shimura varieties of abelian type. We study its analogue for mixed…
The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Ho…
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