We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux...
We study an elliptic-parabolic system of partial differential equations describing formation of biological network structures. The model takes into consideration the evolution of the permeability tensor under the influence of a diffusion term, repres...
Nonlinear effects were observed in a forced vibrating string. The motion of the string becomes elliptic as the amplitude of the vibration increases. The fundamental resonance frequency depends on the amplitude of the vibration. At sufficient high a...
A companion repository to "A low-rank ensemble Kalman filter for elliptic observations" by Le Provost et al. (2022) (⭐ 7)
Over a field $k$, we study rational UFDs of finite transcendence degree $n$ over $k$. We classify such UFDs $B$ when $n=2$, $k$ is algebraically closed, and $B$ admits a positive $\mathbb{Z}$-grading, showing in particular that $B$ is affine over $k$...
A 1976 conjecture of Halperin on positively elliptic spaces was recently confirmed in formal dimensions up to 16. In this article, we shorten the proof and extend the result up to formal dimension 20. We work with Meier's algebraic characterization o...
This paper presents a general technique for the joint Direction-of-Arrival (DoA) and Time-of-Arrival (ToA) estimation in multipath environments. The proposed ultra-wideband technique is based on phase-mode expansions and the use of nearly frequency-i...
We consider the problem of the real analytic dependence of the accessory parameters of Liouville theory on the moduli of the problem, for general elliptic singularities. We give a simplified proof of the almost everywhere real analyticity in the case...
We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic,...
The Krylov-Safonov theorem says that solutions to non-divergence uniformly elliptic equations with rough coefficients are Hölder continuous. The proof combines a basic measure estimate with delicate localization and covering arguments. Here we give...
We establish quantitative bounds for Hölder exponents in the Krylov--Safonov and Evans--Krylov theories when the ellipticity ratio is close to one. Our analysis relies on the Ishii--Lions method for the Krylov--Safonov theory and a Schauder-type per...
Let $K$ be an imaginary quadratic field and $p$ be an odd prime which splits in $K$. Let $E_1$ and $E_2$ be elliptic curves over $K$ such that the $Gal(\bar{K}/K)$-modules $E_1[p]$ and $E_2[p]$ are isomorphic. We show that under certain explicit addi...
We consider a random walk in a stationary ergodic environment in $\mathbb Z$, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right which impli...
This paper is devoted to a coordinate-free approach to several classic geometries such as hyperbolic (real, complex, quaternionic), elliptic (spherical, Fubini-Study), and lorentzian (de Sitter, anti de Sitter) ones. These geometries carry a certain...
We consider a family of gradient Gaussian vector fields on $\Z^d$, where the covariance operator is not translation invariant. A uniform finite range decomposition of the corresponding covariance operators is proven, i.e., the covariance operator can...
We study the essential minimum of the (stable) Faltings height on the moduli space of elliptic curves. We prove that, in contrast to the Weil height on a projective space and the N{é}ron-Tate height of an abelian variety, Faltings' height takes at l...
There exist a number of experiments/applications where the second dimension of the bore of Bitter magnets is not fully utilized. Using an analytical solution for elliptical bore coils, we show that reducing one of the dimensions of the bore can lead...
We exploit the so called atomic condition, recently defined by De Philippis, De Rosa, and Ghiraldin in [Comm. Pure Appl. Math.] and proved to be necessary and sufficient for the validity of the anisotropic counterpart of the Allard rectifiability the...
YanYan Li (also stylized as Yanyan Li, Yan-yan Li, and Yan Yan Li) is a distinguished professor of mathematics at Rutgers University, specializing in elliptic
For a quartic primitive CM field $K$, we say that a rational prime $p$ is {\it evil} if at least one of the abelian varieties with CM by $K$ reduces modulo a prime ideal $\gerp| p$ to a product of supersingular elliptic curves with the product pola...