Stark-Heegner points are conjectural substitutes for Heegner points when the imaginary quadratic field of the theory of complex multiplication is replaced by a real quadratic field $K$. They are constructed analytically as local points on elliptic cu...
In this article we study the fundamental solutions or "$α$-harmonic functions" for some nonlinear positive homogeneous nonlocal elliptic problems in conical domains, such as \begin{eqnarray*}\label{ecbir1a1} {\mathcal F }(u)=0\ \ \hbox{in} \ \ \math...
Despite much work, the connection between dwarf elliptical galaxies (dEs) and dwarf irregulars (dIs) remains unclear. Recently, we found that the surface brightness profiles (SBPs) of dIs in the near-infrared can be well fitted with a hyperbolic se...
Goal of this paper is to study classes of Cauchy-Dirichlet problems which include parabolic equations of the type $$u_t -Δu= a(x,t)f(u)\quad\hbox{in $Ω\times(0,T)$}$$ with $Ω\subset\mathbb{R}^N$ bounded, convex domain and $T\in(0,+\infty]$. Under...
The main point of this paper is to prove the following useful result: If the almost everywhere 2-jet of a locally quasi-convex function u satisfies a degenerate elliptic constraint F, then u is F-subharmonic, i.e., u is a viscosity F-subsolution. Thi...
Whilst many key exchange and digital signature methods use the NIST P256 (secp256r1) and secp256k1 curves, there is often a demand for increased security. With these curves, we have a 128-bit security. These security levels can be increased to 256-bi...
We list up all the possible local orbit types of hyperbolic or elliptic orbits for the isotropy representations of semisimple pseudo-Riemannian symmetric spaces. It is key to give a recipe to determine the local orbit types of hyperbolic principal or...
We prove a semiclassical resolvent estimate for a broad class of non-self-adjoint, non-elliptic pseudodifferential operators in the low-lying spectral regime. The proof relies on improved ellipticity properties for the symbol of the operator, which w...
We discuss how the works of Yves Meyer, together with Raphy Coifman, on Calder{ó}n's program and singular integrals with minimal smoothness in the seventies, paved the way not only to a solution to Kato's conjecture for square roots of elliptic oper...
We generalise the Elliptical Range Theorem to characterise the numerical range of matrices belonging to a subspace of the space of \(3 \times 3\) matrices. Using Specht's Theorem, which characterizes when two matrices are unitarily equivalent, we the...
We propose a theoretical model of the light-induced director slippage effect. In this effect the bulk director reorientation contributes to the surface director reorientation It is found that the director and ellipticity profiles, obtained in the g...
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. T...
Label assignment is a crucial process in object detection, which significantly influences the detection performance by determining positive or negative samples during training process. However, existing label assignment strategies barely consider the...
Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication...
It is well-known that observability (and, by duality, controllability) of the elliptic wave equation, i.e., with a Riemannian Laplacian, in time $T_0$ is almost equivalent to the Geometric Control Condition (GCC), which stipulates that any geodesic...
In this paper, a theoretical framework is presented for the use of a Kansa-like method to numerically solve elliptic partial differential equations on spheres and other manifolds. The theory addresses both the stability of the method and provid...
For a semigroup $P_t$ generated by an elliptic operator on a smooth manifold $M$, we use straightforward martingale arguments to derive probabilistic formulae for $P_t(V(f))$, not involving derivatives of $f$, where $V$ is a vector field on $M$. For...
We study the j-invariant of the canonical lifting of an elliptic curve as a Witt vector. We prove that its Witt coordinates lie in an open affine subset of the j-line and deduce the existence of a universal formula for the j-invariant of the canonica...
Given an elliptic curve E1 over a number field and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over another ell...
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation