Related papers: Hidden Convexity in the l0 Pseudonorm

This article presents a novel and practically useful link between geometric integration, low-discrepancy sampling and code coupling for Lagrangian and Eulerian Vlasov-Poisson solvers. Low-discrepancy sequences, also called quasi-random…

This paper is about hypersurfaces with boundary lying in the Euclidean unit ball, which meet the unit sphere at a fixed angle $\theta\in(0,\frac{\pi}{2}]$. Such hypersurfaces are called $\theta$-capillary hypersurfaces and for those we…

We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…

We describe the structure of Hausdorff locally compact semitopological $0$-bisimple inverse $\omega$-semigroups with compact maximal subgroups. In particular, we show that a Hausdorff locally compact semitopological $0$-bisimple inverse…

A one band Hubbard model with intermediate coupling is shown to describe the two most important unusual features of a normal state: linear resistivity strange metal and the pseudogap. Both the spectroscopic and transport properties of the…

We study how the existence of a negatively pinched K\"ahler metric on a domain in complex Euclidean space restricts the geometry of its boundary. In particular, we show that if a convex domain admits a complete K\"ahler metric, with pinched…

Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…

We study minimal Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric whose first normal space is two-dimensional and whose Gauss curvature $K$ and normal curvature $\varkappa$ satisfy the inequality $K^2-\varkappa^2 >0$.…

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to…

After reviewing the underlying algebraic structures we give a unified realization of split exceptional groups F_{4(4)},E_{6(6)}, E_{7(7)}, E_{8(8)} and of SO(n+3,m+3) as quasiconformal groups that is covariant with respect to their…

We consider a Pfaffian system expressing isomonodromy of an irregular system of Okubo type, depending on complex deformation parameters u=(u_1,...,u_n), which are eigenvalues of the leading matrix at the irregular singuilarity. At the same…

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…

In the paper we investigate topological properties of a topological Brandt $\lambda^0$-extension $B^0_{\lambda}(S)$ of a semitopological monoid $S$ with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff…

Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…

We present the first demonstration of vortices in an electron-type cuprate superconductor, the highest $T_c$ (= 43 K) electron-type cuprate $Sr_{0.9}La_{0.1}CuO_2$. Our spatially resolved quasiparticle tunneling spectra reveal a hidden…

For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional subbuildings $A$ of $\partial_{T}X$ that occur as the asymptotic boundary of closed convex subsets. In particular, we show that triviality of the holonomy of a…

We present arguments in favour of the inequalities $var(X_n^2|X \in B_v(\rho)) \le 2\lambda_n E[X_n^2|X \in B_v(\rho)]$, where $X \sim N_v(0,\Lambda)$ is a normal vector in $v\ge 1$ dimensions, with zero mean and covariance matrix $\Lambda…

Properties of two classes of generally convex sets in the n-dimentional real Euclidean space, called m-semiconvex and weakly m-semiconvex, 1<=m<n, are investigated in the present work. In particular, it is established that an open set with…

We prove a set of inequalities that interpolate the Cauchy-Schwarz inequality and the triangle inequality. Every nondecreasing, convex function with a concave derivative induces such an inequality. They hold in any metric space that…

We reveal the full energy-momentum structure of the pseudogap of underdoped high-Tc cuprate superconductors. Our combined theoretical and experimental analysis explains the spectral-weight suppression observed in the B2g Raman response at…