We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...
In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...
Frustrated Lewis pairs (FLPs), featuring reactive combinations of Lewis acids and Lewis bases, have been utilized for myriad metal-free homogeneous catalytic processes. Immobilizing the active Lewis sites to a solid support, especially to porous scaffolds, ...
The constant urge to construct new molecules in an economical and sustainable fashion led to the development of numerous metal-catalyzed transformations. Organocatalysts consisting of abundant and more sustainable elements offer an elegant solution to over ...
Bicyclic carbocycles containing a high fraction of Csp3 have become highly attractive synthetic targets because of the multiple applications they have found in medicinal chemistry. The formal cycloaddition of bicyclobutanes (BCBs) with two- or three-atom p ...
Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions.
Central to effective decision-making is the discipline of optimization, which seeks th ...
Image information about the state of a building after an earthquake, which can be collected without endangering the post-earthquake reconnaissance activities, can be used to reduce uncertainties in response predictions for future seismic events. This paper ...
Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
The alkyne motif is a versatile functional group often encountered in organic chemistry. It can be involved in various transformations such as the alkyne-azide cycloaddition and has found widespread application in medicinal chemistry, chemical biology and ...
We prove that the set of-y-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all-y =6 0. Our proof relies on the coupling between a GFF and the nested CLE4. In particular, we show that th ...
