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Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...
The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...
Polymers with high surface electric insulation capability are greatly demanded in various electrical devices operating in vacuum ambient. Low secondary electron emission (SEE) is favorable to mitigate vacuum flashover by inhibiting the SEE avalanche across ...
We study the regularity of the regular and of the singular set of the obstacle problem in any dimension. Our approach is related to the epiperimetric inequality of Weiss (Invent Math 138:23-50, Wei99a), which works at regular points and provides an alterna ...
The efficient and bioorthogonal chemical ligation reaction between potassium acyltrifluoroborates (KATs) and hydroxylamines (HAs) was used for the surface functionalization of a self-assembled monolayer (SAM) with biomolecules. An alkane thioether molecule ...
We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that split ...
Tolerancing is an important step toward the fabrication of high-quality and cost-effective lens surfaces. It is critical for wafer-level optics, when up to tens of thousands microlenses are fabricated in parallel and whose surfaces cannot be formed individ ...
Wear of materials plays a key role in the durability of manifactured objects and it has thus an economical importance in our society. In spite of the efforts, a unified picture of the underlying physics of the phenomenon is still far from being reached, be ...
2018
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We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient di ...
Deciphering the calcium silicate hydrate (C-S-H) surface is crucial for unraveling the mechanisms of cement hydration and property development. Experimental observations of C-S-H in cement systems suggest a surface termination which is fundamentally differ ...