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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 ...
Two families A and B, of k-subsets of an n-set are called cross intersecting if A boolean AND B not equal phi for all A,B epsilon b. Strengthening the classical ErclOs-Ko-Rado theorem, Pyber proved that vertical bar A vertical bar vertical bar B vertical b ...
Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence the ellipticity ...
We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions (Invent Math 98:511-547, 1989) proved that, when the damping term is bounded in space and time, the equation is well posed i ...
CORPORA DELICTI, The Significant Detail. The Corpus Delicti is the evidence of a crime. The term denotes the formation of a proof that allows the unmasking of a perpetrator. In the realm of interpretation and language, it could reveal matter on which an ac ...
In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theories for ODE's, by developing a local version of the DiPerna-Lions theory. More precisely, we prove the existence and uniqueness of a maximal regular flow fo ...
Wearable robots can assist motor-impaired individuals in activities of daily living, but weight is paramount for usability. Proximally placed actuators and remote actuation systems (RAS) minimize weight on users' extremities. State-of-the-art RAS employ pn ...
Given the contact forms f and g, and the 1-form h, we discuss the existence of a vector field u verifying L-u(f)= d(u (right perpendicular) f)+ u (right perpendicular) df = h. This is closely related to the pullback equation, where we seek for a diffeomorp ...
We show that Hopfield neural networks with synchronous dynamics and asymmetric weights admit stable orbits that form sequences of maximal length. For N units, these sequences have length T = 2^N; that is, they cover the full state space. We present a mathe ...
A novel dual-band polarization-independent transmitarray is introduced in this paper for communication systems in Ka-band. Thanks to its unit-cell topology, the transmitarray antenna demonstrates almost complete independent performance at two design freque ...