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We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some projective space up to projective equivalence via geometric invariant theory (GIT). We provide an explicit criterion that solves the problem…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.
Metasurfaces represent a powerful paradigm of optical engineering that enables one to control the flow of light across material interfaces. We report on a discovery that metallic metasurfaces of a certain type respond differently to…
We show that the open-loop transfer functions and the stability margins may be defined within the recent model-free control setting. Several convincing computer experiments are presented including one which studies the robustness with…
This paper is concerned with the structural stability of spherical horizons. By this we mean stability with respect to variations of the second member of the corresponding differential equations, corresponding to the inclusion of the…
The relation between differential geometry of surfaces and some Heisenberg ferromagnet models is considered.
A simple model for solid friction is analyzed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal…
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
In this article, we investigate Serrano's conjecture for strictly nef divisors on projective bundles over higher dimensional smooth projective varieties.
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
This article is a continuation of a previous article which concerned the splitting problem for subspaces of superspaces. We begin with a general account of projective superspaces. Subsequently, we specialise to subvarieties of `positive'…
In this article, we developed and analyzed a thresholding method in which soft thresholding estimators are independently expanded by empirical scaling values. The scaling values have a common hyper-parameter that is an order of expansion of…
In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.
We investigate the regularity of the free boundaries in the 3 elastic membranes problem. We show that the two free boundaries corresponding to the coincidence regions between consecutive membranes are $C^{1,\log}$-hypersurfaces near a…
Several workers have established that the Larkin domains for two three dimensional nonmetallic elastic solids in contact with each other at a disordered interface are enormously large. This implies that there should be negligible static…
A plane curve on a the projective space over a field of characteristic zero is free if its associated sheaf T of tangent vector fields tangent is a free module. Relatively few free curves are known. Here we prove that a divisor consisting…
For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
Given an endomorphism f of projective space, we exhibit explicit bounds on the difference between the naive height of a divisor and its canonical height relative to f.