Related papers: Continuous limits of discrete perimeters
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
Inside the symmetric product of a very general curve, we consider the codimension-one subvarieties of symmetric tuples of points imposing exceptional secant conditions on linear series on the curve of fixed degree and dimension. We compute…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
In this article we present certain formulas involving arithmetical functions. In the first part we study properties of sums and product formulas for general type of arithmetic functions. In the second part we apply these formulas to the…
In this paper, we deals with isoperimetric-type inequalities for closed convex curves in the Euclidean plane R^2. We derive a family of parametric inequalities involving the following geometric functionals associated to a given convex curve…
We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…
A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.
This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…
We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^2$, with respect to some asymmetric norms. We allow the boundary of the domain to have corners. We obtain an explicit formula for the second…
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…
We study a discrete approximation of functionals depending on nonlocal gradients. The discretized functionals are proved to be coercive in classical Sobolev spaces
We compute the limits of a class of continued radicals extending the results of a previous note in which only periodic radicals of the class were considered.
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $\mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.
In this paper, we describe the structure of shape derivatives around sets which are only assumed to be of finite perimeter in $\R^N$. This structure allows us to define a useful notion of positivity of the shape derivative and we show it…
We give a classification of generic coadjoint orbits for the group of area-preserving diffeomorphisms of a closed non-orientable surface. This completes V. Arnold's program of studying invariants of incompressible fluids in 2D. As an…
We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…