Related papers: Adventitious angles problem: the lonely fractional…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
Let $A$ be a commutative ring with unity and $B = A[\theta]$ be an integral extension of $A$. Assume that $B$ is an integral domain with quotient field $\mathbb{K}$ and $\mathbb{E}$ is the minimal splitting field of $\theta$ over…
Both null and timelike rays experience trajectory bending in a gravitational field. In this work, we systematically develop a perturbative method to compute the deflection angle of rays with general velocity $v$ in arbitrary static and…
In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional…
In this note we focus on the defect of singular plane curve that was recently introduced by Dimca. Roughly speaking, the defect of a reduced plane curve measures the discrepancy from the property of being a free curve. We find some…
The orienteering problem is a route optimization problem which consists in finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in…
In this article we consider the problem of finding the visibility set from a given point when the obstacles are represented as the level set of a given function. Although the visibility set can be computed efficiently by ray tracing, there…
The formula for the dihedral angle of the simplex of n dimensions, arccos(1/n), is derived using classical geometry.
Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint. In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of…
Building on work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel'fond's transcendence criterion which provides a sufficient condition for a complex or $p$-adic number $\xi$ to be algebraic in terms…
In this paper, we consider the bifurcation problem for fractional Laplace equation \begin{eqnarray*} \begin{array}{ll} (-\Delta)^{s} u = \lambda u + f(\lambda,\,x,\,u)& \mbox{in }\Omega, u = 0 &\mbox{in }\mathbb{R}^n\backslash \Omega,…
The purpose of this paper is to study low degree points on plane curves. We prove results analogous to those of Debarre and Klassen for singular plane curves with a finite number $\delta$ of ordinary nodes/cusps, where $\delta$ is bounded…
In this paper we study the most-demanding predicate for computing the Euclidean Voronoi diagram of axes-aligned line segments, namely the Incircle predicate. Our contribution is two-fold: firstly, we describe, in algorithmic terms, how to…
The degree-diameter problem asks for the maximum number of vertices in a graph with maximum degree $\Delta$ and diameter $k$. For fixed $k$, the answer is $\Theta(\Delta^k)$. We consider the degree-diameter problem for particular classes of…
The fractional Calder\'on problem asks to determine the unknown coefficients in a nonlocal, elliptic equation of fractional order from exterior measurements of its solutions. There has been substantial work on many aspects of this inverse…
We examine the task of locating a target region among those induced by intersections of $n$ halfspaces in $\mathbb{R}^d$. This generic task connects to fundamental machine learning problems, such as training a perceptron and learning a…
We study the discriminant of a degree 4 extension given by a deformed bidouble cover, i.e., by equations z^2= u + a w, w^2= v + bz. We first show that the discriminant surface is a quartic which is cuspidal on a twisted cubic, i.e.,is the…
We extend to higher order a recently published method for calculating the deflection angle of light in a general static and spherically symmetric metric. Since the method is convergent we obtain very accurate analytical expressions that we…
This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral…
A nontrivial solution of the equation A!B! = C! is a triple of positive integers (A, B, C) with A $\le$ B $\le$ C -- 2. It is conjectured that the only nontrivial solution is (6, 7, 10), and this conjecture has been checked up to C = 10 6.…