Related papers: On an upper bound of the set of copulas with a giv…

We answer a 15-year-old open question about the exact upper bound for bivariate copulas with a given diagonal section by giving an explicit formula for this bound. As an application, we determine the maximal asymmetry of bivariate copulas…

Making use of the total variation of particular functions, we give an explicit formula for the pointwise supremum of the set of all copulas with a given curvilinear section. When the pointwise supremum is a copula is characterized. We also…

In this paper, we present a family of bivariate copulas by transforming a given copula function with two increasing functions, named as transformed copula. One distinctive characteristic of the transformed copula is its singular component…

Bivariate copulas with prescribed diagonal section were first studied by Bertino. Their maximality was studied so far only from the point of view of upper bounds which brings quasi-copulas into the picture and limits the resulting set…

In this paper, we investigate several subsets of $n$-copulas and $n$-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain…

Copulas are known to satisfy a number of regularity properties, and one might therefore believe that their densities, when they exist, admit a certain degree of regularity themselves. We show that this is not true in general by constructing…

In this note, pointwise best-possible (lower and upper) bounds on the set of copulas with a given value of the Gini's gamma coefficient are established. It is shown that, unlike the best-possible bounds on the set of copulas with a given…

We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a…

An upper bound of composition series of groups of finite order is obtained. The bound is a nontrivial bound and so far best possible.

We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We…

We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results.

The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…

Finding upper and lower bounds to integrals with respect to copulas is a quite prominent problem in applied probability. In their 2014 paper, Hofer and Iaco showed how particular two dimensional copulas are related to optimal solutions of…

We show that the lower and upper Frech\'{e}t-Hoeffding copulas, which are singular, can be regularized to absolutely continuous copulas. The method, which is constructive and explicit, states sufficient conditions for when an absolutely…

In this paper we study genus-$4$ curves obtained as double covers of elliptic curves. Firstly we shall give explicit defining equations of such curves with explicit criterion for whether it is nonsingular, and show the irreducibility of the…

The main aim of the note is to provide an upper-bound for the characteristic number of conic-line arrangements with ordinary singularities in the complex projective plane.

We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries

We study typical wall singularity of codimension one for locally compact geodesically complete metric spaces with an upper curvature bound. We provide a geometric structure theorem of codimension one singularity, and a geometric…

The existence of a uniform upper bound for the maximum number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line has been subject of interest of hundreds of papers. After more than 30…

In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…