This paper shows that, for any given T-spline, the linear independence of its blending functions can be determined by computing the nullity of the T-spline-to-NURBS transform matrix. The paper analyzes the class of Tsplines for which no perpendicular T-node extensions intersect, and shows that the blending functions for any such T-spline are linearly independent.

The index of a compact orientable superminimal surface of a selfdual Einstein four-manifold M with positive scalar curvature is computed in terms of its genus and area. Also a lower bound of its nullity is obtained. Applications to the cases M = S4 and M = CP2 are given, characterizing the standard Veronese immersions and their twistor deformations as those with lowest index.

For a fixed positive integer , we consider the function of n that counts the number of elements of order in Zn. We show that the average growth rate of this function is C (logn) d( )−1 for an explicitly given constant C , where d( ) is the number of divisors of . From this we conclude that the average growth rate of the number of primitive Dirichlet characters modulo n of order is (d( )− 1)C (l...

In this contribution, we present some formalizations based on the HOL-Multivariate-Analysis session of Isabelle. Firstly, a generalization of several theorems of such library are presented. Secondly, some definitions and proofs involving Linear Algebra and the four fundamental subspaces of a matrix are shown. Finally, we present a proof of the result known in Linear Algebra as the “Rank-Nullity...

Abstract: This paper proposes a model of interactions between two point processes, ruled by a reproduction function h, which is considered as the intensity of a Poisson process. In particular, we focus on the context of neurosciences to detect possible interactions in the cerebral activity associated with two neurons. To provide a mathematical answer to this specific problem of neurobiologists,...