Related papers: Complex Box Splines
We present a completeness characterization of box splines on three-directional triangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties. For any given Type-I box spline, of specific maximum degree…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.
An alternate definition of the box-counting dimension is proposed, to provide a better approximation for fractals involving rotation such as the 'Bradley Spiral' structure. A curve fitting comparison of this definition with the box-counting…
The current article studies certain problems related to complex cycles of holomorphic foliations with singularities in the complex plane. We focus on the case when polynomial differential one-form gives rise to a foliation by Riemann…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite…
We observe algebraic derivations on an affine domain B defined over an algebraically closed field of characteristic 0, which are called locally finite derivations in commutative and non-commutative contexts in other references. We observe…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…
We compute the degree complexity of a family of birational mappings of the plane with high order singularities.
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
In this paper we investigate complex dynamics in infinite dimensions.
In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is a new framework that includes fractal fuzzy…
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…
Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not…
Here we look at some situations that are like the unit circle or the real line in some ways, but which can be more complicated or fractal in other ways.
The article reviews some of the (fairly scattered) information available in the mathematical literature on the subject of angles in complex vector spaces. The following angles and their relations are considered: Euclidean, complex, and…
There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…