Related papers: Complex Box Splines
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
We introduce a symmetry class for higher dimensional partitions - fully complementary higher dimensional partitions (FCPs) - and prove a formula for their generating function. By studying symmetry classes of FCPs in dimension 2, we define…
Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
In this paper we characterize, in two different ways, the Newton polygons which are jacobian Newton polygons of a branch. These characterizations give in particular combinatorial criteria of irreducibility for complex series in two…
In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…
Integer partitions express the different ways that a positive integer may be written as a sum of positive integers. Here we explore the analytic properties of a new polynomial $f_\lambda(x)$ that we call the partition polynomial for the…
In this paper we consider a class of piecewise affine Hamiltonian vector fields whose orbits are piecewise straight lines. We give a first classification result of such systems and show that the orbit-structure of the flow of such a…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
We propose a construction of affine space (or "polynomial rings") over a triangulated category, in the context of stable derivators.
We review some semantic and syntactic complexity classes that were introduced to better understand the relationship between complexity classes P and NP. We also define several new complexity classes, some of which are associated with…
In the current article we study complex cycles of higher multiplicity in a specific polynomial family of holomorphic foliations in the complex plane. The family in question is a perturbation of an exact polynomial one-form giving rise to a…
We define the notion of complex stratification by quasifolds and show that such spaces occur as complex quotients by certain nonclosed subgroups of tori associated to convex polytopes. The spaces thus obtained provide a natural…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
In this paper we investigate the relationships between envelopes of circle families and some special curves in the plane, such as evolutes, pedals, evolutoids and pedaloids.
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…