Related papers: Complex Box Splines
Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose…
In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…
Let $X$ be a real algebraic variety with set of complex points $X_{\mathbb C}$ and set of real points $X_{\mathbb R}$. A complex slice of $X$ is a transverse intersection of $X_{\mathbb R}$ with a complex subvariety $V$ of $X_{\mathbb C}$.…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
We introduce complex order fractional derivatives in models that describe viscoelastic materials. This can not be carried out unrestrictedly, and therefore we derive, for the first time, real valued compatibility constraints, as well as…
Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions…
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
In this paper, we introduce the new class of twisted $B$-splines and study some properties of these B-splines. We also investigate the system of twisted translates and the wavelets corresponding to these twisted $B$-splines.
We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…
A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the…
In this note several computations of equivariant cohomology groups are performed. For the compactly supported equivariant cohomology, the notion of infinitesimal index developed in arXiv:1003.3525, allows to describe these groups in terms…
The fractal and self-similarity properties are revealed in many real complex networks. However, the classical information dimension of complex networks is not practical for real complex networks. In this paper, a new information dimension…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.
In this paper we study analogues of the perfect splines for weighted Sobolev classes of functions defined on the half-line. Maximally oscillating splines play important role in the solution of certain extremal problems. In particular, using…
In this paper we prove complex bounds, also referred to as a priori bounds, for real analytic (and even C3) interval maps. This means that we associate to such a map a complex box mapping (which provides a kind of Markov structure),…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…