Related papers: The Algebraic Theory of Fractional Jumps
A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…
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…
Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…
Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which are obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given
Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…
In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional…
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
Here we construct the conformal mappings with the help of continuous fractions approximations. These approximations converge to the algebraic roots $\sqrt[N]{z}$ for $N \in \mathbb{N}$ and $z$ from the right half-plane of the complex plane.…
We work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs. The generalization is given in terms of homomorphism densities of finite trees and it is…
This article provides a gentle introduction for a general mathematical audience to the factorization theory of motion polynomials and its application in mechanism science. This theory connects in a rather unexpected way a seemingly abstract…
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…
Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential…
We use the Graph Minor Theorem to characterize infinite sequences of finite subsets of factorial and commutative semigroups (here semigroups have a unity element), e.g. the multiplicative semigroup of a unique factorization domain.
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…