Related papers: On the Directonal Derivative Sets and Differential…
We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of roots of unity.
Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of rooted trees a linear map on the noncommutative polynomial algebra in two letters. Evaluated at any admissible word these maps induce linear relations between…
We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…
Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann-Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their…
One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce…
We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete,…
We investigate the initial value problems for non-homogeneous linear differential equations whose solutions are set-valued maps taking values in the space of nonempty compact convex subsets of $\mathbb{R}^2$, denoted by…
We study the set of all determinants of adjacency matrices of graphs with a given number of vertices.
We give a derivation of conductivities in certain classes of graphs based on knowing certain subdeterminants of the response matrix, mainly utilizing the boundary edge and boundary spike formulas given in Curtis' and Morrow's book.
For the dynamics of a discontinuous map on a compact metric space, we describe an approach using suitable closed relations and connect it with the continuous dynamics on an invariant G-delta subset and with the continuous dynamics on the…
We develop a notion of (principal) differential rank for differential-valued fields, in analog of the exponential rank and of the difference rank. We give several characterizations of this rank. We then give a method to define a derivation…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
We formalize the concept of sheaves of sets on a model site by considering variables thereof, or motifs, and we construct functorially defined derived algebraic stacks from them, thereby eliminating the necessity to choose derived…
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…
We investigate the plane dynamical system given by the secant map applied to a polynomial $p$ having at least one multiple root of multiplicity $d>1$. We prove that the local dynamics around the fixed points associated to the roots of $p$…
The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…
We outline the construction of differential invariants for higher--rank tensors.
We introduce and study the notion of a directional complexity and entropy for maps of degree 1 on the circle. For piecewise affine Markov maps we use symbolic dynamics to relate this complexity to the symbolic complexity. We apply a…
This paper points out the usefulness of the concept of derivation along a map in many problems in Geometry and Physics. In particular it will be shown that this approach allows us to translate the usual concepts arising in Geometrical…
Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…