Related papers: Bijectivity and trapping regions for complex conti…
This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of…
It is shown how dual space diagrammatic representation of momentum integrals corresponding to triangle ladder diagrams with an arbitrary number of rungs can be transformed to half-diamonds. In paper arXiv:0803.3420 [hep-th] the…
We study circle valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questions on persistence and in addition encode the topology of the…
We prove in this article the surjectivity of three maps. We prove in Theorem $1.6$ the surjectivity of the Chinese remainder reduction map associated to the projective space of an ideal with a given factorization into ideals whose radicals…
In this Letter we study the interactions of the dissipative domain walls with dielectric particles. It is shown that particles can be steadily trapped by the moving domain walls. The influence of the ratchet effect on particle trapping is…
Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate…
By extending the extreme learning machine by additional control inputs, we achieved almost complete reproduction of bifurcation structures of dynamical systems. The learning ability of the proposed neural network system is striking in that…
In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if $E$ is any arithmetic progression, the set of primes, or the set of squares…
We find a Thron-type continued fraction (T-fraction) for the ordinary generating function of the Ward polynomials, as well as for some generalizations employing a large (indeed infinite) family of independent indeterminates. Our proof is…
Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show that two-dimensional continuous piecewise-linear maps near…
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the…
We will cover the basics of several complex variables in 4 lectures: Basic properties of holomorphic functions in several variables, the notion of pseudoconvexity, CR functions and CR geometry, and the $\bar\partial$-problem. The main…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
The Sinkhorn algorithm has emerged as a powerful tool for solving optimal transport problems, finding applications in various domains such as machine learning, image processing, and computational biology. Despite its widespread use, the…
For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
This paper aims to introduce high school students to the intriguing world of continued fractions, a mathematical concept that provides a unique representation of numbers. The study focuses on the exploration and development of the…