Related papers: The Dynamics of the Fibonacci Partition Function
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems…
Quark-hadron duality is studied in a systematic way for both the unpolarized and polarized structure functions, by taking into account all the available data in the resonance region.In both cases, a detailed perturbative QCD based analysis…
We characterize the regularity of an FI-module using the derivative functors.
The classical Fibonacci sequence is known to exhibit many fascinating properties. In this paper, we explore the Fibonacci sequence and integer sequences generated by second order linear recurrence relations with positive integer…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
The fragmentation processes of exchangeable partitions have already been studied by several authors. In this paper, we examine rather fragmentation of exchangeable compositions, that means partitions of $\mathbb{N}$ where the order of the…
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of the corresponding lie algebras.
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.
Several sets of quaternionic functions are described and studied with respect to hyperholomorphy, addition and (non commutative) multiplication, on open sets of $\mathbb H$. The aim is to get a local function theory.
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
The purpose of this article is to review the developments related to the notion of local fractional derivative introduced in 1996. We consider its definition, properties, implications and possible applications. This involves the local…
We study compositions whose parts are colored by subsequences of the Fibonacci numbers. We give explicit bijections between Fibonacci colored compositions and several combinatorial objects, including certain restricted ternary and…
For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that…
We outline a method of calculation of partition functions of orientable manifolds with fluctuating metric and perform the calculation for the specific case of the unit interval.
The study of nonlocal operators of fractional type possesses a long tradition, motivated both by mathematical curiosity and by real world applications...
We study radial behavior of harmonic functions in the unit disk belonging to the Korenblum class. We prove that functions which admit two-sided Korenblum estimate either oscillate or have slow growth along almost all radii.