Related papers: Fibonacci Numbers, Statistical Convergence and App…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
A Turing machine that computes Fibonacci numbers is described.
We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…
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…
The Fibonacci numbers satisfy the famous recurrence $F_n = F_{n - 1} + F_{n - 2}$. The theory of C-finite sequences ensures that the Fibonacci numbers whose indices are divisible by $m$, namely $F_{mn}$, satisfy a similar recurrence for…
Let $ k \geq 2 $ be an integer. The $ k- $generalized Fibonacci sequence is a sequence defined by the recurrence relation $ F_{n}^{(k)}=F_{n-1}^{(k)} + \cdots + F_{n-k}^{(k)}$ for all $ n \geq 2$ with the initial values $ F_{i}^{(k)}=0 $…
The aim of the paper is to establish a convergence theorem for multi-dimensional stochastic approximation when the "innovations" satisfy some "light" averaging properties in the presence of a pathwise Lyapunov function. These averaging…
In this paper, we first study convergence rates in the law of large numbers for independent and identically distributed random variables. We obtain a strong $L^p$-convergence version and a strongly almost sure convergence version of the law…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
Our main aim is to investigate the approximation properties for the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of…
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the classical \emph{O$ (\cdot ) $} and \emph{o$ (\cdot ) $} notation…
In 2013, Conway and Ryba wrote a fascinating paper called Fibonometry. The paper, as one might guess, is about the connection between Fibonacci numbers and trigonometry. We were fascinated by this paper and looked at how we could generalize…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many…
A review of the superstatistics concept is provided, including various recent applications to complex systems.
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…