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Keywords = q-Catalan numbers

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18 pages, 297 KB  
Article
On Bicomplex (p,q)-Fibonacci Quaternions
by Çağla Çelemoğlu
Mathematics 2024, 12(3), 461; https://doi.org/10.3390/math12030461 - 31 Jan 2024
Cited by 2 | Viewed by 1216
Abstract
Here, we describe the bicomplex p,q-Fibonacci numbers and the bicomplex p,q-Fibonacci quaternions based on these numbers to show that bicomplex numbers are not defined the same as bicomplex quaternions. Then, we give some of their equations, including [...] Read more.
Here, we describe the bicomplex p,q-Fibonacci numbers and the bicomplex p,q-Fibonacci quaternions based on these numbers to show that bicomplex numbers are not defined the same as bicomplex quaternions. Then, we give some of their equations, including the Binet formula, generating function, Catalan, Cassini, and d’Ocagne’s identities, and summation formulas for both. We also create a matrix for bicomplex p,q-Fibonacci quaternions, and we obtain the determinant of a special matrix that gives the terms of that quaternion. With this study, we get a general form of the second-order bicomplex number sequences and the second-order bicomplex quaternions. In addition, we show that these two concepts, defined as the same in many studies, are different. Full article
7 pages, 403 KB  
Proceeding Paper
Sons al Balcó: A Subjective Approach to the WASN-Based LAeq Measured Values during the COVID-19 Lockdown
by Enric Dorca, Daniel Bonet-Solà, Pau Bergadà, Carme Martínez-Suquía and Rosa Ma Alsina-Pagès
Eng. Proc. 2023, 58(1), 124; https://doi.org/10.3390/ecsa-10-16241 - 15 Nov 2023
Cited by 1 | Viewed by 596
Abstract
The lockdown in Spain due to COVID-19 caused a strong decrease in the urban noise levels observed in most cities, clearly followed in the case that these cities had acoustic sensor networks deployed. This fact had an impact on people’s lives, who, at [...] Read more.
The lockdown in Spain due to COVID-19 caused a strong decrease in the urban noise levels observed in most cities, clearly followed in the case that these cities had acoustic sensor networks deployed. This fact had an impact on people’s lives, who, at that time, were mainly locked at home due to health reasons. In this paper, we present a qualitative analysis of the subjective vision of the citizens participating in a data-collecting campaign during the COVID-19 lockdown in Girona, a Catalan city, named ‘Sons al Balcó’. The alignment of the subjective data gathered was too scarce to conduct final conclusions, but already giving a bias of the results indicates that the objective LAeq measurements, which showed a clear decrease in noise in the streets during the lockdown, were supported by the fact that new sounds found during the lockdown were not very annoying. Former existing noise sources, such as road traffic noise or leisure noise, are depicted as annoying but their decrease during the lockdown improved the soundscape of many homes. This paper’s goal is to show the possibility of gathering both objective and calibrated data with perceptive approximation for the first time in ‘Sons al Balcó’, and how this supports our conclusions, in survey with a limited number of participants conducted during the 2020 lockdown period in Catalonia. Full article
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10 pages, 256 KB  
Article
A Note on q-analogue of Degenerate Catalan Numbers Associated with p-adic Integral on Zp
by Waseem A. Khan
Symmetry 2022, 14(6), 1119; https://doi.org/10.3390/sym14061119 - 29 May 2022
Cited by 18 | Viewed by 1632
Abstract
In this paper, we introduce q-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic p-adic q-integrals on Zp and establish some new connections with the degenerate Stirling numbers of the first and second kinds. Furthermore, [...] Read more.
In this paper, we introduce q-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic p-adic q-integrals on Zp and establish some new connections with the degenerate Stirling numbers of the first and second kinds. Furthermore, we also find a few new identities and results of this type of polynomials and numbers. Full article
7 pages, 248 KB  
Article
Some Identities on the Twisted q-Analogues of Catalan-Daehee Numbers and Polynomials
by Dongkyu Lim
Axioms 2022, 11(1), 9; https://doi.org/10.3390/axioms11010009 - 23 Dec 2021
Viewed by 2422
Abstract
In this paper, the author considers twisted q-analogues of Catalan-Daehee numbers and polynomials by using p-adic q-integral on Zp. We derive some explicit identities for those twisted numbers and polynomials related to various special numbers and polynomials. Full article
(This article belongs to the Special Issue p-adic Analysis and q-Calculus with Their Applications)
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