Results 31 to 40 of about 944 (165)

Optical properties of null geodesics emerging from dynamical systems

European Physical Journal C: Particles and Fields, 2022
We study optical metrics via null geodesics as a central force system, deduce the related Binet equation and apply the analysis to certain solutions of Einstein’s equations with and without spherical symmetry.
D. Batic, S. Chanda, P. Guha
doaj   +1 more source

Binomial transform of the bivariate Fibonacci quaternion polynomials and its properties [PDF]

Notes on Number Theory and Discrete Mathematics
The primary aim of this work is to deal with binomial transforms of bivariate Fibonacci quaternion polynomial sequence. The binomial sequence of the bivariate Fibonacci quaternion polynomial is found, and then results are obtained for the recurrence ...
Faruk Kaplan, Arzu Özkoç Öztürk
doaj   +1 more source

The complex-type Pell p-numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define the complex-type Pell p-numbers and give the generating matrix of these defined numbers. Then, we produce the combinatorial representation, the generating function, the exponential representation and the sums of the complex-type ...
Yeşim Aküzüm, Hüseyin Aydın, Ömür Deveci   +2 more
doaj   +1 more source

On an application of Binet’s second formula

Proceedings of the American Mathematical Society, 2017
In this work we apply the second Binet formula for Euler’s gamma function Γ (
openaire   +1 more source

On fourth-order jacobsthal quaternions

Journal of Mathematical Sciences and Modelling, 2018
In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula,
Gamaliel Cerda-morales
doaj   +1 more source

A Context-Free Grammar Associated with Fibonacci and Lucas Sequences

Journal of Mathematics, 2023
We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
doaj   +1 more source

Horadam Octonions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
In this paper, first we define Horadam octonions by Horadam sequence which is a generalization of second order recurrence relations. Also, we give some fundamental properties involving the elements of that sequence.
Karataş Adnan, Halici Serpil
doaj   +1 more source

On a generalization of the Gadovan numbers [PDF]

Mathematica Moravica
In this paper, we define (k, l)-Gadovan numbers. We give the Binet-like formula, the generating functions, the exponential generating function of the (k, l)-Gadovan numbers. Also, we derive Cassinilike identity, Catalan-like identity, Vajda-like identity,
Özkan Engın, Eser Engın, Uysal Mıne
doaj   +1 more source

A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
doaj   +1 more source

Animal Logic: Locke and the Nature of Inference

Noûs, EarlyView.
ABSTRACT Can animals reason? If so, what would their reasoning consist in, and how, if at all, would it differ from its human counterpart? On these questions, John Locke stakes out a position that also merits consideration today. I argue that, for Locke, reasoning is a matter of the subject's construing her mental states as support for a conclusion ...
Walter Ott
wiley   +1 more source