Results 41 to 50 of about 12,986 (183)
On an application of Binet’s second formula
Proceedings of the American Mathematical Society, 2017 Let \(f(x)= \int^\infty_0 ((\sin t)/(t+ x))\,dt\) and \(g(x)= \int^\infty_0 ((\cos t)/(t+ x))\,dt\). The author proves the following representation formulas: \[ \begin{aligned} f(2\pi) &= \pi \sum^\infty_{n=1} {\mu(n)\over n}\,\Biggl(\log\Gamma(nx)- nx\log(nx)+ nx-{1\over 2}\log\Biggl({2\pi\over nx}\Biggr)\Biggr)\qquad\text{and}\\ g(2\pi) &= {1\over 2}\
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
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A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity [PDF]
, 2013 We give a short proof of the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity {\em not} involving determinants.
Konstantopoulos, Takis
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Earth's Future, Volume 14, Issue 4, April 2026.Abstract Carbonate weathering carbon‐sink (CWCS) is a critical yet inaccurately quantified component of terrestrial carbon sequestration. However, the mechanisms through which climate change and vegetation dynamics drive the spatial heterogeneity of CWCS remain unclear.
Junhan Li +10 more
wiley +1 more source
On Some Properties of Tribonacci Quaternions
, 2017 In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for ...
Akkus, Ilker, Kizilaslan, Gonca
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Tribonacci and Tribonacci-Lucas Sedenions
, 2018 The sedenions form a 16-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tribonacci and Tribonacci-Lucas sedenions. Furthermore, we present some properties of these sedenions and derive relationships between them.Comment: 17 pages, 1 ...
Soykan, Yüksel
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Massive Spanning Forests on the Complete Graph: Exact Distribution and Local Limit
Random Structures &Algorithms, Volume 68, Issue 2, March 2026.ABSTRACT We provide new exact formulas for the distribution of massive spanning forests on the complete graph, which give also a new outlook on the celebrated special case of the uniform spanning tree. As a corollary we identify their local limit. This generalizes a well‐known theorem of Grimmett on the local limit of uniform spanning trees on the ...
Matteo D'Achille +2 more
wiley +1 more source
Generalized Bronze Leonardo sequence [PDF]
Notes on Number Theory and Discrete MathematicsIn this study, we define the Bronze Leonardo, Bronze Leonardo–Lucas, and Modified Bronze Leonardo sequences, and some terms of these sequences are given. Then, we give special summation formulas, special generating functions, etc.
Engin Özkan, Hakan Akkuş
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On Dual Quaternions with $k-$Generalized Leonardo Components
Journal of New Theory, 2023 In this paper, we define a one-parameter generalization of Leonardo dual quaternions, namely $k-$generalized Leonardo-like dual quaternions. We introduce the properties of $k$-generalized Leonardo-like dual quaternions, including relations with Leonardo,
Gülsüm Yeliz Saçlı +1 more
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Twisted immanant and matrices with anticommuting entries
, 2015 This article gives a new matrix function named "twisted immanant," which can be regarded as an analogue of the immanant. This is defined for each self-conjugate partition through a "twisted" analogue of the irreducible character of the symmetric group ...
Itoh, Minoru
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