scholarly journals The arrowhead-Jacobsthal sequence

2021 ◽  
Vol 51 ◽  
pp. 31-44
Author(s):  
Yesım Akuzum ◽  
Omur Deveci
Keyword(s):  
Characteristic Polynomial ◽  
Generating Matrix ◽  
Arrowhead Matrix ◽  
Generalized Order

In the present investigation, we define the arrowhead-Jacobsthal sequence by the arrowhead matrix defined with the help of the characteristic polynomial of the generalized order-k Jacobsthal numbers. Next, we derive various properties of the arrowhead-Jacobsthal sequence by using its generating matrix. Also, we give connections between Fibonacci, Jacobsthal, Pell and arrowhead-Jacobsthal numbers.

scholarly journals On the arrowhead-Fibonacci numbers

2016 ◽  
Vol 14 (1) ◽  
pp. 1104-1113 ◽  
Author(s):  
Inci Gültekin ◽  
Ömür Deveci
Keyword(s):  
Characteristic Polynomial ◽  
Fibonacci Numbers ◽  
Fibonacci Sequence ◽  
Cyclic Groups ◽  
Generating Matrix ◽  
Arrowhead Matrix

AbstractIn this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k-step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulo m and we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers when read modulo m. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the arrowhead-Fibonacci sequence modulo m.

scholarly journals Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 335
Author(s):  
Mohamed A. Abd Elgawad ◽  
Haroon M. Barakat ◽  
Shengwu Xiong ◽  
Salem A. Alyami
Keyword(s):  
Order Statistics ◽  
General Framework ◽  
Bivariate Distribution ◽  
Generalized Order Statistics ◽  
Information Measures ◽  
Progressive Type ◽  
Information Number ◽  
Fisher Information Number ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,⋯,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.

Load-Sharing Reliability Models with Different Component Sensitivities to Other Components’ Working States

2021 ◽  
Vol 53 (1) ◽  
pp. 107-132
Author(s):  
Tomasz Rychlik ◽  
Fabio Spizzichino
Keyword(s):  
Order Statistics ◽  
Load Sharing ◽  
Single Component ◽  
Generalized Order Statistics ◽  
Hazard Rates ◽  
System Operation ◽  
Reliability Models ◽  
Mixtures Of Distributions ◽  
Failure Times ◽  
Generalized Order

AbstractWe study the distributions of component and system lifetimes under the time-homogeneous load-sharing model, where the multivariate conditional hazard rates of working components depend only on the set of failed components, and not on their failure moments or the time elapsed from the start of system operation. Then we analyze its time-heterogeneous extension, in which the distributions of consecutive failure times, single component lifetimes, and system lifetimes coincide with mixtures of distributions of generalized order statistics. Finally we focus on some specific forms of the time-nonhomogeneous load-sharing model.

scholarly journals The normalized distance Laplacian

2021 ◽  
Vol 9 (1) ◽  
pp. 1-18
Author(s):  
Carolyn Reinhart
Keyword(s):  
Spectral Radius ◽  
Characteristic Polynomial ◽  
Adjacency Matrix ◽  
Connected Graph ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Diagonal Matrix ◽  
The Matrix

Abstract The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of transmissions of the vertices of the graph. The normalized distance Laplacian, 𝒟𝒧(G) = I−T(G)−1/2 𝒟(G)T(G)−1/2, is introduced. This is analogous to the normalized Laplacian matrix, 𝒧(G) = I − D(G)−1/2 A(G)D(G)−1/2, where D(G) is the diagonal matrix of degrees of the vertices of the graph and A(G) is the adjacency matrix. Bounds on the spectral radius of 𝒟 𝒧 and connections with the normalized Laplacian matrix are presented. Twin vertices are used to determine eigenvalues of the normalized distance Laplacian. The distance generalized characteristic polynomial is defined and its properties established. Finally, 𝒟𝒧-cospectrality and lack thereof are determined for all graphs on 10 and fewer vertices, providing evidence that the normalized distance Laplacian has fewer cospectral pairs than other matrices.

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

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