178,982 research outputs found
Genelleştirilmiş r-Pell ve r-Pell lucas dizileri
No full textPell ve Pell-Lucas dizileri tamsayı dizileri arasında iyi bilinen iki dizidir. Literatürde bu iki
dizinin genelleştirmeleri üzerine yürütülmüş birçok çalışma bulunmaktadır. Bunlardan biri
Brod (2019) tarafından tanımlanan r–Pell sayılarıdır. Bu tezde öncelikle r–Pell sayılarına
uygun olan r–Pell–Lucas sayıları tanımlanacak ve bu iki sayı dizisine ait olan üreteç
fonksiyonları ve Binet formülleri elde edilecektir. Daha sade sonuçlar elde edebilmek için Pell
ve Pell–Lucas sayı dizilerinin yeni genelleştirilmelerine ihtiyaç duyulmaktadır. Bu ikinci
genelleştirme 2. tip olarak isimlendirildikten sonra bu dört sayı dizisine ait başta Vajda,
Catalan, Cassini ve d’Ocagne özdeşlikleri olmak üzere birçok özdeşlik elde edilmiştir
On the spectral norm of r-circulant matrices with the Pell and Pell-Lucas numbers
No full textAbstract Let us define A = C r ( a 0 , a 1 , … , a n − 1 ) to be a n × n r-circulant matrix. The entries in the first row of A = C r ( a 0 , a 1 , … , a n − 1 ) are a i = P i , a i = Q i , a i = P i 2 or a i = Q i 2 ( i = 0 , 1 , 2 , … , n − 1 ), where P i and Q i are the ith Pell and Pell-Lucas numbers, respectively. We find some bounds estimation of the spectral norm for r-Circulant matrices with Pell and Pell-Lucas numbers
On Pellnomial coefficients and Pell–Catalan numbers
No full textWOS:000925932800003In this paper, we first give the Pascal’s identity for Pellno-mial coefficients and then we show that the Pellnomial coefficients are integers. We obtain that the product of r consecutive Pell numbers is divisible by the Pell analog of r!. Also, we introduce the divisibility the-orems between Pell numbers and Pellnomial coefficients. Furthermore, we first define Pell–Catalan numbers and then we derive two formulas for presenting Pell–Catalan numbers. © 2022, University of Tartu Press. All rights reserved
Data for: Temporally explicit life cycle assessment as an environmental performance decision making tool in rare earth project development
No full textLife cycle inventory and calculations for LCIA of Bear Lodge using TRACI 2.
Applications of Pell Polynomials in Rings
No full textIn this paper, we study the Pell polynomials according to modulo mwhere and various properties of these sequences are obtained. Also, Pell polynomials to the ring of complex numbers was defined. We define the Pell Polynomial-type orbits where R be a 2-generator ring and (α,β) is a generating pair of the ring. Furthermore, we obtain the periods of the Pell Polynomial-type orbits P_（α,β){^R}(x) in finite 2-generator rings of order P{^2}.</jats:p
On a new generalization of Pell hybrid numbers
No full textIn this paper, we define and study a new one-parameter generalization of the Pell hybrid numbers. Based on the definition of r-Pell numbers, we define the r-Pell hybrid numbers. We give their properties: character, Binet formula, summation formula, and generating function. Moreover, we present Catalan, Cassini, d’Ocagne, and Vajda type identities for the r-Pell hybrid numbers
The Growing Impact of New Pell Grant Funding: A Statewide Profile of Iowa's Community Colleges
No full textThis is a research project of the Education Policy Center at
The University of Alabama and Iowa State University,
conducted under the auspices of the National Rural Scholars Panel of the
Rural Community College Alliance from June 2011. More than 200 urban, suburban, and rural community colleges responded to the survey. The report presents the findings of a study on Pell Grant funding for the state of Iowa.University of Alabama. Education Policy CenterIowa State University. Education Policy CenterNational Rural Scholars Pane
A STUDY ON PELL EQUATION
No full textPell equation (alternatively called the Pell- Fermat equation) is a
type of a Diophantine equation of the form 2 -Dye 2 =1 for a natural number
D. If D is a perfect square, then pell equation can be rewritten as
y).(x+√y) = 1.similarly, the trivial solution (x,y) = (0,1)
is not very interesting. Therefore it is often assumed that D is not a square
and only nontrivial solution (non zero pairs of integers) are considered
Rational Polynomial Pell Equations.
No full textLet R denote either the integers or the rationals and let d(x) be a square-free polynomial in R[x]. In this thesis we study the question of when does the polynomial Pell equation, f(x)^2-d(x)g(x)^2=1 have solutions f(x), g(x) in R[x] with g(x) non-zero. Over Q[x] there always exist such solutions when d(x) is quadratic, so we study the first non-trivial case which is that of quartic d(x). In particular, we are able to use the theory of elliptic curves to produce a complete list of all quartic, square-free d(x) in Q[x] for which the Pell equation has a solution. Using our formulas, we are able to settle several open problems in the area of polynomial Pell equations. The first problem pertains to periods of continued fractions of sqrt(d(x)). We settle a question of Schinzel by showing that if the continued fraction is periodic then its period is among {1,2,3,4,5,6,7,8,10,14,18,22}. Next, we discuss what happens over the integers, by giving a complete classification of all monic, square-free, quartic d(x) in Z[x] for which the Pell equation has a non-trivial solution over Z[x]. This classification disproves a conjecture of Yokota, and finishes work started by Webb, Yokota and others. Lastly, we discuss generalizations to higher degrees and other number fields.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100026/1/zscherr_1.pd
Penyelesaian persamaan Pell menggunakan metode Pell dan metode Brahmagupta
No full textABSTRAK
Persamaan Pell adalah persamaan dengan dua peubah yang mempunyai tak hingga selesaian pasangan bilangan bulat. Bentuk umum Persamaan Peli dinyatakan dengan x2-dy2=k, dengan d merupakan bilangan bulat positif dan d # a2 untuk aeZ. Pada Persamaan Pell nilai k yang digunakan adalah ±1 dan IM > 1. Pada pembahasan skripsi ini masalah yang dikemukakan adalah Penyelesaian Persamaan Pell X2-dy2 = 1 dengan menggunakan metode Pell dan metode Brahmagupta. Dalam penulisan skripsi ini, penulis menggunakan penelitian kepustakaan (Library Research).
Konsep yang mendasari pada masalah ini antara lain konsep sistem bilangan bulat, keterbagian, faktor persekutuan terbesar, kongruensi, persamaan Diophantine linier dua peubah, persamaan Diophantine non linier dua peubah.
Untuk memperjelas penyelesaian Persamaan Peli dengan menggunakan metode Pell dan metode Brahmagupta, dapat dilakukan dengan menggunakan langkah-langkah, yaitu:
1. Metode Pell
- Menentukan nilai awal r, dan yx yang memenuhi persamaan x2-dy2=\.
- Mencari xn dan yn selanjutnya dengan menggunakan n bilangan bulat.
2. Metode Brahmagupta
- Mencari nilai (a,b) yang memenuhi x2-dy2:k dengan £ = ±L±2,±3,٠٠.
- Mencari nilai awal X1 dan Y1 yang memenuhi persamaan x2 - dy2 = 1.
- Mencari xn dan yn selanjutnya dengan menggunakan (x12+dy12, 2x1y1)
- …
