2,715 research outputs found
Marriner S. Eccles, correspondence with Senator Claiborne Pell
No full textCorrespondence of Marriner S. Eccles with Claiborne Pell, U.S. Senator from Rhode Island. Includes a copy of an article about Senator Pell\u27s opposition to U.S. involvement to the Vietnam War, printed in the San Francisco Examiner on 29 May 1970
On a generalization of the Pell sequence
No full textThe Pell sequence is the second order linear recurrence defined by with initial conditions and . In this paper, we investigate a generalization of the Pell sequence called the -generalized Pell sequence which is generated by a recurrence relation of a higher order. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences. Some interesting identities involving the Fibonacci and generalized Pell numbers are also deduced
Norms Of Hankel-Hessenberg and Toeplitz-Hessenberg Matrices Involving Pell and Pell-Lucas Numbers
No full textWe derive some sum formulas for the squares of Pell and Pell-Lucas numbers. We construct Hankel-Hessenberg andToeplitz-Hessenberg matrices whose entries in the first column are HHP = aij , ij i j a Pï€ = ; Q HH =   ij a , ij i j a Qï€ =and P TH =   ij a , 1 = ij iï€ j a P ; Q TH =   ij a , 1 = ij iï€ j a Q , respectively where n P and n Q denote the usual Pell and Pell-Lucas numbers. Then, we found upper and lower bounds for spectral norm of these matrices
Pell and Pell-Lucas numbers of the form
No full textsummary:In this paper, we find all Pell and Pell-Lucas numbers written in the form , in nonnegative integers , , , with
Pell and Pell–Lucas numbers with applications
No full textPell and Pell–Lucas Numbers has been carefully crafted as an undergraduate/graduate textbook; the level of which depends on the college/university and the instructor’s preference. The exposition moves from the basics to more advanced topics in a systematic rigorous fashion, motivating the reader with numerous examples, figures, and exercises. Only a strong foundation in precalculus, plus a good background in matrices, determinants, congruences, and combinatorics is required. The text may be used in a variety of number theory courses, as well as in seminars, workshops, and other capstone experiences for teachers in-training and instructors at all levels. A number of key features on the Pell family surrounds the historical flavor that is interwoven into an extensive, in-depth coverage of this unique text on the subject. Pell and Pell-Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical community with their beauty and applicability. Beyond the classroom setting, the professional mathematician, computer scientist, and other university faculty will greatly benefit from exposure to a range of mathematical skills involving pattern recognition, conjecturing, and problem-solving techniques; these insights and tools are presented in an array of applications to combinatorics, graph theory, geometry, and various other areas of discrete mathematics. Pell and Pell-Lucas Numbers provides a powerful tool for extracting numerous interesting properties of a vast array of number sequences. It is a fascinating book, offering boundless opportunities for experimentation and exploration for the mathematically curious, from student, to the professional, amateur number theory enthusiast, and talented high schooler. About the author: Thomas Koshy is Professor Emeritus of Mathematics at Framingham State University in Framingham, Massachusetts. In 2007, he received the Faculty of the Year Award and his publication Fibonacci and Lucas numbers with Applications won the Association of American Publishers' new book award in 2001. Professor Koshy has also authored numerous articles on a wide spectrum of topics and more than seven books, among them, Elementary Number Theory with Applications, second edition; Catalan Numbers with Applications; Triangular Arrays with Applications; and Discrete Mathematics with Applications
Pell Equation. III. Graph-theoretical meaning of the solutions of the Pell equation through topological index Z
No full textFor a non-directed graph G composed of vertices and edges the topological index Z_G has been defined by the present author as the total sum of perfect and imperfect matchings. The Z_G values of several typical series of graphs have been known to be equal to Fibonacci, Lucas, and Pell numbers. In this paper the solutions of Pell equation x^2-Dy^2=±N for special values of D with N=1 and 4 are shown to give these series of numbers, which means that this is the first graphical or graph-theoretical interpretation of the solutions of Pell equation. In this analysis the Chebyshev polynomials of the first and second kinds, T_n and U_n, together with their modified version, C_n and S_n, are involved. For any D with N=1 and 4, there were found certain series of graphs whose Z_G values just represent the solutions of Pell equation
Pell Grants: Impact on Minority Groups within California
No full textPell Grants are grants given to students with financial need. Students apply for Pell Grants through a financial aid application, Free Application for Federal Student Aid (FAFSA). FAFSA helps calculate the contribution parents can make towards their children\u27s higher education, which colleges also use to calculate the student\u27s financial aid. Pell grants are paid with taxpayer money, making it essential to determine whether government grants improve graduation outcomes. However, studies have shown that Pell Grants nationwide and statewide are less effective than intended. This study analyzes the effects of Pell Grants on a smaller scale, focusing on students from minority groups who are first-generation and attended the University of California, Irvine, from 2019 to 2021. The study ran a regression discontinuity design and found that Pell Grants are associated with increased graduation rates for Chicano or Mexican-American students who are eligible for Pell Grants and have Cal Grant A. The effect of Pell Grant eligibility on the outcome of Black or African-American students was also analyzed within this study. However, their outcomes were not as significant as Chicano or Mexican-American students. Pell grants do not impact students because other barriers exist
On the sum of Pell and Jacobsthal numbers by the determinants of Hessenberg matrices
No full textInternational Conference on Numerical Analysis and Applied Mathematics (ICNAAM) -- SEP 19-25, 2016 -- Rhodes, GREECEIn this study, we obtain the sum of Pell and Jacobsthal numbers by the determinants of some Hessenberg matrices
A problem of Diophantues and Pell numbers
No full textLet n be an integer. A set of positive integers {a_1, a_2,...,a_m} is said to have the property of Diophantus of order n, symbolically D(n), if a_i*a_j + n is a perfect square for all 1<=i<j<=m. It is known that for any integer l and any set {a, b} with the property D(l^2), where ab is not a perfect square, there exist an infinite number of sets of the form {a, b, c, d} with the property D(l^2). Using this result, we construct such sets with elements given in terms of Pell and Pell-Lucas numbers
- …
