scholarly journals Extremal properties of the derivatives of the Newman polynomials

2003 ◽  
Vol 131 (10) ◽  
pp. 3129-3134 ◽  
Author(s):  
Tamás Erdélyi
Keyword(s):  
Newman Polynomials ◽  
Derivatives Of ◽  
Extremal Properties

scholarly journals Permutation Matrices, Their Discrete Derivatives and Extremal Properties

2020 ◽  
Vol 48 (4) ◽  
pp. 719-740
Author(s):  
Richard A. Brualdi ◽  
Geir Dahl
Keyword(s):  
Permutation Matrix ◽  
Permutation Matrices ◽  
Discrete Derivative ◽  
The Relationship ◽  
Derivatives Of ◽  
Extremal Properties

AbstractFor a permutation π, and the corresponding permutation matrix, we introduce the notion of discrete derivative, obtained by taking differences of successive entries in π. We characterize the possible derivatives of permutations, and consider questions for permutations with certain properties satisfied by the derivative. For instance, we consider permutations with distinct derivatives, and the relationship to so-called Costas arrays.

scholarly journals On Extremal Properties of the Derivatives of Polynomials and Rational Functions

1964 ◽  
Vol 7 (1) ◽  
pp. 121-131
Author(s):  
M.A. Malik
Keyword(s):  
Complex Variable ◽  
Rational Functions ◽  
Finite Sum ◽  
Derivatives Of ◽  
Extremal Properties

Let p(z) be a polynomial of degree n, i. e. a finite sum of the form where cν are any given numbers and z=x+iy is a complex variable. To answer a question raised by the chemist Mendelieff, A. Markoff [3] proved the following theorem.

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