Estimates of the derivatives of rational functions in LP[?1, 1]

1986 ◽  
Vol 39 (3) ◽  
pp. 212-216
Author(s):  
A. A. Pekarskii
Keyword(s):  
Rational Functions ◽  
Derivatives Of

Application of Maple on Solving the Differential Problem of Rational Functions

2013 ◽  
Vol 479-480 ◽  
pp. 855-860
Author(s):  
Chii Huei Yu
Keyword(s):  
Problem Solving ◽  
Research Methods ◽  
Research Method ◽  
Rational Functions ◽  
The Other ◽  
Mathematical Software ◽  
Differential Problem ◽  
Binomial Theorem ◽  
Other Hand ◽  
Derivatives Of

This paper uses the mathematical software Maple as the auxiliary tool to study the differential problem of four types of rational functions. We can obtain the closed forms of any order derivatives of these rational functions by using binomial theorem. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.

A Note on Hilbert's Tenth Problem

1960 ◽  
Vol 3 (2) ◽  
pp. 153-156
Author(s):  
Z. A. Melzak
Keyword(s):  
Decision Procedure ◽  
Rational Functions ◽  
Single Variable ◽  
Hilbert's Tenth Problem ◽  
Integer Coefficients ◽  
Arbitrary Polynomial ◽  
Hilbert’S Tenth Problem ◽  
Derivatives Of

The tenth problem on Hilbert's well known list [1] is the following.(H 10) For an arbitrary polynomial P = P(x1,x2,…,xn) with integer coefficients to determine whether or not the equation P = 0 has a solution in integers.By 'integers' we always mean 'rational integers'. The problem (H 10) is still unsolved but it appears likely that no decision procedure exists; in this connection see [2]. It will be shown here that (H 10) is equivalent to deciding whether or not every member of a certain given countable sec of rational functions of a single variable x is absolutely monotonie. We recall that f(x) is absolutely monotonie in I if f(x) possesses non-negative derivatives of all orders at every x ∊ I.

Some Estimates for the Derivatives of Rational Functions

2009 ◽  
Vol 10 (1) ◽  
pp. 61-79 ◽  
Author(s):  
Mohammed A. Qazi ◽  
Qazi I. Rahman
Keyword(s):  
Rational Functions ◽  
Derivatives Of

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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