scholarly journals Non-Linear Recursive Sequences

1959 ◽  
Vol 11 ◽  
pp. 370-378 ◽  
Author(s):  
Elbert A. Walker

The purpose of this paper is to investigate non-linear recursive sequences of maximum length with elements from GF(2). In particular, the question of whether or not a recursive sequence of maximum length can be equal to its dual is settled. This question, as far as the author knows, was originally asked by Rosser. Part I contains the necessary background for Part II, and in the main is a condensation of some unpublished work (1955) of W. A. Blankinship and R. P. Dilworth.

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 244 ◽  
Author(s):  
Yixue Zhang ◽  
Zhuoyu Chen

In this paper, firstly, we introduced a second order non-linear recursive sequence, then we use this sequence and the combinatorial methods to perform a deep study on the computational problem concerning one kind sums, which includes the Chebyshev polynomials. This makes it possible to simplify a class of complex computations involving the second type Chebyshev polynomials into a very simple problem. Finally, we give a new and interesting identity for it.


Author(s):  
Michaël Cadilhac ◽  
Filip Mazowiecki ◽  
Charles Paperman ◽  
Michał Pilipczuk ◽  
Géraud Sénizergues

AbstractWe study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is bn = n!. Our main result is that the sequence un = nn is not polynomial recursive.


2021 ◽  
Vol 5 (1) ◽  
pp. 65-72
Author(s):  
Albert Adu-Sackey ◽  
◽  
Francis T. Oduro ◽  
Gabriel Obed Fosu ◽  
◽  
...  

The paper proves convergence for three uniquely defined recursive sequences, namely, arithmetico-geometric sequence, the Newton-Raphson recursive sequence, and the nested/composite recursive sequence. The three main hurdles for this prove processes are boundedness, monotonicity, and convergence. Oftentimes, these processes lie in the predominant use of prove by mathematical induction and also require some bit of creativity and inspiration drawn from the convergence monotone theorem. However, these techniques are not adopted here, rather, as a novelty, extensive use of basic manipulation of inequalities and useful equations are applied in illustrating convergence for these sequences. Moreover, we established a mathematical expression for the limit of the nested recurrence sequence in terms of its leading term which yields favorable results.


2008 ◽  
Vol 10 (01) ◽  
pp. 129-136
Author(s):  
DAVID W. K. YEUNG

Strategic behaviors of players depend crucially on the coalition structures of a game. A recursive sequence identifying the number of embedded coalitions in a n-player game is derived. The paper also derives a recursive sequence identifying the number of embedded coalitions in a n-player game where the position of the individual player in a partition counts.


Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 114 ◽  
Author(s):  
Shimeng Shen ◽  
Li Chen

In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the basic and combinatorial methods. Finally, we give an interesting identity.


1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér

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