REGULARITIES OF NUMBERS IN THE FIBONACHI TRIANGLE CONSTRUCTED ON THE DEGREE TRANSFORMATIONS OF A SQUARE THREE MEMBERS

In this paper, it is shown that the Fibonacci triangle is formed from the elements of power transformations of a quadratic trinomial. It is binary structured by domains of rows of equal lengths, in which the sum of numbers forms a sequence of certain numbers. This sequence coincides with the transformed bisection of the classical sequence of Fibonacci numbers. The paper substantiates Pascal's rule for calculating elements in the lines of a Fibonacci triangle. The general relations of two forgings of numbers in lines of a triangle of Fibonacci for arbitrary values are received

Solutions for Several Quadratic Trinomial Difference Equations and Partial Differential Difference Equations in C2

This article is to investigate the existence of entire solutions of several quadratic trinomial difference equations f(z+c)2+2αf(z)f(z+c)+f(z)2=eg(z), and the partial differential difference equations f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z12=eg(z),f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z2+∂f(z)∂z1+∂f(z)∂z22=eg(z). We establish some theorems about the forms of the finite order transcendental entire solutions of these functional equations. We also list a series of examples to explain the existence of the finite order transcendental entire solutions of such equations. Meantime, some examples show that there exists a very significant difference with the previous literature on the growth order of the finite order transcendental entire solutions. Our results show that some functional equations can admit the transcendental entire solutions with any positive integer order. These results make a few improvements of the previous theorems given by Xu and Cao, Liu and Yang.

Entire solutions for several general quadratic trinomial differential difference equations

This paper is devoted to exploring the existence and the forms of entire solutions of several quadratic trinomial differential difference equations with more general forms. Some results about the forms of entire solutions for these equations are some extensions and generalizations of the previous theorems given by Liu, Yang and Cao. We also give a series of examples to explain the existence of the finite order transcendental entire solutions of such equations.

Delay-Dependent Criteria for Absolute Stability of Time-Varying Delay Lurie Control Systems

A new method for constructing a Lyapunov-Razumikhn function to deal with the stability problem of time-varying delay nonlinear uncertain system is presented in this paper. A quadratic trinomial with two variables（ξ,Τ）is obtained, and then the upper bound of the allowable delay Τ can be obtained by solving the optimization problem with varying positive matrix Q. That is to say, we can obtain the optimal combination of Τ and Q matrix.

Factoring the quadratic trinomial

An interesting variation of a very old topic.

Some Experiments Testing the Most Rapid Method of Factoring the Type ax2 + bx + c

For some time there has been considerable debate among the mathematics teachers of Horace Mann High School as to the best method of factoring the quadratic trinomial of the type ax2 + bx + c. It was rather generally agreed that the so-called “cross-product” method is most easily made rational to the pupil and that the method of “splitting the middle term” is least easily taught; also that guessing is involved in all the methods. But it is insisted that either the “splitting-middle-term” method or “multiply-by-a” method is more scientific than the “cross-product” method because a definite system of guessing can be given for the first two which does not apply to the third. This last argument is denied, with no possibility of proof or conviction, but a disagreement upon the question of which method is most rapid was more easily tested and the following experiments made.