In this paper we transfer the van der Waerden problem into a problem of solving special systems of equations and give some properties of the solutions for the systems.
The big upper bound of typical van der Waerden number was investigated through calculating the van der Waerden number on a circle. And the van der Waerden number W h(3,3)=9,W h(3,3,3)≥25 on a circle was calculated ...The big upper bound of typical van der Waerden number was investigated through calculating the van der Waerden number on a circle. And the van der Waerden number W h(3,3)=9,W h(3,3,3)≥25 on a circle was calculated by computer.展开更多
在研究圆周上的van der Waerden数的过程中,将van der Waerden问题转化为矩阵形式的线性不等式组的求解问题,想通过解这个不等式组,来找出van der Waerden数Wh(n,n)的更好的上界.在p=nr±1这两种情况下,我们求得了关于x和bk的p个分...在研究圆周上的van der Waerden数的过程中,将van der Waerden问题转化为矩阵形式的线性不等式组的求解问题,想通过解这个不等式组,来找出van der Waerden数Wh(n,n)的更好的上界.在p=nr±1这两种情况下,我们求得了关于x和bk的p个分量的参数表达.展开更多
设U_0(X)是实数x到与其最近的整数的距离,Van der Waerden于1930年给出了区间[0,1]上的无处可微连续函数sum from k=1 to ∞ 10^(-k)U_0(10~kX)后,人们把Van der Waerden函数的底数从a=10推广到了a=4,a=2^(1,2)。本文把底数进一步推广为...设U_0(X)是实数x到与其最近的整数的距离,Van der Waerden于1930年给出了区间[0,1]上的无处可微连续函数sum from k=1 to ∞ 10^(-k)U_0(10~kX)后,人们把Van der Waerden函数的底数从a=10推广到了a=4,a=2^(1,2)。本文把底数进一步推广为a是不小于2的任意整数,即证明了定理如果a是整数且a>2。则函数 f(x)=sum from k=1 to ∞U_0(a^kx)在区间(-∞,+∞)展开更多
本文在研究van der Waerden数的过程中,在把van der Waerden数的问题转化成关于线性不等式组解数问题的基础上,发现局部不等式组的解数S_p与经典Lucas- Fibonacci序列有关,同时在此基础上给出了经典Lucas-Fibonacci序列S_p的一个上、下...本文在研究van der Waerden数的过程中,在把van der Waerden数的问题转化成关于线性不等式组解数问题的基础上,发现局部不等式组的解数S_p与经典Lucas- Fibonacci序列有关,同时在此基础上给出了经典Lucas-Fibonacci序列S_p的一个上、下界公式.展开更多
文摘In this paper we transfer the van der Waerden problem into a problem of solving special systems of equations and give some properties of the solutions for the systems.
文摘The big upper bound of typical van der Waerden number was investigated through calculating the van der Waerden number on a circle. And the van der Waerden number W h(3,3)=9,W h(3,3,3)≥25 on a circle was calculated by computer.
文摘设U_0(X)是实数x到与其最近的整数的距离,Van der Waerden于1930年给出了区间[0,1]上的无处可微连续函数sum from k=1 to ∞ 10^(-k)U_0(10~kX)后,人们把Van der Waerden函数的底数从a=10推广到了a=4,a=2^(1,2)。本文把底数进一步推广为a是不小于2的任意整数,即证明了定理如果a是整数且a>2。则函数 f(x)=sum from k=1 to ∞U_0(a^kx)在区间(-∞,+∞)
