关于Diophantine方程(a~n-1)((a+1)~n-1)=x~2

本文研究了指数Diophantine方程(an-1)((a+1)n-1)=x2的正整数解(n,x),其中a是大于1的正整数.运用初等数论方法证明了:当a≡2或3(mod4)时,该方程无解.     

方程y~2=nx(x~2±1)的正整数解数的上界(英文)

设n是无平方因子正整数.本文利用二次和四次Diophantine方程解数的结果,讨论了方程y~2=nx(x~2±1)的正整数解个数的上界,证明了该方程至多有2~w(n)个正整数解(x,y),其中w(n)是n的不同素因数的个数.     

一个包含新的Smarandache函数的方程

定义一个新的Smarandache函数(?)(n),并研究一个包含该函数的方程.利用初等方法,给出了一个包含函数(?)(n)的方程的正整数解.方程只有五个正整数解.     

一个包含新的F．Smarandache函数的方程

定义一个新的F.Smarandache函数(?)(n),并研究一个包含该函数的方程.利用初等方法.给出了一个包含函数(?)(n)的方程的正整数解.该方程只有两个正整数解.     

关于一类广义Ramanujan-Nagell方程的正整数解

本文研究了一类广义Ramanujan-Nagell方程有正整数解的条件.利用二次域中的重要理论,给出了一个典型的Ramanujan-Nagell方程的所有正整数解,推广了文献[1]和[2]的结果.     

关于Schinzel-Sierpiński方程

本文研究了Schinzel-Sierpiński方程的正整数解,运用Pell方程的基本性质,获得了全部解的明显表达式.     

关于Diophantine方程x3+1=py2

在素数p=3（8t＋4）（8t＋5）＋1和p=3（8t＋3）（8t＋4）＋1的情形下,运用初等数论的方法给出了丢番图方程x3＋1=py2无正整数解的充分条件,并得到无数个6k＋1型的素数p使得方程x3＋1=py2无正整数解.     

关于广义Ramanujan-Nagell方程的一个猜想

本文研究广义Ramanujan-Nagell方程的正整数解.利用初等数论方法,证实了杨仕椿关于广义Ramanujan-Nagell方程的一个猜想.     

关于指数Diophantine方程$x^3-1=2py^2$

设p是奇素数,本文证明了:当p=48t~2 1,其中t是正整数时,方程x~3-1=2py~2无正整数解(x,y).     

关于广义Ramanujan-Nagell方程的一点注记

本文研究了广义Ramanujan-Nagell方程的正整数解,利用初等方法,得到了它的所有偶数解,从而部分地解决了该方程的求解问题.     

ℒ1 subspaces ofl 1

It is proved that every subspace ofl ₁ which is an Λ_{1, λ} space with λ close enough to 1 is isomorphic tol ₁.     

-1=1?

推证 :- 1 =i2 =( i4) 12 =1 .显然结论错误 ,但究竟错在哪里呢 ?诡辩揭密 :关于复数指数幂运算律 ,详见人教版原高二代数教材 P1 91有 :　　　　 ( zm) n =zmn,　　　　 zm . zn =zm+ n,　　　　 zmzn =zm-n,其中 m、n∈ N.实质上 ,m,n∈ Z也成立 .可见 ,i2 ≠ ( i4) 12 ,即 - 1≠ 1 .-1=1?!712000$陕西省咸阳市天王中学@曹万宏     

On almost 1-1 extensions

We show that a broad class of extensions of measure preserving systems in the context of ergodic theory can be realized by topological models for which the extension is “almost one-one”.     

BestL 1-approximations of classesW 1 r by Splines fromW 1 r

We obtain the exact values of the bestL ₁-approximations of the classesW ₁ ^r of periodic functions by periodic polynomial splines of degreer and defect 1 with equidistant knots that belong to the classW ₁ ^r .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1410–1413, October, 1994.     

Non-linear oscillations of a satellite at 1:1:1 resonance

The motion of a satellite about its centre of mass in a central Newtonian gravitational field is investigated. The satellite is considered to be a dynamically symmetrical rigid body. It is assumed that the ratio of the polar and equatorial principal central moments of inertia of the satellite is 4/3, or close to this. The orbit of the centre of mass is elliptic, and the orbit eccentricity is assumed to be small. In the limit case, when the orbit of the centre of mass is circular, a steady motion exists (corresponding to relative equilibrium of the satellite in the orbital system of coordinates) in which the axis of dynamic symmetry is directed along the velocity vector of the centre of mass of the satellite; here, the frequencies of the small linear oscillations of the axis of symmetry are equal or close to one another. But in an elliptic orbit of small eccentricity, multiple 1:1:1 resonance occurs in this case, as the oscillation frequencies mentioned are equal or close to the frequency of motion of the centre of mass of the satellite in orbit. The non-linear problem of the existence, bifurcations and stability of periodic motions of the satellite with a period equal to the rotation period of its centre of mass in orbit is investigated.