粘弹性阻尼对非线性弹性杆内纵向应变孤波运动的影响

本文采用基于KdV方程的守恒量建立起来的孤波参数的演化方程组,重新研究了粘弹性阻尼对非线性弹性杆内纵向应变孤波运动的影响,得到了孤波参数的演化规律。结果表明,粘弹性阻尼使孤波逐渐变矮、增宽、速度减慢,最后导致孤波的消失。     

具有正负系数差分方程解的振动性

考虑一类具有正负系数的差分方程,获得它的所有解振动的充分条件．     

Decomposing trait and state variability in general and specific subjective task value beliefs

Expectancy-value researchers have theorized about the extent to which subjective task value components are more trait-like or more state-like. Using a bifactor representation of subjective task value data, the current study aimed to examine the degree of trait-state variation in general subjective task value, specific attainment value, specific intrinsic value, and specific utility value. The relations of both between and within components of the subjective task value constructs with academic self-efficacy beliefs were also examined. Results indicate that, in an undergraduate life science learning context (n = 169), the general subjective task value factor was the most trait-like of the subjective task value constructs. With respect to specific value beliefs, attainment value was composed of nearly equal amounts of trait and state variation, intrinsic value was composed of the largest amount of trait variation, and utility value exhibited the most state-like variation. Additionally, findings suggest that trait-like and state-like general subjective task value, trait-like specific intrinsic value, and state-like attainment value were positively associated with self-efficacy. Finally, we propose a model of trait- state dynamics in subjective task value.     

一类广义Liénard方程周期解的不存在性

研究一类广义Liénard方程周期解的不存在性,给出了其周期解不存在的两个充分条件,用极限集理论与Poincaré切性曲线法证明了所得结果。     

关于不定方程x（x+d）（x+2d）（x+3d）=p2ky（y+d）（y+2d）（y+3d）

设p是素数,k为自然数,d>1为奇数。该文运用初等方法证明了不定方程x(x+d)(x+2d)(x+3d)=p2ky(y+d)(y+2d)(y+3d)没有正整数解。     

具有多滞后的时变区间动力系统的指数稳定性

引进了多滞后时变区间动力系统的指数稳定的概念，用矩阵测度和时滞微分不等式研究了具有多滞后的时变区间动力系统χ(t)=N[P(t)，Q(t)]χ(t) ∑（i=1，m）N[Pi(t)，Qi(t)]χ(t-τi)，τi0(i=1，2，…，m)的指数稳定性，得到了其指数稳定的一些判据，并给出了应用的例子，改进和推广了前人的工作。     

改进的余弦形超声变幅杆

本文推导了改进的余弦形超声变幅杆的频率方程、各参数的计算公式,并与其它类型的变幅杆进行了比较．结果表明此类变幅杆具有和指数形变幅杆相同的放大系数和频率方程,也适合于作为单一的变幅杆使用;并且其输入阻抗的表达式比指数形、圆锥形、悬链线形的都要简捷;在面积系数不太大的情况下,其形状因数比指数形、圆锥形、悬链线形的大得多。     

求解非线性方程的一种连分式法

在文献[1][2]的基础上给出了求方程f（x）=0实根的连分式法．不论函数f（x）是否可导，在有实根的情况下，一般都能通过该方法求出一个实根．     

关于Diophantine方程x3-1=Dyn

设D是无平方因子正整数.本文证明了:当D不能被形如6k 1之形素数整除时,方程,-1=Dyn仅当D=17时有正整数解(x,y,n)=(18,7,3)适合n＞2.     

关于Diophantine方程x~3-3~(3m)=Dy~2

设D是无平方因子正奇数.本文证明了:当D不能被6k+1之形素数整除时,如果方程x3-33m=Dy2有适合gcd(x,Y)=1的正整数解(x,y,m),则D≡7(mod 8),D的素因数p都满足了p≡11(mod 12),而且D的素因数个数必为奇数.