The construction of statistically self-similar measures

We have studied statistically self-similar measures together with statistically self-similar sets in this paper. A special kind of statistically self-similar measures has been constructed and a class of statistically self-similar sets as well. Supported by the National Natural Science Fundation and the Doctral Programme Fundation of China Hu Dihe: born in May 1935, Professor     

Kock曲线的Hausdorff测度

对 Kock曲线的 Hausdorff测度进行了估计 ,并给出了一个公式 .由此公式 ,得到了 Kock曲线的Hausdorff测度的上界估计 ,并推翻了关于它的一个猜测 .     

非均匀Cantor型集的Hausdorff维数和测度

计算了非均匀Ｃａｎｔｏｒ型集的Ｈａｕｓｄｏｒｆｆ维数，并给出了其Ｈａｕｓｄｏｒｆｆ测度的上界。     

一类齐次Cantor集的Hausdorff测度

用一种比较初等的方法估计了一类齐次Cantor集的Hausdorff测度的下限,再用k阶基本区间作为覆盖类估计了该类齐次Cantor集的上限,从而得到了该类齐次Cantor集的Hausdorff测度的准确值.     

Koch曲线的Hausdorff测度

在文〖１〗的基础上,给出Ｋｏｃｈ曲线的Ｈａｕｓｄｏｒｆｆ测度上界的进一步估计。     

一个特殊分形集的Hausdorff测度估计

利用满足开集条件的自相似分形的性质，得到一个特殊分形Hausdorff测度的上界估计公式。由此公式，对它的Hausdorff测度的上界进行了估计，并用两种方法估计了它的Hausdorff测度的下界。     

一类耦合的非线性KdV方程组的Hausdorff维数和分形维数

研究了一类耦合的非线性KdV方程组解的渐进性质，根据非线性Galerkin方法和Leray-Schauder定理，应用线性变分的方法，得到了Hausdorff维数dH(A)≤J0和分形维数dF(A)≤[1 2b√b/3c/aJ0^3-bJ0]的上界估计。     

Sierpinski垫片的Hausdorff测度的上界估计

研究分形集的中心任务是计算或估计分形集的Hausdorff维数与Hausdorff测度。本文研究Sierpinski垫片的Hausdorff测度的上界估计,利用部分估计的方法,归纳出了关于Sierpinski垫片的某种部分覆盖所包含的小三角形的个数以及这种覆盖的直径的规律,得到了Sierpinski垫片的Hausdorff测度的一个更好的上界估计值Hs(S)≤1377811/09286×(2431/3072)s≈0.870031853。     

Hodograph computation and bound estimation for rational B-spline curves

It is necessary to compute the derivative end estimate the bound of rational B-spline curves in design system,which has not been studied to date.To improve the function of computer aided design (CAD) system,end to enhance the efficiency of different algo- rithms of rational B-spline curves,the representation of scaled hodograph and bound of derivative magnitude of uniform planar rational B- spline curves are derived by applying Dir function,which indicates the direction of Cartesian vector between homogeneous points,discrete B-spline theory end the formula of translating the product into a summation of B-spline functions.As an application of the result above, upper bound of parametric distance between any two points in a uniform planar rational B-spline curve is further presented.     

强阻尼的半线性波动方程全局吸引子的Hausdorff维数

运用全局吸引子在高正则空间范数下的有界性,得到了非线性项具有临界增长指数的强阻尼半线性波动方程的全局吸引子的Hausdorff维数的上界估计式,改进了非临界指数时已有的上界估计．     

Hodograph computation and bound estimation for rational B-spline curves

It is necessary to compute the derivative and estimate the bound of rational B-spline curves in design system, which has not been studied to date. To improve the function of computer aided design (CAD) system, and to enhance the efficiency of different algorithms of rational B-spline curves, the representation of scaled hodograph and bound of derivative magnitude of uniform planar rational B-spline curves are derived by applying Dir function, which indicates the direction of Cartesian vector between homogeneous points, discrete B-spline theory and the formula of translating the product into a summation of B-spline functions. As an application of the result above, upper bound of parametric distance between any two points in a uniform planar rational B-spline curve is further presented.     

一类广义Sierpinski地毯的Hausdorff测度

得到正方形上一类Sierpinski地毯En的等价构造,即为一类六边形上的Sierpinski地毯Qn;通过在Qn上定义一个质量分布,由质量分布原理得到下界,从而完全确定了En的Hausdorff测度的准确值.     

紧集上N维非退化扩散过程样本水平集的Hausdorff维数

主要讨论了在一定的条件下,紧集上N维非退化扩散过程样本水平集的Hausdorf维数的上界.     

Hybrid fiber optical bistability and optical signal processing

A hybrid fiber optical bistable device with electrical feedback has been proposed and analyzed. Bistability operation and some applications for optical signal processing have been realized experimentally. Supported by the National Natural Science Fundation of China Song Qian: born in Aug. 1937, Professor     

完全杂凑族的一个新下界

考虑(n,m,w)-完全杂凑族的下界,运用初等的方法给出一个新的下界,并给出新的下界比著名的Fredman-Komlos下界好的条件.     

抛物线型量子线中束缚极化子基态能变分计算

费曼路径积分的变分方法是计算束缚极化子基态能的最有效方法。文章给出了抛物线型量子线中束缚极化子的哈密顿量 ,运用费曼路径积分的变分方法统一推导出抛物线型量子线约束势中杂质库仑束缚势下极化子的基态能 ,讨论了量子阱的一些特殊情况 :有、无杂质库仑束缚势的量子点和有、无杂质库仑束缚势的量子阱束缚势的量子阱 ,以及自由极化子     

山东省自然科学基金项目绩效评价研究

为进一步加强对山东省自然科学基金的管理、优化科技资源、提高科技投入的资金运行效率,在国内外相关学者已有的研究基础上,建立山东省自然科学基金绩效的概念模型和评价指标体系,采用两阶段数据包络分析模型对山东省自然科学基金项目进行评价。实证分析结果显示,山东省自然科学基金项目整体绩效水平较高,但不同项目类别、不同学科之间差距较大,对此应进一步扶持弱势学科,加大财政科技投入及对基础研究领军人才的引进和培养。     

达到Gilbert-Varshamov界的准扭码

准扭码是循环码的一种推广,1-生成准扭码同构于多项式剩余类环的1-生成子模.Gilbert-Varshamov界是衡量准扭码好坏的一个重要标准.利用不可约多项式的性质得到任意的一个1-生成准扭码,有很大概率渐进达到Gilbert-Varshamov界.