THE DISTRIBUTIONAL DIMENSION OF FRACTALS

In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.

带径向函数的粗糙核的Marcinkiewicz积分算子在乘积空间上的有界性

研究了带径向函数的粗糙核的Marcinkiewicz积分算子 μΩ ,b在乘积空间Rn×Rm(n ,m≥ 2 )中的有界性 .在Ω∈L(log+ L) 2 (Sn - 1×Sm - 1) ,b(|x|,|y|)∈l∞(Lq) (R+ ×R+ )条件下 ,证明了 μΩ ,b是Lp(Rn×Rm)有界的 ,这里当 1<q≤ 2时 ,|1/p - 1/ 2 |<1/q′ ;当q >2时 ,q′ <p <∞ (q′为q的共扼指标 ) .

适用于转录组测序的大豆根总RNA的提取方法研究

[目的]获得高质量、高产量并能满足转录组测序要求的大豆根总RNA。[方法]比较分析了Trizol法、CTAB-Li Cl法和试剂盒法的提取效果。[结果]3种方法均能从大豆根中提取出总RNA。但与Trizol法、CTAB法相比,试剂盒法提取的大豆根总RNA纯度高、完整性好,平均浓度达413.9 ng/μL,A260/A280≈2.14,A260/A230≈2.10,方法可重复性好。[结论]试剂盒法提取的RNA满足转录组测序的质量要求,可进行后续的转录组测序和其他分子生物学相关研究工作。