Origin, Alternative Expressions of Newcomb-Benford Law and Deviations of Digit Frequencies

The Newcomb-Benford law, which describes the uneven distribution of the frequencies of digits in data sets, is by its nature probabilistic. Therefore, the main goal of this work was to derive formulas for the permissible deviations of the above frequencies (confidence intervals). For this, a previously developed method was used, which represents an alternative to the traditional approach. The alternative formula expressing the Newcomb-Benford law is re-derived. As shown in general form, it is numerically equivalent to the original Benford formula. The obtained formulas for confidence intervals for Benford’s law are shown to be useful for checking arrays of numerical data. Consequences for numeral systems with different bases are analyzed. The alternative expression for the frequencies of digits at the second decimal place is deduced together with the corresponding deviation intervals. In general, in this approach, all the presented results are a consequence of the positionality property of digital systems such as decimal, binary, etc.

我国商法体系缺陷的补救:民商区分

在我国"民商不分的混合立法模式"下,由混合于民法规范的商法规范与单行商法构成的商法规范体系存在着明显缺陷。为克服我国现行商法体系缺陷,应推动我国总纲性商法规范的立法化,实现民商区分的立法要求。在具体立法形式上,目前最现实的方案是制定《商法通则》,但不排除制定《商法典》的可能性。所谓民商区分,就是要对民事关系和商事关系区分对待,分别适用不同法律或者根据不同法律理念适用相同法律规范。因此,民商区分的关键问题就在于确定民事关系与商事关系的判断标准。在民商分立国家的商法典中,是以商人身份作为适用商法的依据,而商人身份又涉及商行为的判断问题。易言之,商人与商行为既是商法的核心范畴,也是确定商事关系的判断标准。但我国总纲性商法规范的核心范畴可确定为经营者与经营行为,并将其确定为民商区分的判断标准。至于营业制度,则不必纳入基本商法基本范畴,而将其作为总纲性商法规范的重要内容即可。