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 permissi...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.展开更多
Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number great...Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers.展开更多
Objective To explore the expression of S100A14 in breast cancer tissue,and the EGF and S100A14 feedback regulatory mechanism.Methods S100A14 mRNA level in 52 cases of breast cancer and adjacent normal tissue was detec...Objective To explore the expression of S100A14 in breast cancer tissue,and the EGF and S100A14 feedback regulatory mechanism.Methods S100A14 mRNA level in 52 cases of breast cancer and adjacent normal tissue was detected by quantitative real-time PCR.S100A14 protein in 21 cases of breast cancer and adjacent normal tissue was detected by Western blot.展开更多
文摘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.
文摘Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers.
文摘Objective To explore the expression of S100A14 in breast cancer tissue,and the EGF and S100A14 feedback regulatory mechanism.Methods S100A14 mRNA level in 52 cases of breast cancer and adjacent normal tissue was detected by quantitative real-time PCR.S100A14 protein in 21 cases of breast cancer and adjacent normal tissue was detected by Western blot.
