Turing computability, probability, and prime numbers

We present an original theoretical approach to prove that $\pi (n)-Li(n)=o(M(n)\sqrt{Li(n)})$ almost certainly stands, where $\pi (n)$ is the number of primes not greater than $n$, $Li(n)$ is a logarithmic integral function, and $M(n)$ is an arbitrary function such that $M(n)\rightarrow\infty$.Comment: Revision of the contents over the whole range of the pape

Detection of a circadian enhancer in the mDbp promoter using prokaryotic transposon vector-based strategy

In mammals, the expression of 5–10% of genes occurs with circadian fluctuation in various organs and tissues. This cyclic transcription is thought to be directly or indirectly regulated through circadian transcriptional/translational feedback loops consisting of a set of clock genes. Among the clock genes in mammals, expression of the Dbp mRNA robustly oscillates both in vivo and in culture cells. Here, we present circadian enhancer detection strategy using prokaryotic transposon system. The mDbp promoter drives reporter gene expression in robust circadian cycles in rat-1 fibroblasts. To identify the circadian enhancer generating this robust rhythm, we developed a prokaryotic transposon-based enhancer detecting vector for in vitro transposition. Using this system, we identified a strong circadian enhancer region containing the CATGTG sequence in the 5′ flanking region of the mDbp gene; this enhancer region is critical for the ability of the mDbp promoter to drive robust oscillation in living cells. This enhancer is classified as a CANNTG type non-canonical E-box. These findings strongly suggest that CANNTG-type non-canonical E-boxes may contribute, at least in part, to the regulation of robust circadian gene expression. Furthermore, these data may help explain the wider effects of the CLOCK/BMAL1 complex in control of clock output genes

The Influences of Composition of Culturing Medea to Immuno-logical Properties of Nucleic Acid and Relative Substances of Microorganisms

Hemolytic and precipitin reaction of nucleic acid and nucloprotein fractions from Sh. flexneri 2 a and St. aureus were studied and the results as follow are obtained. 1 In these microorganisms, hemolytic reactions of nucleic acid fractions were negative, and precipitin reactions were positive. 2 Nucleoprotein fraction from Sh. flexneri 2 a grown on glucose added medea showed a stronger positive hemolytic reaction, whereas that from St. aureus tended to negative. 3 Nucleic acid fractions from these microorganisms grown on Fe⁺⁺ deficient medea by adding α, α'-dipyridyl showed a negative hemolytic reactions. 4 From these results it could be seen that the immunological properties of nucleic acid or nucleoprotein fractions were affected by the composition of culturing medea

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