Arithmetical properties of Multiple Ramanujan sums

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic properties of the multiple Ramanujan sum and study several types of Dirichlet series involving the multiple Ramanujan sum. As an application, we evaluate higher-dimensional determinants of higher-dimensional matrices, the entries of which are given by values of the multiple Ramanujan sum.Comment: 19 page

Effect of very high pressure on life of plants and animals

We studied the tolerance of living organisms, such as a small animal (Milnesium tardigradum), a small crustacean (Artemia), non-vascular plants or moss (Ptichomitrium and Venturiella), and a vascular plant (Trifolium) to the extremely high hydrostatic pressure of 7.5 GPa. It turned out that most of the high pressure exposed seeds of white clover were alive. Those exposed to 7.5 GPa for up to 1 day and seeded on agar germinated roots. Those exposed for up to 1 hour and seeded on soil germinated stems and leaves. Considering the fact that proteins begins to unfold around 0.3 GPa, it seems difficult to understand that all the living samples which have been investigated can survive after exposure to 7.5 GPa