Microcolumn ion chromatography with conductimetric detection

Summary A miniaturized flow cell for an electrical conductivity detector has been made and applied to the ion chromatography of inorganic anions. It consisted of stainless steel tubes (0.13 mm ID×0.31 mm OD) and PTFE tubes (0.25 mm ID×2 mm OD). The detection limit for chloride at S/N=3 was 36 pg or 0.33 ppm for a 0.11 l injection.     

Packing chromatic number, $$\mathbf (1, 1, 2, 2) $$ ( 1 , 1 , 2 , 2 ) -colorings,and characterizing the Petersen graph

The packing chromatic number $$\chi _{\rho }(G)$$     

Isolation and structure determination of a new lasso peptide subterisin from Sphingomonas subterranea

A new lasso peptide named subterisin was isolated from the culture broth of Sphingomonas subterranea NBRC 16086^T. The molecular formula of subterisin was established as C₇₈H₁₂₁O₂₂N₂₁ based on accurate mass analysis. The chemical structure of subterisin was determined by 2D NMR experiments. The presence of macrolactam ring of Gly1–Glu8 was indicated by NOESY experiment and MS/MS analysis. The three-dimensional structure of subterisin in solution was established by calculation based on NMR data. The proposed biosynthetic gene cluster of subterisin was found on the genome of S. subterranea.     

The mathematical technique in Fermat's deduction of the law of refraction

This article attempts to explain Fermat's not quite obvious calculations connected with his deduction of the law of refraction in Analysis ad refractiones (1662), and to describe the development which led to these calculations. In 1657 Fermat tried to deduce a law of refraction based on the principle that light follows the quickest path between two given points. He did not succeed because he found that the calculations were too long and tedious. The calculations are indeed complicated, but if Fermat, in 1657, had been willing to accept Descartes' law of refraction he would probably also have seen that it solved his problem. However, Fermat was of the opinion that Descartes' law was wrong and, therefore, he did not expect that solution. Only in 1662, when he succeeded in reducing the calculations substantially, did he realize that they led to the sine law of Descartes.     

Restrictions of relatively Tauberian operators

For operators T with the property which in addition satisfy a spectral condition we consider conditions under which the restriction of T to a closed invariant subspace also satisfies the same inclusion on the subspace.