Non-linear traces on the algebra of compact operators and majorization

We study non-linear traces of the Choquet type and the Sugeno type on the algebra of compact operators. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both the Choquet type and the Sugeno type respectively. There exists a close relation between non-linear traces of the Choquet type and majorization theory. We study trace class operators for non-linear traces of the Choquet type. More generally we discuss Schatten–von Neumann $p$-class operators for non-linear traces of the Choquet type. We determine when they form Banach spaces. This is an attempt at non-commutative integration theory for non-linear traces of the Choquet type on the algebra of compact operators. We also consider the triangle inequality for non-linear traces of the Sugeno type.     

Sensitivity comparison of gas chromatography–mass spectrometry with Cold EI and standard EI

Gas chromatography–mass spectrometry (GC–MS) with Cold EI is based on interfacing GC and MS with supersonic molecular beams (SMBs) along with electron ionization of vibrationally cold sample compounds in SMB in a fly-through ion source (hence the name Cold EI). Cold EI improves all the central performance aspects of GC–MS, and in this paper, we focus on its improvement of signal-to-noise ratio (S/N) and limits of detection (LODs). We found that the harder the compound for analysis with standard EI, the greater the Cold EI gain in S/N and LOD. The lower LOD and higher S/N of Cold EI emerge from a few reasons: (a) similar ionization yield as standard EI, (b) enhanced abundance of molecular ions, (c) elimination of vacuum background noise, (d) elimination of ion source-related peak tailing and degradation, (e) ability to lower the elution temperatures via the use of high column flow rates, and (f) greater range of thermally labile and low-volatility compounds that can be analyzed. We demonstrate the superior S/N and lower LOD of Cold EI versus standard EI in a range of compounds, from the simple-to-analyze octafluoronaphthalene all the way to reserpine and an organo-metallic compound that cannot be analyzed by standard EI. These compounds include methyl stearate, cholesterol, n-C₃₂H₆₆, large polycyclic aromatic hydrocarbons, dioctyl phthalates, diundecyl phthalate, pentachlorophenol, benzidine, lambda-cyhalothrin, and methidathion. The significantly lower Cold EI LODs that can be over 1000 times better than in standard EI further result in far superior response linearity and greater measurement dynamic range.