Fast preparation of nanocrystalline cellulose by microwave-assisted hydrolysis

In this work we report on the procedure for fast and controlled preparation of nanocrystalline cellulose (NCC) from commercially available microcrystalline cellulose using microwave-assisted hydrolysis. By varying the sulfuric acid concentration and hydrolysis temperature, an average hydrodynamic diameter of NCC between 126 and 1,310 nm with corresponding yields between 16 and 82 %, respectively, was obtained in a very short reaction time of 10 min. An additional advantage of the described procedure is its high reproducibility and ability to fine-tune the average NCC particle size by adjusting the reaction conditions, i.e., the sulfuric acid concentration and/or reaction temperature.     

Ab initio calculation of magnetic shielding and susceptibility. Finite perturbation calculation of susceptibility with GIAO's

The magnetic susceptibility of hydrogen fluoride is calculated with four different basis sets of gauge invariant atomic orbitals (GIAO's). The Roothaan equations are solved for various values of the magnetic field strength and the susceptibility is deduced by a numerical differentiation of the energy.     

Probability for Type I errors in gamma-ray spectrometric measurements of drinking water samples

In gamma-ray spectra, acquired in the absence of the sample, peaks occur which belong to the spectrometer background. When samples are measured, which contain radionuclides that appear in the background also and have activities near the detection level, the background contributes substantially to the peak areas. In the extreme case, when the contribution of the sample is much smaller than the contribution of the background, the peak area attributed to the radionuclide within a sample has the same probability of being positive or negative. Therefore, to interpret the results obtained from measurements of low-activity samples, the performance of the spectrum analysis procedure near the detection level must be known. To test the performance of the spectrum analysis procedure at low activities, the spectrometer background spectra were analyzed as if they had been water samples, prepared as dry residue obtained by evaporation of 50 L of water. The probabilities for false positives together with their decision thresholds are given for radionuclides appearing in the background spectra. For some of the radionuclides that do not appear in the background spectra, probabilities for false detection are given as well.     

Toward characterizing locally common graphs

A graph $H$ is common if the number of monochromatic copies of $H$ in a 2-edge-coloring of the complete graph is asymptotically minimized by the random coloring. The classification of common graphs is one of the most intriguing problems in extremal graph theory. We study the notion of weakly locally common graphs considered by Csóka, Hubai, and Lovász [arXiv:1912.02926], where the graph is required to be the minimizer with respect to perturbations of the random 2-edge-coloring. We give a complete analysis of the 12 initial terms in the Taylor series determining the number of monochromatic copies of $H$ in such perturbations and classify graphs $H$ based on this analysis into three categories:

• Graphs of Class I are weakly locally common.
• Graphs of Class II are not weakly locally common.
• Graphs of Class III cannot be determined to be weakly locally common or not based on the initial 12 terms.

As a corollary, we obtain new necessary conditions on a graph to be common and new sufficient conditions on a graph to be not common.