Raman spectra and structure of multicomponent oxide planar waveguides prepared by sol-gel

This work was aimed at understanding the structure of SiO₂–MO₂ (M = Ti, Zr, Hf) and SiO₂–HfO₂–MO₂ (M = Ti, Zr) materials, used as mixed oxide glass hosts for Er³⁺ ions in the fabrication of optical planar waveguides by sol-gel processing. This structural study was performed by Waveguide Raman Spectroscopy (WRS), complemented with X-ray diffraction (XRD). The admixture of TiO₂ to HfO₂, SiO₂–HfO₂ and HfO₂–ZrO₂ compositions was found to cause precipitation of nanocrystals of tetragonal HfO₂ or ZrO₂, or the formation of hafnia-titania mixed crystals, depending on the HfO₂/TiO₂ molar ratio.     

Improved square coloring of planar graphs

Square coloring is a variant of graph coloring where vertices within distance two must receive different colors. When considering planar graphs, the most famous conjecture (Wegner, 1977) states that $\frac{3}{2}\mathrm{\Delta }+1$ colors are sufficient to square color every planar graph of maximum degree Δ. This conjecture has been proven asymptotically for graphs with large maximum degree. We consider here planar graphs with small maximum degree and show that $2\mathrm{\Delta }+7$ colors are sufficient, which improves the best known bounds when $6?\mathrm{\Delta }?31$.     

Vertex partitions of (C3,C4,C6)-free planar graphs

A graph is $(k_1,k_2)$-colorable if it admits a vertex partition into a graph with maximum degree at most $k_1$ and a graph with maximum degree at most $k_2$. We show that every $(C_3,C_4,C_6)$-free planar graph is $(0,6)$-colorable. We also show that deciding whether a $(C_3,C_4,C_6)$-free planar graph is $(0,3)$-colorable is NP-complete.     

Multidimensional gas chromatography for the characterization of permanent gases and light hydrocarbons in catalytic cracking process

An integrated gas chromatographic system has been successfully developed and implemented for the measurement of oxygen, nitrogen, carbon monoxide, carbon dioxide and light hydrocarbons in one single analysis. These analytes are frequently encountered in critical industrial petrochemical and chemical processes like catalytic cracking of naphtha or diesel fuel to lighter components used in gasoline. The system employs a practical, effective configuration consisting of two three-port planar microfluidic devices in series with each other, having built-in fluidic gates, and a mid-point pressure source. The use of planar microfluidic devices offers intangible advantages like in-oven switching with no mechanical moving parts, an inert sample flow path, and a leak-free operation even with multiple thermal cycles. In this way, necessary features such as selectivity enhancement, column isolation, column back-flushing, and improved system cleanliness were realized. Porous layer open tubular capillary columns were employed for the separation of hydrocarbons followed by flame ionization detection. After separation has occurred, carbon monoxide and carbon dioxide were converted to methane with the use of a nickel-based methanizer for detection with flame ionization. Flow modulated thermal conductivity detection was employed to measure oxygen and nitrogen. Separation of all the target analytes was achieved in one single analysis of less than 12 min. Reproducibility of retention times for all compounds were found to be less than 0.1% (n = 20). Reproducibility of area counts at two levels, namely 100 ppm_v and 1000 ppm_v over a period of two days were found to be less than 5.5% (n = 20). Oxygen and nitrogen were found to be linear over a range from 20 ppm_v to 10,000 ppm_v with correlation coefficients of at least 0.998 and detection limits of less than 10 ppm_v. Hydrocarbons of interest were found to be linear over a range from 200 ppb_v to 1000 ppm_v with correlation coefficients of greater than 0.999 and detection limits of less than 100 ppb_v.     

Universal point sets for planar three-trees

For every $n\in \mathbb{N}$, we present a set $S_n$ of $O(n^{3/2}\log n)$ points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of $S_n$. This is the first subquadratic upper bound on the cardinality of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs.