Analysis of anions in hydrofluoro ethers by ion chromatography

Hydrofluoro ethers (HFES) are considered to be an ideal cleaning solvent in applications like vapor degreasing and wet cleaning. It is also a good solvent replacement for CFCs (chlorofluorocarbons), HCFCs (hydrochlorofluorocarbons), HFCs (hydrofluorocarbons) and chlorinated solvents because they have a short atmospheric lifetime and low global warming potential. Based upon their properties, hydrofluoro ethers are ideally suited for the demands of the electronics industry. However, the electronics industry requires these solvents to have high purity, especially in the area of residual anions. This paper will present information on an extraction methodology for the transfer of anions from the hydrofluoro ether to water. Then, an analytical method utilizing ion chromatography that is capable of detection of 10 anions (fluoride, acetate, formate, chloride, nitrite, bromide, nitrate, sulfate, oxalate, and phosphate) in the part per billion level will be demonstrated.     

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

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

Positive-, negative-, and orthogonal-phase-velocity propagation of electromagnetic plane waves in a simply moving medium

Planewave propagation in a simply moving, dielectric-magnetic medium that is isotropic in the co-moving reference frame, is classified into three different categories: positive-, negative-, and orthogonal-phase-velocity (PPV, NPV, and OPV). Calculations from the perspective of an observer located in a non-co-moving reference frame show that, whether the nature of planewave propagation is PPV or NPV (or OPV in the case of non-dissipative mediums) depends strongly upon the magnitude and direction of that observer's velocity relative to the medium. PPV propagation is characterized by a positive real wavenumber, NPV propagation by a negative real wavenumber. OPV propagation only occurs for non-dissipative mediums, but weakly dissipative mediums can support nearly OPV propagation.     

Simple Explicit Formulas for the Frame-Stewart Numbers

Several different approaches to the multi-peg Tower of Hanoi problem are equivalent. One of them is Stewart's recursive formula ¶¶ S (n, p) = min {2S (n₁, p) + S (n-n₁, p-1) | n₁, n-n₁ ? \mathbbZ⁺}. S (n, p) = min \{2S (n_1, p) + S (n-n_1, p-1)\mid n_1, n-n_1 \in \mathbb{Z}^+\}. ¶¶In the present paper we significantly simplify the explicit calculation of the Frame-Stewart's numbers S(n, p) and give a short proof of the domain theorem that describes the set of all pairs (n, n₁), such that the above minima are achieved at n₁.     

On graphs with largest possible game domination number

Let $\gamma \left(G\right)$ and ${\gamma }_g\left(G\right)$ be the domination number and the game domination number of a graph $G$, respectively. In this paper ${\gamma }_g$-maximal graphs are introduced as the graphs $G$ for which ${\gamma }_g\left(G\right)=2\gamma \left(G\right)?1$ holds. Large families of ${\gamma }_g$-maximal graphs are constructed among the graphs in which their sets of support vertices are minimum dominating sets. ${\gamma }_g$-maximal graphs are also characterized among the starlike trees, that is, trees which have exactly one vertex of degree at least $3$.     

Sierpiński graphs as spanning subgraphs of Hanoi graphs

Hanoi graphs H _p ⁿ model the Tower of Hanoi game with p pegs and n discs. Sierpinski graphs S _p ⁿ arose in investigations of universal topological spaces and have meanwhile been studied extensively. It is proved that S _p ⁿ embeds as a spanning subgraph into H _p ⁿ if and only if p is odd or, trivially, if n = 1.     

Partition distance in graphs

If G is a graph and \(\mathcal{P}\) is a partition of V(G), then the partition distance of G is the sum of the distance between all pairs of vertices that lie in the same part of \(\mathcal{P}\). This concept generalizes several metric concepts and is dual to the concept of the colored distance due to Dankelmann, Goddard, and Slater. It is proved that the partition distance of a graph can be obtained from the Wiener index of weighted quotient graphs induced by the transitive closure of the Djokovi?–Winkler relation as well as by any partition coarser than it. It is demonstrated that earlier results follow from the obtained theorems. Applying the main results, upper bounds on the partition distance of trees with prescribed order and radius are proved and corresponding extremal trees characterized.