Modelling and measurement accuracy enhancement of flue gas flow using neural networks

This paper discusses the modeling of the flue gas flow in industrial ducts and stacks using artificial neural networks (ANN's). Based upon the individual velocity and other operating conditions, an ANN model has been developed for the measurement of the volume flow rate. The model has been validated by the experiment using a case-study power plant. The results have shown that the model can largely compensate for the nonrepresentativeness of a sampling location and, as a result, the measurement accuracy of the flue gas flow can be significantly improved

Graphs with 3-rainbow index n−1n-1 and n−2n-2

Let $G$ be a nontrivial connected graph with an edge-coloring $c:E(G)\rightarrow \{1,2,\ldots,q\},$ $q\in \mathbb{N}$, where adjacent edges may be colored the same. A tree $T$ in $G$ is a $rainbow tree$ if no two edges of $T$ receive the same color. For a vertex set $S\subseteq V(G)$, the tree connecting $S$ in $G$ is called an $S$-tree. The minimum number of colors that are needed in an edge-coloring of $G$ such that there is a rainbow $S$-tree for each $k$-set $S$ of $V(G)$ is called the $k$-rainbow index of $G$, denoted by $rx_k(G)$. In \cite{Zhang}, they got that the $k$-rainbow index of a tree is $n-1$ and the $k$-rainbow index of a unicyclic graph is $n-1$ or $n-2$. So there is an intriguing problem: Characterize graphs with the $k$-rainbow index $n-1$ and $n-2$. In this paper, we focus on $k=3$, and characterize the graphs whose 3-rainbow index is $n-1$ and $n-2$, respectively.Comment: 14 page