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

The 3-rainbow index of a graph

Let $G$ be a nontrivial connected graph with an edge-coloring $c: E(G)\rightarrow \{1,2,...,q\},$ $q \in \mathbb{N}$, 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 subset $S\subseteq V(G)$, a tree that connects $S$ 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 $k$-subset $S$ of $V(G)$ is called $k$-rainbow index, denoted by $rx_k(G)$. In this paper, we first determine the graphs whose 3-rainbow index equals 2, $m,$ $m-1$, $m-2$, respectively. We also obtain the exact values of $rx_3(G)$ for regular complete bipartite and multipartite graphs and wheel graphs. Finally, we give a sharp upper bound for $rx_3(G)$ of 2-connected graphs and 2-edge connected graphs, and graphs whose $rx_3(G)$ attains the upper bound are characterized.Comment: 13 page

Shaking table test and numerical simulation for acceleration response laws of shallow-buried biased double-arch tunnel

In order to reveal the acceleration response law of shallow-buried bias double-arch tunnel under earthquake. The acceleration response of the shallow-buried biased double-arch tunnel under the action of Wenchuan wave was studied by the combination of shaking table test and numerical simulation. The effects of non-bias and bias on the acceleration response of shallow-buried biased double-arch tunnels were discussed. Research indicates: (1) Horizontal acceleration amplification factor of the left-hole (non-biased side) for the shallow-buried biased double-arch tunnel is V-shaped, and the right-hole (bias side) is ∩-shaped. The vertical acceleration amplification factor of the left-hole tends to increase continuously, and the right-hole shows a trend of decreasing first and then increasing continuously. (2) In the state of both the bias and the non-biased tunnel, the acceleration response in the vertical direction is stronger than that in the horizontal direction. (3) In the two states of bias and non-bias, the difference between the horizontal and vertical acceleration amplification factors of the double-arch tunnel is larger. It indicates that the excitation direction of the seismic wave has a great influence on the acceleration response of the double-arch tunnel. (4) Relatively biased double-arch tunnels, the regularity of non-biased double-arch tunnels is better, indicating that the bias voltage has a greater impact on double-arch tunnels

The temporal changes in the emission spectrum of Comet 9P/Tempel 1 after Deep Impact

The time dependence of the changes in the emission spectra of Comet 9P/Tempel 1 after Deep Impact are derived and discussed. This was a unique event because for the first time it gave astronomers the opportunity to follow the time history of the formation and decay of O(1S), OH, CN, C2, C3, NH, and NH2. Least squares fits of a modified Haser model with constraints using known rate constants were fit to the observed data. In the case of OH a simple two-step Haser model provides a reasonable fit to the observations. Fitting the emissions from O(1S), CN, C2, C3, NH, and NH2 requires the addition of a delayed component to a regular two or three step Haser model. From this information a picture of the Deep Impact encounter emerges where there is an initial formation of gas and dust, which is responsible for the prompt emission that occurs right after impact. A secondary source of gas starts later after impact when the initial dust has dissipated enough so that solar radiation can reach the surface of freshly exposed material. The implications of this and other results are discussed in terms of the implications on the structure and composition of the comet's nucleus.Comment: Accepted for publication in The Astrophysical Journal; 26 pages including 8 figures and 1 tabl

Aerosols Monitored by Satellite Remote Sensing

Aerosols, small particles suspended in the atmosphere, affect the air quality and climate change. Their distributions can be monitored by satellite remote sensing. Many images of aerosol properties are available from websites as the by-products of the atmospheric correction of the satellite data. Their qualities depend on the accuracy of the atmospheric correction algorithms. The approaches of the atmospheric correction for land and ocean are different due to the large difference of the ground reflectance between land and ocean. A unified atmospheric correction (UAC) approach is developed to improve the accuracy of aerosol products over land, similar to those over ocean. This approach is developed to estimate the aerosol scattering reflectance from satellite data based on a lookup table (LUT) of in situ measured ground reflectance. The results show that the aerosol scattering reflectance can be completely separated from the satellite measured radiance over turbid waters and lands. The accuracy is validated with the mean relative errors of 22.1%. The vertical structures of the aerosols provide a new insight into the role of aerosols in regulating Earth\u27s weather, climate, and air quality

Dopamine dysregulation in a mouse model of paroxysmal nonkinesigenic dyskinesia.

Paroxysmal nonkinesigenic dyskinesia (PNKD) is an autosomal dominant episodic movement disorder. Patients have episodes that last 1 to 4 hours and are precipitated by alcohol, coffee, and stress. Previous research has shown that mutations in an uncharacterized gene on chromosome 2q33-q35 (which is termed PNKD) are responsible for PNKD. Here, we report the generation of antibodies specific for the PNKD protein and show that it is widely expressed in the mouse brain, exclusively in neurons. One PNKD isoform is a membrane-associated protein. Transgenic mice carrying mutations in the mouse Pnkd locus equivalent to those found in patients with PNKD recapitulated the human PNKD phenotype. Staining for c-fos demonstrated that administration of alcohol or caffeine induced neuronal activity in the basal ganglia in these mice. They also showed nigrostriatal neurotransmission deficits that were manifested by reduced extracellular dopamine levels in the striatum and a proportional increase of dopamine release in response to caffeine and ethanol treatment. These findings support the hypothesis that the PNKD protein functions to modulate striatal neuro-transmitter release in response to stress and other precipitating factors

Nudel functions in membrane traffic mainly through association with Lis1 and cytoplasmic dynein

Nudel and Lis1 appear to regulate cytoplasmic dynein in neuronal migration and mitosis through direct interactions. However, whether or not they regulate other functions of dynein remains elusive. Herein, overexpression of a Nudel mutant defective in association with either Lis1 or dynein heavy chain is shown to cause dispersions of membranous organelles whose trafficking depends on dynein. In contrast, the wild-type Nudel and the double mutant that binds to neither protein are much less effective. Time-lapse microscopy for lysosomes reveals significant reduction in both frequencies and velocities of their minus end–directed motions in cells expressing the dynein-binding defective mutant, whereas neither the durations of movement nor the plus end–directed motility is considerably altered. Moreover, silencing Nudel expression by RNA interference results in Golgi apparatus fragmentation and cell death. Together, it is concluded that Nudel is critical for dynein motor activity in membrane transport and possibly other cellular activities through interactions with both Lis1 and dynein heavy chain