The extremal unicyclic graphs of the revised edge Szeged index with given diameter

Let $G$ be a connected graph. The revised edge Szeged index of $G$ is defined as $Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\in E(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0}(e|G)}{2})$, where $m_{u}(e|G)$ (resp., $m_{v}(e|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), and $m_{0}(e|G)$ is the number of edges equidistant from both ends of $e$, respectively. In this paper, the graphs with minimum revised edge Szeged index among all the unicyclic graphs with given diameter are characterized.Comment: arXiv admin note: text overlap with arXiv:1805.0657

No mixed graph with the nullity η(G~)=∣V(G)∣−2m(G)+2c(G)−1\eta(\widetilde{G})=|V(G)|-2m(G)+2c(G)-1

A mixed graph $\widetilde{G}$ is obtained from a simple undirected graph $G$, the underlying graph of $\widetilde{G}$, by orienting some edges of $G$. Let $c(G)=|E(G)|-|V(G)|+\omega(G)$ be the cyclomatic number of $G$ with $\omega(G)$ the number of connected components of $G$, $m(G)$ be the matching number of $G$, and $\eta(\widetilde{G})$ be the nullity of $\widetilde{G}$. Chen et al. (2018)\cite{LSC} and Tian et al. (2018)\cite{TFL} proved independently that $|V(G)|-2m(G)-2c(G) \leq \eta(\widetilde{G}) \leq |V(G)|-2m(G)+2c(G)$, respectively, and they characterized the mixed graphs with nullity attaining the upper bound and the lower bound. In this paper, we prove that there is no mixed graph with nullity $\eta(\widetilde{G})=|V(G)|-2m(G)+2c(G)-1$. Moreover, for fixed $c(G)$, there are infinitely many connected mixed graphs with nullity $|V(G)|-2m(G)+2c(G)-s$ $( 0 \leq s \leq 3c(G), s\neq1 )$ is proved

On the extremal cacti with minimum Sombor index

Let $H$ be a graph with edge set $E_H$. The Sombor index and the reduced Sombor index of a graph $H$ are defined as $SO(H) = \sum\limits_{uv\in E_H}\sqrt{d_{H}(u)^{2}+d_{H}(v)^{2}}$ and $SO_{red}(H) = \sum\limits_{uv\in E_H}\sqrt{(d_{H}(u)-1)^{2}+(d_{H}(v)-1)^{2}}$, respectively. Where $d_{H}(u)$ and $d_{H}(v)$ are the degrees of the vertices $u$ and $v$ in $H$, respectively. A cactus is a connected graph in which any two cycles have at most one common vertex. Let $\mathcal{C}(n, k)$ be the class of cacti of order $n$ with $k$ cycles. In this paper, the lower bound for the Sombor index of the cacti in $\mathcal{C}(n, k)$ is obtained and the corresponding extremal cacti are characterized when $n\geq 4k-2$ and $k\geq 2$. Moreover, the lower bound of the reduced Sombor index of cacti is obtained by similar approach

The extremal unicyclic graphs with given diameter and minimum edge revised Szeged index

Let $H$ be a connected graph. The edge revised Szeged index of $H$ is defined as $Sz^{\ast}_{e}(H) = \sum\limits_{e = uv\in E_H}(m_{u}(e|H)+\frac{m_{0}(e|H)}{2})(m_{v}(e|H)+\frac{m_{0}(e|H)}{2})$, where $m_{u}(e|H)$ (resp., $m_{v}(e|H)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than to vertex $v$ (resp., $u$), and $m_{0}(e|H)$ is the number of edges equidistant from $u$ and $v$. In this paper, the extremal unicyclic graphs with given diameter and minimum edge revised Szeged index are characterized

RecycleGPT: An Autoregressive Language Model with Recyclable Module

Existing large language models have to run K times to generate a sequence of K tokens. In this paper, we present RecycleGPT, a generative language model with fast decoding speed by recycling pre-generated model states without running the whole model in multiple steps. Our approach relies on the observation that adjacent tokens in a sequence usually have strong correlations and the next token in a sequence can be reasonably guessed or inferred based on the preceding ones. Experiments and analysis demonstrate the effectiveness of our approach in lowering inference latency, achieving up to 1.4x speedup while preserving high performance.Comment: Technical Repor

Formation of highly oxygenated organic molecules from chlorine-atom-initiated oxidation of alpha-pinene

Highly oxygenated organic molecules (HOMs) from atmospheric oxidation of alpha-pinene can irreversibly condense to particles and contribute to secondary organic aerosol (SOA) formation. Recently, the formation of nitryl chloride (C1NO(2)) from heterogeneous reactions, followed by its subsequent photolysis, is suggested to be an important source of chlorine atoms in many parts of the atmosphere. However, the oxidation of monoterpenes such as alpha-pinene by chlorine atoms has received very little attention, and the ability of this reaction to form HOMs is completely unstudied. Here, chamber experiments were conducted with alpha-pinene and chlorine under low- and high-nitrogen-oxide (NOx, NOx = NO+NO2) conditions. A nitrate-based CI-APi-ToF (chemical ionization-atmospheric pressure interface-time of flight) mass spectrometer was used to measure HOM products. Clear distributions of monomers with 9-10 carbon atoms and dimers with 18-20 carbon atoms were observed under low-NOx conditions. With increased concentration of NOx within the chamber, the formation of dimers was suppressed due to the reactions of peroxy radicals with NO. We estimated the HOM yields from chlorine-initiated oxidation of alpha-pinene under low-NOx conditions to be around 1.8 %, though with a substantial uncertainty range (0.8 %-4 %) due to lack of suitable calibration methods. Corresponding yields at high NOx could not be determined because of concurrent ozonolysis reactions. Our study demonstrates that also the oxidation of alpha-pinene by chlorine atoms and yield low-volatility organic compounds.Peer reviewe

Molecular Composition of Oxygenated Organic Molecules and Their Contributions to Organic Aerosol in Beijing

The understanding at a molecular level of ambient secondary organic aerosol (SOA) formation is hampered by poorly constrained formation mechanisms and insufficient analytical methods. Especially in developing countries, SOA related haze is a great concern due to its significant effects on climate and human health. We present simultaneous measurements of gas-phase volatile organic compounds (VOCs), oxygenated organic molecules (OOMs), and particle-phase SOA in Beijing. We show that condensation of the measured OOMs explains 26-39% of the organic aerosol mass growth, with the contribution of OOMs to SOA enhanced during severe haze episodes. Our novel results provide a quantitative molecular connection from anthropogenic emissions to condensable organic oxidation product vapors, their concentration in particle-phase SOA, and ultimately to haze formation.Peer reviewe

Unprecedented Ambient Sulfur Trioxide (SO3) Detection : Possible Formation Mechanism and Atmospheric Implications

Sulfur trioxide (SO3) is a crucial compound for atmospheric sulfuric acid (H2SO4) formation, acid rain formation, and other atmospheric physicochemical processes. During the daytime, SO3 is mainly produced from the photo-oxidation of SO2 by OH radicals. However, the sources of SO3 during the early morning and night, when OH radicals are scarce, are not fully understood. We report results from two field measurements in urban Beijing during winter and summer 2019, using a nitrate-CI-APi-LTOF (chemical ionization-atmospheric pressure interface-long-time-offlight) mass spectrometer to detect atmospheric SO3 and H2SO4. Our results show the level of SO3 was higher during the winter than during the summer, with high SO3 levels observed especially during the early morning (similar to 05:00 to similar to 08:30) and night (similar to 18:00 to similar to 05:00 the next day). On the basis of analysis of SO2, NOx, black carbon, traffic flow, and atmospheric ions, we suggest SO3 could be formed from the catalytic oxidation of SO2 on the surface of traffic-related black carbon. This previously unidentified SO3 source results in significant H2SO4 formation in the early morning and thus promotes sub-2.5 nm particle formation. These findings will help in understanding urban SO3 and formulating policies to mitigate secondary particle formation in Chinese megacities.Peer reviewe

A 3D study on the amplification of regional haze and particle growth by local emissions

The role of new particle formation (NPF) events and their contribution to haze formation through subsequent growth in polluted megacities is still controversial. To improve the understanding of the sources, meteorological conditions, and chemistry behind air pollution, we performed simultaneous measurements of aerosol composition and particle number size distributions at ground level and at 260 m in central Beijing, China, during a total of 4 months in 2015-2017. Our measurements show a pronounced decoupling of gas-to-particle conversion between the two heights, leading to different haze processes in terms of particle size distributions and chemical compositions. The development of haze was initiated by the growth of freshly formed particles at both heights, whereas the more severe haze at ground level was connected directly to local primary particles and gaseous precursors leading to higher particle growth rates. The particle growth creates a feedback loop, in which a further development of haze increases the atmospheric stability, which in turn strengthens the persisting apparent decoupling between the two heights and increases the severity of haze at ground level. Moreover, we complemented our field observations with model analyses, which suggest that the growth of NPF-originated particles accounted up to similar to 60% of the accumulation mode particles in the Beijing-Tianjin-Hebei area during haze conditions. The results suggest that a reduction in anthropogenic gaseous precursors, suppressing particle growth, is a critical step for alleviating haze although the number concentration of freshly formed particles (3-40 nm) via NPF does not reduce after emission controls.Peer reviewe

Role of iodine oxoacids in atmospheric aerosol nucleation

Iodic acid (HIO3) is known to form aerosol particles in coastal marine regions, but predicted nucleation and growth rates are lacking. Using the CERN CLOUD (Cosmics Leaving Outdoor Droplets) chamber, we find that the nucleation rates of HIO3 particles are rapid, even exceeding sulfuric acid-ammonia rates under similar conditions. We also find that ion-induced nucleation involves IO3- and the sequential addition of HIO3 and that it proceeds at the kinetic limit below +10 degrees C. In contrast, neutral nucleation involves the repeated sequential addition of iodous acid (HIO2) followed by HIO3, showing that HIO2 plays a key stabilizing role. Freshly formed particles are composed almost entirely of HIO3, which drives rapid particle growth at the kinetic limit. Our measurements indicate that iodine oxoacid particle formation can compete with sulfuric acid in pristine regions of the atmosphere.Peer reviewe