Modified Linear Programming and Class 0 Bounds for Graph Pebbling

Given a configuration of pebbles on the vertices of a connected graph $G$, a \emph{pebbling move} removes two pebbles from some vertex and places one pebble on an adjacent vertex. The \emph{pebbling number} of a graph $G$ is the smallest integer $k$ such that for each vertex $v$ and each configuration of $k$ pebbles on $G$ there is a sequence of pebbling moves that places at least one pebble on $v$. First, we improve on results of Hurlbert, who introduced a linear optimization technique for graph pebbling. In particular, we use a different set of weight functions, based on graphs more general than trees. We apply this new idea to some graphs from Hurlbert's paper to give improved bounds on their pebbling numbers. Second, we investigate the structure of Class 0 graphs with few edges. We show that every $n$-vertex Class 0 graph has at least $\frac53n - \frac{11}3$ edges. This disproves a conjecture of Blasiak et al. For diameter 2 graphs, we strengthen this lower bound to $2n - 5$, which is best possible. Further, we characterize the graphs where the bound holds with equality and extend the argument to obtain an identical bound for diameter 2 graphs with no cut-vertex.Comment: 19 pages, 8 figure

Metagenomic insights into the relationship between gut microbiota and residual feed intake of small-sized meat ducks

IntroductionThe objective of this study was to determine the regulatory effects of gut microbiota on the feed efficiency (FE) of small-sized meat ducks by evaluating correlations between gut microbiota and residual feed intake (RFI).MethodsA total of 500 21-day-old healthy male ducks with similar initial body weights (645 ± 15.0 g) were raised contemporaneously in the same experimental facility until slaughter at 56 days of age. In total, nine low-RFI (LR) and nine high-RFI (HR) birds were selected for further gut microbiota composition and functional analyses based on the production performance, and the RFI was calculated from 22 to 56 days of age.ResultsGrowth performance results indicated a significantly lower RFI, feed conversion ratio, feed intake, and average daily feed intake in the LR ducks (P < 0.05). Taxonomy results of gut microbiota showed the identification of 19 kinds of phyla and more than 250 kinds of genera in all samples. No significant discrepancies in cecal bacterial α-diversity were discovered between the LR and HR groups, which indicated that the microbial modulatory effects on RFI may be attributed to the bacterial composition, rather than the species diversity. Differential analysis of bacterial communities between the LR and HR groups showed a significant increment of Firmicutes and a significant decline of Bacteroidetes in the LR group (P < 0.05). Specifically, genera of Erysipelatoclostridium, Parasutterella, Fournierella, and Lactococcus significantly proliferated, while Bacteroides significantly decreased in the LR group (P < 0.05). Furthermore, correlation analysis showed that the RFI was significantly correlated with carbohydrate metabolism-related bacteria including Bacteroides, Alistipes, Bifidobacterium, Ruminiclostridium_9, Sellimonas, Oscillibacter, Escherichia-Shigella, Lactococcus, and Streptococcus.ConclusionIn conclusion, the communities related to carbohydrate metabolism had positive regulatory effects on the FE of small-sized meat ducks, promoting it by improving the relative abundance and utilization of these communities. The present study provides valuable insight into the dynamics of gut microbiota underlying the variations in the FE of small-sized meat ducks

Research Status and Prospects of Converter Limestone Instead of Lime for Slagging and Steelmaking

Research status and development trend of limestone instead of lime for steelmaking and slagging technology are systematically analyzed. Through comparative analysis, it can be seen that the current converter limestone slagging and steelmaking technology simplifies the entire slagging process, improves the slag dephosphorization effect, and reduces steel slag. The production volume has increased the economic benefit per ton of steel. On the whole, the limestone steelmaking slagging process is a high-efficiency, low-consumption, and environmentally-friendly new slagging method, which is of great significance to promoting energy conservation, emission reduction and sustainable development of steel enterprises. However, the decomposition of limestone requires a large amount of heat, which affects the slagging rate. Therefore, in order to further optimize the limestone steelmaking slagging process, a limestone powder spraying slagging technology is proposed, which can effectively solve the heat caused by the direct limestone slagging process. Slagging and CO2 utilization problems caused by high consumption

The Kinetic Mechanism of the Thermal Decomposition Reaction of Small Particles of Limestone at Steelmaking Temperatures

Converter blowing limestone powder making slag steelmaking process has the advantages of low carbon and high efficiency, and can realize the resource utilization of CO2 in the metallurgical process, which is in line with the development direction of green metallurgy. Based on a thermogravimetric-differential thermal analyzer, the kinetic mechanism of decomposition of small limestone at steelmaking temperatures was investigated by a modified double extrapolation method. The results showed that with a higher rate of heating, limestone decomposition lagged, and decomposition temperature increased. Furthermore, the smaller the limestone particle size, the lower the activation energy of decomposition. Compared with N2, air, and O2, small limestone powder used for converter blowing could complete more rapid decomposition, and the time required for decomposition shortened by about 1/3, although the decomposition temperature increased in the CO2. The limestone decomposition rate increased and then decreased at low to high CO2 partial pressures. With a limiting link, the inhibition was more significant under high CO2 partial pressure, but the reaction can be fully completed by 1000 °C. The decomposition type modeled was stochastic nucleation and subsequent growth. As the partial pressure of CO2 increased from 25% to 100%, the number of reaction stages, n, increased

Thermodynamic Analysis of Hydrogen Production from Bio-Oil Steam Reforming Utilizing Waste Heat of Steel Slag

(1) Background: The discharged temperature of steel slag is up to 1450 °C, representing heat having a high calorific value. (2) Motivation: A novel technology, integrating bio-oil steam reforming with waste heat recovery from steel slag for hydrogen production, is proposed, and it is demonstrated to be an outstanding method via thermodynamic calculation. (3) Methods: The equilibrium productions of bio-oil steam reforming in steel slag under different temperatures and S/C ratios (the mole ratio of steam to carbon) are obtained by the method of minimizing the Gibbs free energy using HSC 6.0. (4) Conclusions: The hydrogen yield increases first and then decreases with the increasing temperature, but it increases with the increasing S/C. Considering equilibrium calculation and actual application, the optimal temperature and S/C are 706 °C and 6, respectively. The hydrogen yield and hydrogen component are 109.13 mol/kg and 70.21%, respectively, and the carbon yield is only 0.08 mol/kg under optimal conditions. Compared with CaO in steel slag, iron oxides have less effect on hydrogen production from bio-oil steam reforming in steel slag. The higher the basicity of steel slag, the higher the obtained hydrogen yield and hydrogen component of bio-oil steam reforming in steel slag. It is demonstrated that appropriately decreasing iron oxides and increasing basicity could promote the hydrogen yield and hydrogen component of bio-oil steam reforming that utilizes steel slag as a heat carrier during the industrial application

The Thermodynamic Characterizations of Hydrogen Production from Catalyst-Enhanced Steam Reforming of Bio-Oil over Granulated Blast Furnace Slag as Heat Carrier

To promote the efficiency of waste heat recovery from granulated blast furnace (BF) slag, a novel method of catalyst-enhanced steam reforming of bio-oil to recover heat from slag is proposed. CaO is utilized as a superior catalyst for the process of catalyst-enhanced steam reforming. The thermodynamic production of the catalyst-enhanced steam reforming of bio-oil in granulated BF slag is obtained using HSC 6.0 software. The optimal conditions are mainly assessed according to the hydrogen yield, hydrogen concentration and carbon production. Through the thermodynamic production and industrial application, the temperature of 608 °C, S/C of eight and pressure of 1 bar are found as the optimal conditions. At the optimal conditions, the hydrogen yield, hydrogen concentration and carbon production are 95.25%, 76.89% and 0.28 mol/kg, respectively. Taking the temperature of 625 °C, S/C of eight and pressure of 1 bar as an example, the catalyst could improve the hydrogen yield and hydrogen concentration from 93.99% and 70.31% to 95.15% and 76.49%, respectively. It is implied that utilizing the catalyst could promote the hydrogen yield and hydrogen concentration of steam reforming of bio-oil to recover waste heat from granulated BF slag. The mechanism of catalyst-enhanced steam reforming of bio-oil to recover waste heat from granulated BF slag is obtained to guide the subsequent industry application