Neutral operator with variable parameter and third-order neutral differential equation

Additional file 1. The TRS sequences of structural genes in the HP-PRRSV/SD16 genome (GenBank: JX087437)

Random Copolycarbonates Based on a Renewable Bicyclic Diol Derived from Citric Acid

To address the poor thermal stability of isohexides while at the same time retain rigidity, we developed a novel bicyclic diol octahydro-2,5-pentalenediol (OPD) from naturally occurring citric acid in this study. Owing to the bicyclic skeleton composed of two fused cyclopentane rings, OPD is supposed to have perfect rigidity but higher thermal stability compared to isohexides. Herein, OPD was first converted to octahydro-2,5-pentalenediol bis­(methyl carbonate) (OPBMC) by reacting with dimethyl carbonate. The absolute stereochemistry of OPBMC was investigated by 2D ¹H NMR and ¹³C NMR as well as single crystal X-ray diffraction. By polymerization of OPBMC with several aliphatic diols [1,8-octanediol (A₈), 1,10-decanediol (A₁₀), and 1,12-dodeacnediol (A₁₂)] and alicyclic diols [1,4-cyclohexane­dimethanol (CHDM), 1,2,2-trimethyl­cyclopentane-1,3-dimethanol (TCDM), and octahydro-2,5-pentalenediol (OPD)], a series of bio-based copolycarbonates (co-PCs) with intriguing properties were synthesized. NMR spectra revealed that the stereochemistry of OPBMC was preserved after polymerization. Both differential scanning calorimetry and wide-angle X-ray diffraction analyses revealed that co-PCs made from A₈, A₁₀, A₁₂, and OPD are semicrystalline, while co-PCs based on CHDM and TCDM are amorphous. A relatively high <i>T</i>_5% of 276 °C and outstanding high <i>T</i>_g up to 80.4 °C were detected for fully OPD-based co-PC, confirming the excellent thermal stability and rigidity of OPD. This work addresses some critical needs for high performance polymers such as improving the sustainability of raw materials and achieving both high <i>T</i>_g values and thermal stability

The ratio of the number of final recovered nodes by ClusterRank to those by out-degree centrality, PageRank and LeaderRank.

<p>The non-overlapped nodes in the top-50 lists are initially infected. We set . Each data point is obtained by averaging over 100 independent runs.</p

Kendall’s tau between ranking scores provided by different methods and the real spreading abilities.

<p>Here we focus on the ranks of the top- ( = 20 and 50) nodes with maximal out-degrees. We abbreviate ClusterRank, LeaderRank, PageRank and Out-degree centrality by CR, LR, PR and DR, respectively.</p

An example network with 38 nodes and 110 directed edges.

<p>Although nodes 0 and 37 have the same out-degree, node 37 is of higher influence (subject to spreading dynamics) than node 0. The clustering coefficients of these two nodes are and .</p

for top- ranked nodes by out-degree centrality (squares), PageRank (diamond), LeaderRank (triangle) and ClusterRank (circles).

<p>We set and . Each data point is obtained by averaging over 100 independent runs.</p

Kinetic Aspects for the Reduction of CO₂ and CS₂ with Mixed-Ligand Ruthenium(II) Hydride Complexes Containing Phosphine and Bipyridine

A new water-soluble ruthenium hydride complex [Ru­(H)­(bpy)₂(PTA)]­PF₆ (bpy = 2,2′-bipyridine, PTA = 1,3,5-triaza-7-phosphaadamantane) (<b>1a</b>) was prepared. <b>1a</b> reacted with CO₂ and CS₂ to give the corresponding formate and dithioformate complexes, respectively. Both the insertions of CO₂ and CS₂ into the Ru–H bond of <b>1a</b> followed second-order kinetics. The second-order rate constant (<i>k</i>₂) of CO₂ insertion reaction varied from (9.40 ± 0.41) × 10^–4 M^–1 s^–1 in acetone to (1.13 ± 0.08) × 10^–1 M^–1 s^–1 in methanol; moreover, the ln­(<i>k</i>₂) is in good linear relationship with the acceptor number (AN) of the solvent used. Although, the <i>k</i>₂ of CS₂ insertion reaction ranged from (3.43 ± 0.10) M^–1 s^–1 in methanol to (24.0 ± 0.5) M^–1 s^–1 in <i>N</i>,<i>N</i>-dimethylformamide, which is 1000 times faster than CO₂ insertion. Generally, the <i>k</i>₂ of CS₂ insertion increased with the static dielectric constant (<i>D</i>_s) of the reaction medium investigated. For comparison purposes, we further investigated the reactivity of [Ru­(H)­(bpy)₂(PPh₃)]­PF₆ (PPh₃ = triphenylphosphine) (<b>1b</b>) with CO₂ and CS₂. <b>1b</b> reacted with CO₂ slowly in the methanol with a <i>k</i>₂ of (1.46 ± 0.09) × 10^–3 M^–1 s^–1, yielding a formate complex [Ru­(η¹-OC­(H)O)­(bpy)₂(PPh₃)]­PF₆ (<b>2b</b>). The reaction of <b>1b</b> with CS₂ is 1000 times faster than that of CO₂. The structures of <b>1a</b>, <b>1b</b>, and <b>2b</b> were determined by X-ray crystallographic analysis

The dependence of on parameter .

<p>The initially infected nodes are the top-50 nodes obtained by out-degree centrality (squares), PageRank (diamonds), LeaderRank (triangles) and ClusterRank (circles). We set . Each data point is obtained by averaging over 100 independent runs.</p

Ranking correlation measured by Kendall’s tau between different methods.

<p>Here we focus on the ranks of the top- ( = 20 and 50) nodes with maximal out-degrees. We abbreviate ClusterRank, LeaderRank, PageRank and Out-degree centrality by CR, LR, PR and DR, respectively.</p

The dependance of on parameter in undirected Delicious and Cond-mat networks. We set .

<p>In (a) and (c), the initial infected nodes are those non-overlapped nodes in the top-50 places regardless of whether they are connected or not. In (b) and (d), the initial infected nodes are the non-overlapped nodes in top-50 places under constraint that any two of them are not connected. Each data point is obtained by averaging over 100 independent runs.</p