Connectivity keeping stars or double-stars in 2-connected graphs

In Mader (2010), Mader conjectured that for every positive integer $k$ and every finite tree $T$ with order $m$, every $k$-connected, finite graph $G$ with $\delta \left(G\right)\ge ?\frac{3}{2}k?+m?1$ contains a subtree $T^{\prime }$ isomorphic to $T$ such that $G?V\left(T^{\prime }\right)$ is $k$-connected. In the same paper, Mader proved that the conjecture is true when $T$ is a path. Diwan and Tholiya (2009) verified the conjecture when $k=1$. In this paper, we will prove that Mader’s conjecture is true when $T$ is a star or double-star and $k=2$.     

Direct Numerical Simulation of Head-On Quenching of Statistically Planar Turbulent Premixed Methane-Air Flames Using a Detailed Chemical Mechanism

A three-dimensional compressible Direct Numerical Simulation (DNS) analysis has been carried out for head-on quenching of a statistically planar stoichiometric methane-air flame by an isothermal inert wall. A multi-step chemical mechanism for methane-air combustion is used for the purpose of detailed chemistry DNS. For head-on quenching of stoichiometric methane-air flames, the mass fractions of major reactant species such as methane and oxygen tend to vanish at the wall during flame quenching. The absence of \(\text {OH}\) at the wall gives rise to accumulation of carbon monoxide during flame quenching because \(\text {CO}\) cannot be oxidised anymore. Furthermore, it has been found that low-temperature reactions give rise to accumulation of \(\text {HO}_{2}\) and \(\mathrm {H}_{2}\mathrm {O}_{2}\) at the wall during flame quenching. Moreover, these low temperature reactions are responsible for non-zero heat release rate at the wall during flame-wall interaction. In order to perform an in-depth comparison between simple and detailed chemistry DNS results, a corresponding simulation has been carried out for the same turbulence parameters for a representative single-step Arrhenius type irreversible chemical mechanism. In the corresponding simple chemistry simulation, heat release rate vanishes once the flame reaches a threshold distance from the wall. The distributions of reaction progress variable c and non-dimensional temperature T are found to be identical to each other away from the wall for the simple chemistry simulation but this equality does not hold during head-on quenching. The inequality between c (defined based on \(\text {CH}_{4}\) mass fraction) and T holds both away from and close to the wall for the detailed chemistry simulation but it becomes particularly prominent in the near-wall region. The temporal evolutions of wall heat flux and wall Peclet number (i.e. normalised wall-normal distance of \(T = 0.9\) isosurface) for both simple and detailed chemistry laminar and turbulent cases have been found to be qualitatively similar. However, small differences have been observed in the numerical values of the maximum normalised wall heat flux magnitude \(\left ({\Phi }_{\max } \right )_{\mathrm {L}}\) and the minimum Peclet number \((Pe_{\min })_{\mathrm {L}}\) obtained from simple and detailed chemistry based laminar head-on quenching calculations. Detailed explanations have been provided for the observed differences in behaviours of \(\left ({\Phi }_{\max }\right )_{\mathrm {L}}\) and \((Pe_{\min })_{\mathrm {L}}\). The usual Flame Surface Density (FSD) and scalar dissipation rate (SDR) based reaction rate closures do not adequately predict the mean reaction rate of reaction progress variable in the near-wall region for both simple and detailed chemistry simulations. It has been found that recently proposed FSD and SDR based reaction rate closures based on a-priori DNS analysis of simple chemistry data perform satisfactorily also for the detailed chemistry case both away from and close to the wall without any adjustment to the model parameters.     

General π‐Electron‐Assisted Strategy for Ir,Pt, Ru,Pd, Fe,Ni Single‐Atom Electrocatalysts with Bifunctional Active Sites for Highly Efficient Water Splitting

Both the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) are crucial to water splitting, but require alternative active sites. Now, a general π‐electron‐assisted strategy to anchor single‐atom sites (M=Ir, Pt, Ru, Pd, Fe, Ni) on a heterogeneous support is reported. The M atoms can simultaneously anchor on two distinct domains of the hybrid support, four‐fold N/C atoms (M@NC), and centers of Co octahedra (M@Co), which are expected to serve as bifunctional electrocatalysts towards the HER and the OER. The Ir catalyst exhibits the best water‐splitting performance, showing a low applied potential of 1.603 V to achieve 10 mA cm^?2 in 1.0 m KOH solution with cycling over 5 h. DFT calculations indicate that the Ir@Co (Ir) sites can accelerate the OER, while the Ir@NC₃ sites are responsible for the enhanced HER, clarifying the unprecedented performance of this bifunctional catalyst towards full water splitting.     

Post‐Treatment of CH3NH3PbI3/PbI2 Composite Films with Methylamine to Realize High‐Performance Photoconductor Devices

Organometallic halide perovskites have attracted great research interest as light‐active materials for use in optoelectronics. Here, we report a high‐performance photoconductor based on a methylammonium lead iodide (MAPbI₃) film that was prepared from a methylamine‐treated MAPbI₃/PbI₂ perovskite film. An ultrahigh responsivity of 3.6 A W^?1 and detectivity of 5.4×10¹² Jones were obtained for the film under 0.5 mW cm^?2 white‐light illumination. In addition, under 420 nm light irradiation, the film exhibited its highest responsivity and detectivity of 30 A W^?1 and 2.4×10¹⁴ Jones, respectively. The excellent photo‐response performance results from the improved electronic quality and suppressed nonradiative recombination channels of the treated perovskite thin film.     

On s-hamiltonian line graphs of claw-free graphs

For an integer $s\ge 0$, a graph $G$ is $s$-hamiltonian if for any vertex subset $S?V\left(G\right)$ with $\left|S\right|\le s$, $G?S$ is hamiltonian, and $G$ is $s$-hamiltonian connected if for any vertex subset $S?V\left(G\right)$ with $\left|S\right|\le s$, $G?S$ is hamiltonian connected. Thomassen in 1984 conjectured that every 4-connected line graph is hamiltonian (see Thomassen, 1986), and Ku?zel and Xiong in 2004 conjectured that every 4-connected line graph is hamiltonian connected (see Ryjá?ek and Vrána, 2011). In Broersma and Veldman (1987), Broersma and Veldman raised the characterization problem of $s$-hamiltonian line graphs. In Lai and Shao (2013), it is conjectured that for $s\ge 2$, a line graph $L\left(G\right)$ is $s$-hamiltonian if and only if $L\left(G\right)$ is $(s+2)$-connected. In this paper we prove the following.(i) For an integer $s\ge 2$, the line graph $L\left(G\right)$ of a claw-free graph $G$ is $s$-hamiltonian if and only if $L\left(G\right)$ is $(s+2)$-connected.(ii) The line graph $L\left(G\right)$ of a claw-free graph $G$ is 1-hamiltonian connected if and only if $L\left(G\right)$ is 4-connected.     

Photobleaching of Submicron DAST Crystals in a PMMA Film by Direct Laser Writing

Optics and Spectroscopy - Selective photobleaching of DAST (trans-4'-(dimethylamino)-Nmethyl-4-stilbazolium tosylate) non-linear crystals in a 2-μm-thick polymethacrylate film using direct...     

Analysis of Chuanxiong Rhizoma substrate on production of ligustrazine in endophytic Bacillus subtilis by ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry

Ligustrazine was the active ingredient of the traditional Chinese medicine Chuanxiong Rhizoma. However, the content of ligustrazine is very low. We proposed a hypothesis that ligustrazine was produced by the mutual effects between endophytic Bacillus subtilis and the Ligusticum chuanxiong Hort. This study aimed to explore whether the endophytic B. subtilis LB5 could make use of Chuanxiong Rhizoma fermentation matrix to produce ligustrazine and clarify the mechanisms of action preliminarily. Ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry analysis showed the content of ligustrazine in Chuanxiong Rhizoma was below the detection limit (0.1 ng/mL), while B. subtilis LB5 produced ligustrazine at the yield of 1.0268 mg/mL in the Chuanxiong Rhizoma‐ammonium sulfate fermentation medium. In the fermented matrix, the reducing sugar had a significant reduction from 12.034 to 2.424 mg/mL, and rough protein content increased from 2.239 to 4.361 mg/mL. Acetoin, the biosynthetic precursor of ligustrazine, was generated in the Chuanxiong Rhizoma‐Ammonium sulfate (151.2 mg/mL) fermentation medium. This result showed that the endophytic bacteria B. subtilis LB5 metabolized Chuanxiong Rhizoma via secreted protein to consume the sugar in Chuanxiong Rhizoma to produce a considerable amount of ligustrazine. Collectively, our preliminary research suggested that ligustrazine was the interaction product of endophyte, but not the secondary metabolite of Chuanxiong Rhizoma itself.     

Lithium intercalation and conduction in Fe-containing tantalum oxide films synthesized with an atmospheric pressure plasma jet

Journal of Solid State Electrochemistry - Lithium ionic intercalation and conduction performance of tantalum oxides films improved by adding with iron oxides using an atmospheric pressure plasma...     

Multi-targeted molecular docking,drug-likeness and ADMET studies of derivatives of few quinoline- and acridine-based FDA-approved drugs for anti-breast cancer activity

Structural Chemistry - Quinoline- and acridine-based drugs are widely used as anti-breast cancer agents. These drugs act through various mechanisms of action; for example, neratinib acts on...