Perfect matchings extend to two or more hamiltonian cycles in hypercubes

Kreweras conjectured that every perfect matching of a hypercube $Q_n$ for $n\ge 2$ can be extended to a hamiltonian cycle of $Q_n$. Fink confirmed the conjecture to be true. It is more general to ask whether every perfect matching of $Q_n$ for $n\ge 2$ can be extended to two or more hamiltonian cycles of $Q_n$. In this paper, we prove that every perfect matching of $Q_n$ for $n\ge 4$ can be extended to at least $2^{2^{n?4}}$ different hamiltonian cycles of $Q_n$.     

Development and validation of a simple and sensitive high‐resolution LC/MS method for determination of PF‐04620110 in dog plasma: Application to a pharmacokinetic study

In this study, a more sensitive and reliable quantitative method based on ultra‐high performance liquid chromatography coupled with Q‐Exactive‐Orbitrap‐MS in full‐mass scan was developed and validated for the determination of PF‐04620110 in dog plasma. After protein precipitation with acetonitrile, the sample separations were carried out on an Acquity BEH C₁₈ column with 1 mm ammonium acetate in water and acetonitrile containing 0.1% acetic acid as mobile phase, at a flow rate of 0.4 mL/min. The assay showed excellent linearity over the concentration range of 1–2000 ng/mL with correlation coefficient >0.9980 (r > 0.9980). The LLOQ was 1 ng/mL. The inter‐ and intra‐day precision (RSD, %) was within 9.69% while the accuracy (RE, %) was in the range of ?8.59–11.24%. The extraction recovery was >85.37% and the assay was free of matrix effects. PF‐04620110 was demonstrated to be stable under various processing and handing conditions. The validated method was successfully applied to the pharmacokinetic study of PF‐04620110 in dogs and the results revealed that PF‐04620110 was slowly eliminated from plasma with a clearance of 60.81 ± 7.11 mL/h/kg for intravenous administration and 81.44 ± 25.79 mL/h/kg for oral administration. The oral bioavailability was determined to be 77.89% in dogs.     

Effect of the Reaction Temperature on the Removal of Diesel Particulate Matter by Ozone Injection

This study seeks to investigate the removal efficiency of particulate matter (PM) from the actual diesel exhaust at various reaction temperatures by using non-thermal plasma (NTP). The effect of the reaction temperature on removal efficiency was reflected by the change in the concentration of particles in different modes and the weight fraction of volatile organics in PM. The Arrhenius equation was used to determine the apparent activation energies E_a of the soot in PM. In addition, the difference in the oxidation reaction at various reaction temperatures and the effect of NTP on the properties of PM were discussed. After considering the decreasing ranges of the total concentration and the weight of the PM, it was determined that 120 °C is the optimal temperature choice for PM removal. The decreasing range of the total concentration reached 57.13% and 66.79% of PM was removed when the PM is measured by weight. NTP has better effect on the removal of smaller particles. The weight fraction of the volatile fraction markedly decreases after the reaction and the apparent activation energy of soot noticeably decreased. The oxidizability of the excited species in NTP was enhanced with the increase of the reaction temperature. However, the excited species concentration declined concurrently, resulting in the occurrence of the optimized range of reaction temperature. The particles were removed by the oxidation that occurred on the surface of the primary particle and the disintegration of the structure of the particles.

     

NMR Reveals That a Highly Reactive Nonheme FeIV=O Complex Retains Its Six-Coordinate Geometry and S=1 State in Solution

The [Fe^IV(O)(Me₃NTB)]²⁺ (Me₃NTB=tris[(1-methyl-benzimidazol-2-yl)methyl]amine) complex 1 has been shown by Mössbauer spectroscopy to have an S=1 ground state at 4 K, but is proposed to become an S=2 trigonal-bipyramidal species at higher temperatures based on a DFT model to rationalize its very high C−H bond-cleavage reactivity. In this work, ¹H NMR spectroscopy was used to determine that 1 does not have C₃-symmetry in solution and is not an S=2 species. Our results show that 1 is unique among nonheme Fe^IV=O complexes in retaining its S=1 spin state and high reactivity at 193 K, providing evidence that S=1 Fe^IV=O complexes can be as reactive as their S=2 counterparts. This result emphasizes the need to identify factors besides the ground spin state of the Fe^IV=O center to rationalize nonheme oxoiron(IV) reactivity.     

Phase transition layers with boundary intersection for an inhomogeneous Allen–Cahn equation

We consider the nonlinear problem of inhomogeneous Allen–Cahn equation

${?}^2\mathrm{\Delta }u+V(y)u(1?u^2)=0\text{in}\mathrm{\Omega },\frac{?u}{?\nu }=0\text{on}?\mathrm{\Omega },$

where Ω is a bounded domain in ${\mathbb{R}}^2$ with smooth boundary, ? is a small positive parameter, ν denotes the unit outward normal of ?Ω, V is a positive smooth function on $\overline{\mathrm{\Omega }}$. Let Γ be a curve intersecting orthogonally with ?Ω at exactly two points and dividing Ω into two parts. Moreover, Γ satisfies stationary and non-degenerate conditions with respect to the functional ${\int }_{\mathrm{\Gamma }}{V}^{1/2}$. We can prove that there exists a solution $u_{?}$ such that: as $?\to 0$, $u_{?}$ approaches +1 in one part of Ω, while tends to ?1 in the other part, except a small neighborhood of Γ.     

Advanced Li-Ion Batteries with High Rate,Stability, and Mass Loading Based on Graphene Ribbon Hybrid Networks

To optimize the cycle life and rate performance of lithium-ion batteries (LIBs), ultra-fine Fe₂O₃ nanowires with a diameter of approximately 2 nm uniformly anchored on a cross-linked graphene ribbon network are fabricated. The unique three-dimensional structure can effectively improve the electrical conductivity and facilitate ion diffusion, especially cross-plane diffusion. Moreover, Fe₂O₃ nanowires on graphene ribbons (Fe₂O₃/GR) are easily accessible for lithium ions compared with the traditional graphene sheets (Fe₂O₃/GS). In addition, the well-developed elastic network can not only undergo the drastic volume expansion during repetitive cycling, but also protect the bulk electrode from further pulverization. As a result, the Fe₂O₃/GR hybrid exhibits high rate and long cycle life Li storage performance (632 mAh g⁻¹ at 5 A g⁻¹, and 471 mAh g⁻¹ capacity maintained even after 3000 cycles). Especially at high mass loading (≈4 mg cm⁻²), the Fe₂O₃/GR can still deliver higher reversible capacity (223 mAh g⁻¹ even at 2 A g⁻¹) compared with the Fe₂O₃/GS (37 mAh g⁻¹) for LIBs.     

New Type of Columnar Liquid Crystal Superlattice in Double-Taper Ionic Minidendrons

Wedge-shaped molecules, such as dendrons, are among the most important building blocks for directed supramolecular self-assembly. Here we present a new approach aimed at widening the range and complexity of potential mesophases by introducing double-tapered mesogens. Two series of compounds are presented, both alkali metal salts (Li, Na, Cs) of 3,4,5-tris-alkoxybenzoic acid with a second tapered tris-alkoxyaryl group attached at the end of an alkoxy chain. The double-tapered compounds all display an unusual hexagonal columnar phase consisting of one ionic and three non-ionic columns per unit cell. The cation size has an unexpectedly drastic effect on unit cell size. Unlike most columnar phases, the current phases show unusually high dimensional stability on heating, and high stiffness in spite of being 80–85 % aliphatic, attributed to their molecular topology. The described approach may lead to co-assemblies of multifunctional materials, for example, parallel p- and n-semiconducting nanowires or parallel ionic and electronic conductors.     

Impact of post-injection strategy on the physicochemical properties and reactivity of diesel in-cylinder soot

Post injection has significant benefit in the reduction of diesel soot emissions. Therefore, there is a need to understand the effect of post-injection strategy on soot physicochemical properties and reactivity because they play an important role in soot oxidation process that governs the final soot emissions. This work focuses on the impact of post injection on the physicochemical properties and reactivity of diesel in-cylinder soot using a main plus post injection (M*P) and a single injection (M) strategy. The soot was sampled by a developed total cylinder sampling system, and the dividing points of soot formation-dominant and oxidation-dominant phases were used for studying the impacts of post injection on the characteristics of in-cylinder soot. The physicochemical properties of the soot samples, including primary particle size, nanostructure, carbon chemical state and surface functional groups, were characterized. The soot reactivity was evaluated in terms of peak temperature, burnout temperature and apparent activation energy. In the oxidation-dominant phase, the M*P soot initially possesses smaller primary particle size, shorter fringe length, larger tortuosity, lower sp²/sp³ hybridization ratio of carbon atoms and higher content of aliphatic CH groups than the M soot. The beneficial influence of physicochemical properties on soot reactivity when using post injection is validated by the thermogravimetric data, which shows that the M*P soot is more reactive than the M soot at the onset of the oxidation-dominant phase. In the M*P case, the soot generated from the main-injection combustion has lower reactivity than the soot from the post-injection combustion after they experience the soot formation-dominant phase. The results indicate that the use of post injection leads to in-cylinder soot with physicochemical properties that favor reactivity. The enhancement of reactivity means that the soot will be more readily oxidized in the subsequent combustion process, and consequently contributes to a reduction in final soot emissions.     

Nonparametric Quantile Inference for Cause-specific Residual Life Function Under Length-biased Sampling

Acta Mathematicae Applicatae Sinica, English Series - This paper considers a competing risks model for right-censored and length-biased survival data from prevalent sampling. We propose a...