Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.Comment: 9 pages, 5 figures, revised version, to appear in Discrete Mathematic

A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

Determination of alkylamine carbonate nonionic-anion oil displacement agent in oil-field water using HPLC after derivatization with 4- methoxybenzenesulfonyl fluoride

In this study, a method for the determination of alkylamine carbonate (AAC) nonionic-anion oil displacement agent in oil-field water was developed for the first time, involving pre-column derivatization using a novel labeling agent and HPLC with diode-array detection. The derivatization and chromatographic separation conditions were investigated thoroughly. The analyte was labeled with 4-methoxybenzenesulfonyl fluoride at 50 °C for 20 min. When the method was applied in the determination of C18A5C (an AAC oil displacement agent containing eighteen alkyl and five amino groups) a linear calibration curve was obtained from 1.0 to 100.0 μg mL-1 with a correlation coefficient of more than 0.999 and a detection limit of 0.05 μg mL-1. In the determination of real oil-field water samples, the recovery range of C18A5C was 91.8% to 96.2%, and the intra-day and inter-day relative standard deviations were 2.9-3.5% and 3.8-4.3%, respectively. The experimental results demonstrate that this method, with its merits of simplicity in pretreatment, rapidity in derivatization, and stability of the derivatives, can be employed in the analysis of C18A5C and has potential application in the detection of other oil displacement surfactants containing amino groups. It is of great significance to develop a fast, easy-to-operate, sensitive and reliable method for environmental impact assessment. © The Royal Society of Chemistry 2013

An advanced fuzzy Bayesian-based FMEA approach for assessing maritime supply chain risks

This paper aims to develop a novel model to assess the risk factors of maritime supply chains by incorporating a fuzzy belief rule approach with Bayesian networks. The new model, compared to traditional risk analysis methods, has the capability of improving result accuracy under a high uncertainty in risk data. A real case of a world leading container shipping company is investigated, and the research results reveal that among the most significant risk factors are transportation of dangerous goods, fluctuation of fuel price, fierce competition, unattractive markets, and change of exchange rates in sequence. Such findings will provide useful insights for accident prevention

Facile Fabrication of Superhydrophobic Surface from Fluorinated POSS Acrylate Copolymer via One-Step Breath Figure Method and Its Anti-Corrosion Property

Novel fluorinated polyhedral oligomeric silsesquioxane (POSS) acrylic copolymers were synthesized by the radical solution polymerization. The superhydrophobic coating was prepared using a one-step breath figure method. Chemical constitution, morphology, hydrophobicity, and anticorrosion ability of as-prepared coatings were investigated by the corresponding equipment. The addition of proper fluorinated POSS can synchronously promote the formation of the micro-nano convex structure and the enrichment of fluorinated groups on the surface. Compared to commercial acrylic coating, the fluorinated POSS coating presented enhanced anticorrosion performance. The impedance was the highest and the corrosion current density was the lowest for superhydrophobic coating with 25 wt % fluorinated POSS.</jats:p

Anomalous thermoelectric effects of ZrTe5_{5} in and beyond the quantum limit

Thermoelectric effects are more sensitive and promising probes to topological properties of emergent materials, but much less addressed compared to other physical properties. Zirconium pentatelluride (ZrTe$_{5}$) has inspired active investigations recently because of its multiple topological nature. We study the thermoelectric effects of ZrTe$_{5}$ in a magnetic field and find several anomalous behaviors. The Nernst response has a steplike profile near zero field when the charge carriers are electrons only, suggesting the anomalous Nernst effect arising from a nontrivial profile of Berry curvature. Both the thermopower and Nernst signal exhibit exotic peaks in the strong-field quantum limit. At higher magnetic fields, the Nernst signal has a sign reversal at a critical field where the thermopower approaches to zero. We propose that these anomalous behaviors can be attributed to the Landau index inversion, which is resulted from the competition of the $\sqrt{B}$ dependence of the Dirac-type Landau bands and linear-$B$ dependence of the Zeeman energy ($B$ is the magnetic field). Our understanding to the anomalous thermoelectric properties in ZrTe$_{5}$ opens a new avenue for exploring Dirac physics in topological materials.Comment: 6 pages, 4 figure