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

Characteristics of novel Ti–10Mo-xCu alloy by powder metallurgy for potential biomedical implant applications

When biomaterials are implanted in the human body, the surfaces of the implants become favorable sites for microbial adhesion and biofilm formation, causing peri-implant infection which frequently results in the failure of prosthetics and revision surgery. Ti–Mo alloy is one of the commonly used implant materials for load-bearing bone replacement, and the prevention of infection of Ti–Mo implants is therefore crucial. In this study, bacterial inhibitory copper (Cu) was added to Ti–Mo matrix to develop a novel Ti–Mo–Cu alloy with bacterial inhibitory property. The effects of Cu content on microstructure, tensile properties, cytocompatibility, and bacterial inhibitory ability of Ti–Mo–Cu alloy were systematically investigated. Results revealed that Ti–10Mo–1Cu alloy consisted of α and β phases, while there were a few Ti_{2}Cu intermetallic compounds existed for Ti–10Mo–3Cu and Ti–10Mo–5Cu alloys, in addition to α and β phases. The tensile strength of Ti–10Mo-xCu alloy increased with Cu content while elongation decreased. Ti–10Mo–3Cu alloy exhibited an optimal tensile strength of 1098.1 MPa and elongation of 5.2%. Cytocompatibility study indicated that none of the Ti–10Mo-xCu alloys had a negative effect on MC3T3-E1 cell proliferation. Bacterial inhibitory rates against S. aureus and E. coli increased with the increase in Cu content of Ti–10Mo-xCu alloy, within the ranges of 20–60% and 15–50%, respectively. Taken together, this study suggests that Ti–10Mo–3Cu alloy with high strength, acceptable elongation, excellent cytocompatibility, and the bacterial inhibitory property is a promising candidate for biomedical implant applications