Towards a quaternionic function theory linked with the Lamé's wave functions

Over the past few years, considerable attention has been given to the role played by the Lamé's Wave Functions (LWFs) in various problems of mathematical physics and mechanics. The LWFs arise via the method of separation of variables for the wave equation in ellipsoidal coordinates. The present paper introduces the Lamé's Quaternionic Wave Functions (LQWFs), which extend the LWFs to a non‐commutative framework. We show that the theory of the LQWFs is determined by the Moisil‐Theodorescu type operator with quaternionic variable coefficients. As a result, we explain the connections between the solutions of the Lamé's wave equation, on one hand, and the quaternionic hyperholomorphic and anti‐hyperholomorphic functions on the other. We establish analogues of the basic integral formulas of complex analysis such as Borel‐Pompeiu's, Cauchy's, and so on, for this version of quaternionic function theory. We further obtain analogues of the boundary value properties of the LQWFs such as Sokhotski‐Plemelj formulae, the ‐hyperholomorphic extension of a given Hölder function and on the square of the singular integral operator. We address all the text mentioned earlier and explore some basic facts of the arising quaternionic function theory. We conclude the paper showing that the spherical, prolate, and oblate spheroidal quaternionic wave functions can be generated as particular cases of the LQWFs. Copyright © 2015 John Wiley & Sons, Ltd.     

A Simple Approach for Multi‐fidelity Experimentation Applied to Financial Engineering

In practical applications, information about the accuracy or ‘fidelity’ of alternative surrogate systems may be ambiguous and difficult to determine. To address this problem, we propose to treat surrogate system fidelity level as a categorical factor in optimal response surface design. To design the associated experiments, we apply the Expected Integrated Mean Squared Error optimal design criterion, which takes into account both variance and bias errors. The performance of the proposed design was compared using three test cases to four types of alternatives using the Empirical Integrated Squared Error. Because of its ability to foster relatively accurate predictions, the proposed design is recommended in fidelity experimental design, particularly when the experimenters lack sufficient information about the fidelity levels of surrogate systems. The method was applied to the case of intraday trading optimization in which data were collected from the Taiwan Futures Exchange. We also calculated the implied volatility from the Merton's Jump‐diffusion model via the fast Fourier transform algorithm with three different models of varying fidelity levels. Copyright © 2014 John Wiley & Sons, Ltd.     

Characterization of size‐segregated aerosols using ToF‐SIMS imaging and depth profiling

Size‐segregated particles were collected with a ten‐stage micro‐orifice uniform deposit impactor from a busy walkway in a downtown area of Hong Kong. The surface chemical compositions of aerosol samples from each stage were analyzed using time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) operated in the static mode. The ToF‐SIMS spectra of particles from stage 2 (5.6–10 µm), stage 6 (0.56–1 µm), and stage 10 (0.056–0.1 µm) were compared, and the positive ion spectra from stage 2 to stage 10 were analyzed with principal component analysis (PCA). Both spectral analysis and PCA results show that the coarse‐mode particles were associated with inorganic ions, while the fine particles were associated with organic ions. PCA results further show that the particle surface compositions were size dependent. Particles from the same mode exhibited more similar surface features. Particles from stage 2 (5.6–10 µm), stage 6 (0.56–1 µm), and stage 10 (0.056–0.1 µm) were further selected as representatives of the three modes, and the chemical compositions of these modes of particles were examined using ToF‐SIMS imaging and depth profiling. The results reveal a non‐uniform chemical distribution from the outer to the inner layer of the particles. The coarse‐mode particles were shown to contain inorganic salts beneath the organics surface. The accumulation‐mode particles contained sulfate, nitrate, ammonium salts, and silicate in the regions below a thick surface layer of organic species. The nucleation‐mode particles consisted mainly of soot particles with a surface coated with sulfate, hydrocarbons, and, possibly, fullerenic carbon. The study demonstrated the capability of ToF‐SIMS depth profiling and imaging in characterizing both the surface and the region beneath the surface of aerosol particles. It also revealed the complex heterogeneity of chemical composition in size and depth distributions of atmospheric particles. Copyright © 2014 John Wiley & Sons, Ltd.     

Influence of surface properties on the interfacial adhesion in carbon fiber/epoxy composites

A polyacrylonitrile‐based carbon fiber was electrochemically oxidized in an aqueous ammonium bicarbonate solution with current density of up to 2.76 A/m² at room temperature. X‐ray photoelectron spectroscopy revealed that the oxygen content increased with increasing current density before approaching saturation. The increase can be divided into two regions, the rapid increase region (0–1.78 A/m²) and a plateau region (1.78–2.76 A/m²). The surface chemistry analysis showed that the interlaminar shear strength (ILSS) value of the carbon fiber/epoxy composite could be improved by 24.7%. The carbon structure was examined using Raman spectroscopy in terms of order/disorder in the graphite structure and the results indicated that the relative percentage of graphite carbon in the form of sp² hybridization increased above a current density of 1.39 A/m². The increasing non‐polar graphite carbon on the carbon fiber surface decreased the surface energy. As a result, both the surface free energy () and its polar component () decreased when current density increased above 1.78 A/m². The ILSS value had no direct relationship with the nature and surface density of the oxygen‐containing functional groups nor with the carbon structure. It is the surface free energy (), especially the polar component (), which played a critical role in affecting the interfacial adhesion of carbon fiber/epoxy composites. The ILSS value changed with increasing current density and could be divided into three distinct regions, as chemical interaction region (I), anchor force region (II) and matrix damage region (III). Copyright © 2013 John Wiley & Sons, Ltd.     

Multiple plasmonic effect on photocurrent generation of metal‐loaded titanium dioxide composite/dye films on gold grating surface

We demonstrate the multiple plasmonic effect on the photocurrent properties of photoanodes containing Ag or Au nanoparticles (NPs) loaded onto titanium dioxide film (Ag–TiO₂ or Au–TiO₂) on Au grating surfaces. Ag–TiO₂ or Au–TiO₂ nanocomposite particles are prepared by a flame spray pyrolysis route. The structures and morphologies of the prepared products are characterized by high‐resolution transmission electron microscopy. The Ag–TiO₂ or Au–TiO₂ composite NPs are deposited by spin coating onto the Au grating surfaces. The photoanode electrode is a layered structure of blu‐ray disc‐recordable grating substrate/Au/Ag (or Au)–TiO₂/dye/electrolyte/indium‐tin oxide. The plasmonic effect is induced when Ag or Au NPs are located within the propagating surface plasmon (SP) field on the Au grating surface. The short‐circuit photocurrent is increased by exciting the grating‐coupled propagating SP on the Au gratings and is further enhanced by positioning the Ag or Au NPs within the grating‐coupled SP field. Copyright © 2014 John Wiley & Sons, Ltd.     

Ultraviolet light absorber with low surface energy: synthesis and characterization

Novel fluorine-containing ultraviolet absorbers (FBPs) with low surface energy were successfully synthesized based on 2,4-dihydroxy benzophenone (BP-1), and their structures were characterized by ¹H NMR, ¹³C NMR, FTIR, and HRMS. UV absorption of FBPs was studied in 10⁻⁴ M dichloromethane (CH₂Cl₂), which demonstrated the superior UV absorption capability of FBPs (ca. ?=1.7×10⁴ to 2.2×10⁴ at λ_max) over the matrix (?=1.7×10⁴ at λ_max). Quantum chemistry calculation was performed to investigate the stable structure and UV electronic absorption bands of FBPs. The surface chemistry information of high-chlorinated polyethylene (HCPE) coating films embedded with ultraviolet absorbers (UVAs) was given by X-ray photoelectron spectroscopy (XPS) and contact angle measurement. The results show that the surface enrichment capability of FBPs is remarkably better than traditional UVAs (including BP-1, BP-3, BP-12) because of the low surface energy properties of FBPs.     

Acceleration of self‐consistent field convergence in ab initio molecular dynamics simulation with multiconfigurational wave function

The Lagrange interpolation of molecular orbital (LIMO) method, which reduces the number of self‐consistent field iterations in ab initio molecular dynamics simulations with the Hartree–Fock method and the Kohn–Sham density functional theories, is extended to the theory of multiconfigurational wave functions. We examine two types of treatments for the active orbitals that are partially occupied. The first treatment, as denoted by LIMO(C), is a simple application of the conventional LIMO method to the union of the inactive core and the active orbitals. The second, as denoted by LIMO(S), separately treats the inactive core and the active orbitals. Numerical tests to compare the two treatments clarify that LIMO(S) is superior to LIMO(C). Further applications of LIMO(S) to various systems demonstrate its effectiveness and robustness. © 2014 Wiley Periodicals, Inc.     

The READY program: Building a global potential energy surface and reactive dynamic simulations for the hydrogen combustion

READY (REActive DYnamics) is a program for studying reactive dynamic systems using a global potential energy surface (PES) built from previously existing PESs corresponding to each of the most important elementary reactions present in the system. We present an application to the combustion dynamics of a mixture of hydrogen and oxygen using accurate PESs for all the systems involving up to four oxygen and hydrogen atoms. Results at the temperature of 4000 K and pressure of 2 atm are presented and compared with model based on rate constants. Drawbacks and advantages of this approach are discussed and future directions of research are pointed out. © 2014 Wiley Periodicals, Inc.     

Industrial Applications of Dimeric Surfactants: A Review

Dimeric surfactants also known as gemini surfactants have received lots of attention for high performance formulations in the various scientific and commercial products. Due to the greater amount of hydrocarbon per molecule, the critical micelle concentrations (CMC) of dimeric are typically one order of magnitude lower than the corresponding monomeric surfactant. They are ten to hundred times more efficient at reducing the surface tension of water and the interfacial tension of the oil-water interface than conventional surfactants. Besides, the Krafft temperatures of gemini surfactants with hydrophilic spacers are generally very low giving these surfactants the capacity to be used in cold water. These surfactants display a range of interesting properties, including elevated surface activity, extremely low CMC and extraordinary rheology and self-assimilation aspect. As a consequence of these properties, they have many potential applications include detergents and cleaning agents, cosmetics, textile, and dyeing, dispersion stabilization and emulsion polymerization, genetics science, pharmaceutical, and biological applications.      

Synthesis,Characterization, and Surface Properties of Cationic Gemini Surfactants

New pyridinium gemini surfactants have been synthesized by esterification of renewable fatty acids with mercaptoethanol furnishing respective esters (mercaptomethyl decanoate, mercaptomethyl dodecanoate, mercaptomethyl tetradecanoate, mercaptomethyl hexadecanoate) followed by their subsequent treatment with 4-dimethyl amino pyridine resulting in the formation of title gemini surfactants: 1-(5-(decanoyloxy)-2-hydroxypentyl)-4-((5-(decanoyloxy)-2-hydroxypentyl)dimethyl ammonio)pyridin-1-ium chloride (9), 1-(5-(dodecanoyloxy)-2-hydroxypentyl)-4-((5-(dodecanoyloxy)-2-hydroxypentyl)dimethyl ammonio)pyridin-1-ium chloride (10), 1-(5-(tetradecanoyloxy)-2-hydroxypentyl)-4-((5-(tetradecanoyloxy)-2-hydroxypentyl)dimethyl ammonio)pyridin-1-ium chloride (11), and 1-(5-(hexadecanoyloxy)-2-hydroxypentyl)-4-((5-(hexadecanoyloxy)-2-hydroxypentyl)dimethyl ammonio)pyridin-1-ium chloride (12). Their identifications are based on infrared, ¹H NMR, ¹³C NMR, distortionless enhanced polarization transfer, co-relational spectroscopy (COSY), and mass spectral studies. Their surface active properties are also evaluated on the basis of surface tension and conductivity measurements. Thermal stability of these long chain cationic gemini surfactants have been measured by thermal gravimetric analysis under nitrogen atmosphere.