A Sort of Gray-scale Morphological Dilations and Erosions

We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive pairs. The duality between the dilation and the erosion and some other properties, such as the commuting property with translation and homothety, of these operators are discussed as well.     

Classification of edges using compactly supported shearlets

We analyze the detection and classification of singularities of functions $f={\chi }_S$, where $S?{\mathbb{R}}^d$ and $d=2,3$. It will be shown how the set ?S can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if ?S is a $d?1$ dimensional piecewise smooth manifold with $d=2$ or 3, we will classify smooth and non-smooth components of ?S. This improves previous results given for shearlet systems with a certain band-limited generator, since the estimates we derive are uniform. Moreover, we will show that our bounds are optimal. Along the way, we also obtain novel results on the characterization of wavefront sets in 3 dimensions by compactly supported shearlets. Finally, geometric properties of ?S such as curvature are described in terms of the continuous shearlet transform of f.     

Unifying pricing formula for several stochastic volatility models with jumps

In this paper, we introduce a unifying approach to option pricing under continuous‐time stochastic volatility models with jumps. For European style options, a new semi‐closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro‐differential equation. This approach is successfully applied to models with different volatility diffusion and jump processes. We also discuss how to price options with different payoff functions in a similar way. In particular, we focus on a log‐normal and a log‐uniform jump diffusion stochastic volatility model, originally introduced by Bates and Yan and Hanson, respectively. The comparison of existing and newly proposed option pricing formulas with respect to time efficiency and precision is discussed. We also derive a representation of an option price under a new approximative fractional jump diffusion model that differs from the aforementioned models, especially for the out‐of‐the money contracts. Copyright © 2017 John Wiley & Sons, Ltd.     

贯通中学和大学数学教与学 集成造就学生数学素养和创新实践能力

针对如何破解我国从应试教育向素质教育转变步履维艰的难题,本文详细介绍了如何贯通中学和大学数学教与学,集成培养学生数学素养和创新实践能力的具体做法和成效.     

Accurate Geometry and Non-Covalent Interactions in 1-Phenylethanol and its Monohydrate: A Rotational Study

The pure rotational spectra of 1-phenylethanol and its monohydrate were measured by using a pulsed jet Fourier transform microwave spectrometer. One conformer of the 1-phenylethanol monomer with the trans form was observed in the pulsed jet. The experimental values of rotational constants of ten isotopologues, including eight mono-substituted ¹³C and one D isotopologues, allow an accurate structure determination of the skeleton of 1-phenylethanol. For its monohydrate, only one isomer has been observed, of which 1-phenylethanol adopts the trans form and binds with water through an O−H⋅⋅⋅O_w and an O_w−H⋅⋅⋅π hydrogen bond. Each rotational transition displays a doublet with a relative intensity ratio of 1 : 3, due to a hindered internal rotation of water around its C₂ axis. This study provides the information on accurate geometry of 1-phenylethanol (PE) and large amplitude motion of water in the PE monohydrate.     

Facile Formation of Sulfurized Nanorod-Like ZnO/Zn(OH)2 and Hierarchical Flower-Like γ-Zn(OH)2/ϵ-Zn(OH)2 from a Green Synthesis and Application as Luminescent Solar Concentrator

This research endeavors to overcome the significant challenge of developing materials that simultaneously possess photostability and photosensitivity to UV-visible irradiation. Sulfurized nanorod (NR)-like ZnO/Zn(OH)₂ and hierarchical flower-like γ-Zn(OH)₂/ϵ-Zn(OH)₂ were identified from XRD diffraction patterns and Raman vibrational modes. The sulfurized material, observed by FEG-SEM and TEM, showed diameters ranging from 10 and 40 nm and lengths exceeding 200 nm. The S²⁻ ions intercalated Zn²⁺, modulating NRs to dumbbell-like microrods. SAED and HRTEM illustrated the atomic structure in (101) crystal plane. Its direct band gap of 3.0 eV was attributed to the oxygen vacancies, which also contribute to the deep-level emissions at 422 and 485 nm. BET indicated specific surface area of 4.4 m² g⁻¹ and pore size as mesoporosity, which are higher compared to the non-sulfurized analogue. These findings were consistent with the observed photocurrent, photostability and photoluminescence (PL), further supporting the suitability of sulfurized NR-like ZnO/Zn(OH)₂ as a promising candidate for Luminescent solar concentrators (LSC)-photovoltaic (PV) system.     

The simultaneous elimination of arsenic and mercury ions via hollow fiber supported liquid membrane and their reaction mechanisms: Experimental and modeling based on DFT and generating function

This study investigates the simultaneous removal of low concentrations of arsenic and mercury ions from synthetic produced water via hollow fiber supported liquid membrane (HFSLM). Results show that HFSLM can remove both arsenic and mercury ions from synthetic produced water to less than 0.02 and 0.001 mg·L^-1, respectively. These final concentrations comply with the wastewater standard of Thailand. Percentages of extraction for arsenic and mercury ions proved to be about 100 %. Those of recovery for arsenic and mercury ions reached 70 % and 75 %, respectively. A quantum model based on density functional theory (DFT) is introduced to analyze the forming and breaking of supramolecular complex species in the processes of extraction and recovery, respectively. Furthermore, the concept of Generating Function is applied to construct a mathematical model for forecasting the potential of removing metal ions via HFSLM. The mathematical model conforms to the experimental data, having an average relative deviation of 5 %. The results of this study provide a better understanding of the transport mechanisms of arsenic and mercury ions.