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.     

Applications of Vibrational Spectroscopy for Analysis of Connective Tissues

Advances in vibrational spectroscopy have propelled new insights into the molecular composition and structure of biological tissues. In this review, we discuss common modalities and techniques of vibrational spectroscopy, and present key examples to illustrate how they have been applied to enrich the assessment of connective tissues. In particular, we focus on applications of Fourier transform infrared (FTIR), near infrared (NIR) and Raman spectroscopy to assess cartilage and bone properties. We present strengths and limitations of each approach and discuss how the combination of spectrometers with microscopes (hyperspectral imaging) and fiber optic probes have greatly advanced their biomedical applications. We show how these modalities may be used to evaluate virtually any type of sample (ex vivo, in situ or in vivo) and how “spectral fingerprints” can be interpreted to quantify outcomes related to tissue composition and quality. We highlight the unparalleled advantage of vibrational spectroscopy as a label-free and often nondestructive approach to assess properties of the extracellular matrix (ECM) associated with normal, developing, aging, pathological and treated tissues. We believe this review will assist readers not only in better understanding applications of FTIR, NIR and Raman spectroscopy, but also in implementing these approaches for their own research projects.     

长链支化聚丙烯的非线性流变行为

通过大幅振荡剪切试验方法, 研究了长链支化聚丙烯的非线性流变学行为, 揭示了长链支化结构与非线性黏弹响应的关系. 利用傅里叶变换流变学方法得到试样的三次倍频相对振幅I_3/1与应变的标度关系, 用于界定线性聚丙烯和长链支化聚丙烯非线性流变行为的差异, 并定义了非线性系数来量度长链支化程度. 在高应变下, I_3/1与应变的变化关系可以进一步描述长链支化在非线性流场下的特性, 并得到了长链支化程度与其非线性响应之间的变化关系. 通过应力波的Lissajous曲线分解, 发现了环内和环间黏弹性的差异, 长链支化结构在大应变流场下的非线性黏弹性响应弱于线性结构, 支化程度越高非线性响应越弱.     

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A Mellin transform approach to pricing barrier options under stochastic elasticity of variance

This article considers a problem of evaluating barrier option prices when the underlying dynamics are driven by stochastic elasticity of variance (SEV). We employ asymptotic expansions and Mellin transform to evaluate the option prices. The approach is able to efficiently handle barrier options in a SEV framework and produce explicitly a semi-closed form formula for the approximate barrier option prices. The formula is an expansion of the option price in powers of the characteristic amplitude scale and variation time of the elasticity and it can be calculated easily by taking the derivatives of the Black–Scholes price for a barrier option with respect to the underlying price and computing the one-dimensional integrals of some linear combinations of the Greeks with respect to time. We confirm the accuracy of our formula via Monte-Carlo simulation and find the SEV effect on the Black–Scholes barrier option prices.     

Effects of post-deposition annealing on chemical composition of SiNx film in SiO2/SiNx/SiO2/Si stacked structure

To systematically evaluate the quality of SiN_x films in multi-stacked structures, we investigated the effects of post-deposition annealing (PDA) on the film properties of SiN_x within the SiO₂/SiN_x/SiO₂/Si stacked structure by performing X-ray photoelectron spectroscopy (XPS), X-ray reflectivity (XRR), Fourier transform infrared (FT-IR) spectroscopy, and scanning transmission electron microscope–electron energy loss spectroscopy (STEM-EELS) analyses. The XPS results showed that PDA induces the oxidation of the SiN_x layer. In particular, new finding is that Si-rich SiN_x in the SiN_x layer is preferentially oxidized by PDA even in multi-stacked structure. The XRR results showed that the SiN_x layer becomes thinner, whereas the interface layer between the SiN_x layer and Si becomes thicker. It is concluded by STEM-EELS and XPS that this interface layer is SiON layer. The density of N–H and Si–H bonding within the stacked structure strongly depends on the PDA temperature. Our study helps elucidate the properties of SiN_x films in stacked structures from various perspectives.     

Magnetite nanoparticle mediated catalytic aquathermolysis of Omani heavy crude oil

The worldwide demand for energy continues to grow and the production of heavy crude is escalating due to shortage of conventional light crude. The transportation of heavy crude oil from the head-well to the refinery is a challenging task due to its high viscosity and low API gravity. Catalytic aquathermolysis is one of the most significant and cost-effective viscosity reduction techniques employed in the up gradation of the crude oil at elevated temperatures and hence to enhance oil extraction process. In this study, catalytic aquathermolysis of Omani heavy crude oil was performed using magnetite nanoparticles (NPs). The NPs were synthesised by reverse co-precipitation method using iron salts in alkaline medium. The synthesised NPs were characterized using Scanning Electron Microscopy (SEM), X-Ray Powder Diffraction (XRD), Energy Dispersive X- Ray analysis (EDX) and Fourier Transform Infrared Spectroscopy (FTIR). The XRD results exhibited a characteristic peak confirming the high purity of iron oxide nanoparticles. The FTIR spectral analysis designated two well-defined peaks corresponding to wave numbers of 500 ?cm^?1 and 630 ?cm^?1, endorses the presence of Fe–O. The catalytic aquathermolysis experiments were carried out in a Parr high temperature-high pressure batch reactor at different experimental conditions. The processing parameters in temperature range of 250 ?°C - 300 ?°C, 0.1% to 0.3% catalyst loading, water to oil ratio of 1:7 to 3:7 with 24–72 ?h of reaction time. The initial pressure in the reactor was maintained at 32 ?bars and the optimization was performed using the Taguchi method to maximize the level of heavy oil. An orthogonal array was employed to analyse the effects of mean response and mean signal-to-noise ratio (S/N) to upgrade the heavy oil. The regression analysis was used to establish a relationship between the viscosity and experimental parameters. The experimental outcomes indicates that the maximum reduction in viscosity occurred at a processing temperature of 300 ?°C, 1:7 ?W/O ratio, 0.1 ?wt% of catalyst concentration and 48 ?h of reaction time. Similarly, the optimum conditions for the reduction in API gravity were obtained at 280 ?°C temperature, 3:7 ?W/O ratio, 0.2 ?wt% of catalyst concentration and a reaction time of 24 ?h.