Positive numerical splitting method for the Hull and White 2D Black–Scholes equation

We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015     

Large Hexagonal Bi‐ and Trilayer Graphene Single Crystals with Varied Interlayer Rotations

Bi‐ and trilayer graphene have attracted intensive interest due to their rich electronic and optical properties, which are dependent on interlayer rotations. However, the synthesis of high‐quality large‐size bi‐ and trilayer graphene single crystals still remains a challenge. Here, the synthesis of 100 μm pyramid‐like hexagonal bi‐ and trilayer graphene single‐crystal domains on Cu foils using chemical vapor deposition is reported. The as‐produced graphene domains show almost exclusively either 0° or 30° interlayer rotations. Raman spectroscopy, transmission electron microscopy, and Fourier‐transformed infrared spectroscopy were used to demonstrate that bilayer graphene domains with 0° interlayer stacking angles were Bernal stacked. Based on first‐principle calculations, it is proposed that rotations originate from the graphene nucleation at the Cu step, which explains the origin of the interlayer rotations and agrees well with the experimental observations.     

Cisplatin-induced alteration on membrane composition of A549 cells revealed by ToF-SIMS

Cisplatin has been clinically used for treatment of solid tumors such as non–small-cell lung cancer for decades. However, tumor resistance may be acquired with losing the antitumor activity of cisplatin. As cellular membrane is the first barrier that cisplatin has to overcome before its further action inside the cells, the membrane composition must play a vital role in the cisplatin uptake and excretion, which further influences cisplatin sensitivity. In this work, we applied time-of-flight secondary ion mass spectrometry (ToF-SIMS) surface analysis combined with principle component analysis to distinguish the differences of cell membrane composition between non–small-cell lung cancer cells (A549) and its cisplatin resistant counterpart A549/DDP cells. The decreased phosphatidylcholine content and more abundant cholesterol were observed in the drug resistant cell surfaces, indicating the decreased membrane fluidity of A549/DDP cells. Moreover, we further compared membrane composition of A549 and A549/DDP cells after being treated with different concentrations of cisplatin. A higher composition level of proteins was discovered on all groups of A549/DDP cell membranes. The altered surface chemistry of cellular membranes induced by cisplatin indicates the significance of membrane structures in the drug resistance, which deserves further investigations to this regard.     

Fe3O4(001)-B表面水煤气变换反应机理第一性原理研究

采用自旋极化的密度泛函理论方法系统地研究了Fe_3O_4(001)-B表面水煤气变换的反应机理,计算了整个反应历程。结果表明,对于Fe_3O_4(001)-B表面上的水煤气变换反应,氧化还原、联合和再生三种反应路径共存,但氧化还原和联合机理的有效能垒较低,因而更占优势。对于生成H_2的基元反应,其活性受表面H浓度和催化剂表面O缺陷浓度影响;较高的表面H浓度和O缺陷浓度均有利于H_2生成。这些结果有助于进一步认识铁氧催化剂上的水煤气变换反应机理。     

Prediction of the Frontier Electronic States in a Finite Single-wall Carbon Nanotube

A theoretical model is summarized into the shorter vector principle. It is used to predict the topological structure of wave function and the oscillation rule of energy gap in various types of finite carbon nanotubes (CNTs). The theoretical model indicates that the characteristics of the electronic states only depend on the nanotube size and its symmetry along the shorter vector direction. In this direction, the wave functions of the original 3m (or 3m/2) periodicity are also suitable for armchair, chiral and zigzag finite CNTs with the C2 (Cs), C1 and Cn point groups, respectively. Energy gaps present the oscillation with 3m (or 3m/2) or odd-even n. The first principle calculations for some prototype systems are performed. The results are consistent with the theoretical model.     

The uncertain premium principle based on the distortion function

In this paper, we discuss the premium principle in uncertain environment. First, the net premium principle for uncertain risks is presented within the framework of uncertainty theory. With the help of distortion function, a new uncertain premium principle is derived from the uncertain net premium. Some properties of uncertain distortion premium principle are proved. Furthermore, a sufficient and necessary condition that an uncertain premium principle is an uncertain distortion premium principle has been characterized. Finally, some examples are given to illustrate the calculations of the uncertain distortion premium.     

AN EFFICIENT SEQUENTIAL DESIGN FOR SENSITIVITY EXPERIMENTS

In sensitivity experiments, the response is binary and each experimental unit has a critical stimulus level that cannot be observed directly. It is often of interest to estimate extreme quantiles of the distribution of these critical stimulus levels over the tested products. For this purpose a new sequential scheme is proposed with some commonly used models. By using the bootstrap repeated-sampling principle, reasonable prior distributions based on a historic data set are specified. Then, a Bayesian strategy for the sequential procedure is provided and the estimator is given. Further, a high order approximation for such an estimator is explored and its consistency is proven. A simulation study shows that the proposed method gives superior performances over the existing methods.     

Full potential calculation of electronic properties of rutile RO2 (R=Si, Ge, Sn and Pb) compounds via modified Becke Johnson potential

The electronic properties of RO₂ (R=Si, Ge, Sn and Pb; a group IVA element) compounds in rutile structure have been calculated using WIEN2k implementation of full potential linearized augmented plane wave (FPLAPW) method. The exchange and correlation (XC) effects are taken into account by an orbital independent modified Becke Johnson (MBJ) potential as coupled with Local Density Approximation (LDA) for all the compounds except for PbO₂ where only Generalized Gradient Approximation (GGA) is considered for the same. We predict a direct band gap in all these compounds with continuous decrease as the atomic size of IVA element increases such that there is an appearance of semimetallic band structure for the last compound, PbO₂. The largest band gap (7.66 eV) has been found for SiO₂, which governs its insulating nature. We observe that MBJLDA results for band gaps of these compounds are far better than those obtained using GGA and Engel-Vosko's GGA (EV-GGA). A very good agreement is observed between MBJLDA band gaps with corresponding experimental values as compared to other calculations. The electronic band structures are also analyzed in terms of contributions from various electrons.     

Traveling waves for a reaction–diffusion–advection predator–prey model

In this paper we study a reaction–diffusion–advection predator–prey model in a river. The existence of predator-invasion traveling wave solutions and prey-spread traveling wave solutions in the upstream and downstream directions is established and the corresponding minimal wave speeds are obtained. While some crucial improvements in theoretical methods have been established, the proofs of the existence and nonexistence of such traveling waves are based on Schauder’s fixed-point theorem, LaSalle’s invariance principle and Laplace transform. Based on theoretical results, we investigate the effect of the hydrological and biological factors on minimal wave speeds and hence on the spread of the prey and the invasion of the predator in the river. The linear determinacy of the predator–prey Lotka–Volterra system is compared with nonlinear determinacy of the competitive Lotka–Volterra system to investigate the mechanics of linear and nonlinear determinacy.     

Chromatographic determination of some biomarkers of liver cirrhosis and hepatocellular carcinoma in Egyptian patients

Metabolomics has been shown to be an effective tool for disease diagnosis, biomarker screening and characterization of biological pathways. A total of 140 subjects were included in this study; urine metabolomes of patients with liver cirrhosis (LC, n = 40), patients with hepatocellular carcinoma (HCC; n = 55) and healthy male subjects (n = 45) as a control group were studied. Gas chromatography/mass spectrometry‐based urine metabolomics profiles were investigated for all participants. Diagnostic models were constructed with a combination of marker metabolites, using principal components analysis and receiver operator characteristic curves. A total of 57 peaks could be auto‐identified of which 13 marker metabolites (glycine, serine, threonine, proline, urea, phosphate, pyrimidine, arabinose, xylitol, hippuric acid, citric acid, xylonic acid and glycerol) were responsible for the separation of HCC group from healthy subjects. Also, eight markers metabolites (glycine, serine, threonine, proline, citric acid, urea, xylitol and arabinose) showed significant differences between the LC group and healthy subjects. No significant difference was detected between HCC and LC groups regarding all these metabolites. Metabolomic profile using GC–MS established an optimized diagnostic model to discriminate between HCC patients and healthy subjects; also it could be useful for diagnosis of LC patients. However, it failed to differentiate between HCC and LC patients.