A note on random walks with absorbing barriers and sequential Monte Carlo methods

In this article, we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of one-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS and SMC procedures. We take advantage of some explicit spectral formulae available for these models to derive sharp and explicit estimates; this provides stability properties of the associated normalized Feynman–Kac semigroups. Our analysis allows one to compare the variance of SMC and IS techniques for these models. The work in this article is one of the few to consider an in-depth analysis of an SMC method for a particular model-type as well as variance comparison of SMC algorithms.     

A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein–Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard in the context of modelling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on 1 year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques.     

Optimized Quantitative Method for Determining Isoflavones and Equol in Bovine Digestive Fluids and Feces

Many studies have been conducted on the impact of animal feed on isoflavones and their metabolite concentrations in bovine milk, but few studies have focused on the development and validation of analytical protocols for quantifying these compounds in biological matrices other than milk and plants. The purpose of this study was to develop a method that would enable four isoflavones and equol in cows’ feces and digestive fluids to be quantified simultaneously. The method is based on aglycones released by methanolic ultrasound-assisted extraction, followed by enzymatic hydrolysis and high-performance liquid chromatography tandem–mass spectrometry analysis. The sample preparation was optimized using the Box–Behnken design. The selected extraction conditions were 80°C, 10?min, and 50% methanol for digestive fluids and 70°C, 35?min, and 60% methanol for feces. For hydrolysis, the selected conditions were 37°C, 1?h, and a pH of 6 for both matrices. The analytical method showed a good linear regression model ranging from 5 to 125?ng?mL^?1. Both inter- and intraday accuracy (≤8.5 and ≤12.3%) and precision (≤11.1 and ≤15.2%) were suitable. No matrix effects were found. There was good repeatability and extract stability for at least 4 days of storage at???20 and 6°C. All recoveries were in the acceptable range of 70–120% for both matrices, except for biochanin A in feces, where the value was approximately 43%. This sensitive and reliable method will be useful for monitoring the passage of isoflavones and equol in the digestive system of ruminants.     

The numerical solution of the acoustic wave scattering from penetrable obstacles by a least-squares method

This paper documents a numerical method for a two dimensional time-harmonic wave scattering problem by penetrable obstacles. The Fourier–Bessel function combining a multipole expansion is used to give an approximation of the scattering field. This method is based on the least-squares technique. Especially, we find a simple function to control the errors, and then give the theoretical results of the presented method. The continuity across the element boundaries is enforced by minimizing a simple quadratic functional. This method does not need to truncate the domain and could obtain high accuracy by increasing the number of basis functions with even coarse mesh. At last, we give some examples to illustrate the effectiveness of the approach including the solution domain being multiple or even multi-connected.     

地球静止轨道远程交会过程导航性能评估

远程交会是静止轨道共位卫星自主定点置入的关键途径。针对远程交会过程中大距离跨度下相对运动模型的误差信号特性,理论推导了误差的传递机理,给出了相对导航EKF算法期望及噪声特性的定量分析模型。研究表明,确定距离区间存在最优过程噪声量级及其对应的最优滤波性能,且滤波误差与交会距离正相关,可作为全局最优滤波器的定量设计依据,解决了静止轨道远程交会过程EKF导航算法性能的量化评估问题。仿真表明,分析结论正确,相对速度滤波误差全程优于0.005 m/s(1σ),满足交会任务需求。     

UV–vis and fluorescence detection by receptors based on an isophthalamide bearing a phenylethynyl group

We have successfully prepared 5-(2-phenylethynyl)isophathalilc acid as a signaling unit and the corresponding derivatives for an anion receptor 2 and a barbiturate receptor 4. Receptor 2 showed characteristic UV–vis changes and dramatic fluorescence quenching upon the addition of anions and receptor 4 showed UV–vis and an OFF-ON fluorescence changes upon the addition of dibutylbarbituric acid based on the diphenylethyne moiety.     

Stationary Oberbeck–Boussinesq model of generalized Newtonian fluid governed by multivalued partial differential equations

A generalization of the Oberbeck–Boussinesq model consisting of a system of steady state multivalued partial differential equations for incompressible, generalized Newtonian of the p-power type, viscous flow coupled with the nonlinear heat equation is studied in a bounded domain. The existence of a weak solution is proved by combining the surjectivity method for operator inclusions and a fixed point technique.     

Quantification of 1‐(propan‐2‐ylamino)‐4‐propoxy‐9H‐thioxanthen‐9‐one (TX5), a newly synthetized P‐glycoprotein inducer/activator,in biological samples: method development and validation

A simple, rapid and economical method was developed and validated for the analysis and quantification of 1‐(propan‐2‐ylamino)‐4‐propoxy‐9H ‐thioxanthen‐9‐one (TX5), a P‐glycoprotein inducer/activator, in biological samples, using reverse‐phase high‐performance liquid chromatography (HPLC). A C₁₈ column and a mobile phase composed of methanol–water (90/10, v /v) with 1% (v/v) triethylamine, at a flow rate of 1 mL/min, were used for chromatographic separation. TX5 standards (0.5–150 μm ) were prepared in human serum. Methanol was used for TX5 extraction and serum protein precipitation. After filtration, samples were injected into the HPLC apparatus and TX5 was quantified by a conventional UV detector at 255 nm. The TX5 retention time was 13 min in this isocratic system. The method was validated according to ICH guidelines for specificity/selectivity, linearity, accuracy, precision, limits of detection and quantification (LOD and LOQ) and recovery. The method was proved to be selective, as there were no interferences of endogenous compounds with the same retention time of TX5. Also, the developed method was linear (r ² ≥ 0.99) for TX5 concentrations between 0.5 and 150 μm and the LOD and LOQ were 0.08 and 0.23 μm , respectively. The results indicated that the reported method could meet the requirements for TX5 analysis in the trace amounts expected to be present in biological samples.     

Studies on pharmacokinetics,body distribution,plasma protein binding rate,and excretion of 1-methyl hydantoin in rats in vivo

In this paper, plasma concentration, plasma protein binding rate, body distribution, and excretion of both oral and intravenous administration of rats were determined by high performance liquid chromatography (HPLC) combining with UV detector. The blood drug concentration of oral and intravenous administration was summarized. The bioavailability of T_1/2 was approximately 0.75?hr. At the meanwhile, the bioavailability was about 18.84?±?2.21%. The plasma protein binding rate of 1-methyl hydantoin was about 24.36?±?0.93%, belonging to low protein binding drug. The result shows that 1-methyl hydantoin can be rapidly distributed in various organs and tissues and quickly eliminated within 6?hr without accumulation in the organs. Its discharge from the urine and feces was 16.58?±?4.48% and 3.37?±?0.71%, respectively. All of the results showed that the recovery rate, liner relationship, specificity, stability, and precision of the method were good. The study also proved that 1-methyl hydantoin has been eliminated quite faster in rats.     

Delayed stability switches in singularly perturbed predator–prey models

In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed planar systems in which there occurs a transcritical bifurcation of the quasi steady states. The proof uses the one-dimensional result proved by V.F. Butuzov, N.N. Nefedov and K.R. Schneider, and an appropriate monotonicity assumption on the vector field. The result is applied to identify all possible predator–prey models with quadratic vector fields allowing for the existence of canard solutions.