Small time convergence of subordinators with regularly or slowly varying canonical measure

We consider subordinators $X_{\alpha }={\left(X_{\alpha }\left(t\right)\right)}_{t\ge 0}$ in the domain of attraction at 0 of a stable subordinator ${\left(S_{\alpha }\left(t\right)\right)}_{t\ge 0}$ (where $\alpha \in (0,1)$); thus, with the property that ${\overline{\Pi }}_{\alpha }$, the tail function of the canonical measure of $X_{\alpha }$, is regularly varying of index $?\alpha \in (?1,0)$ as $x\downarrow 0$. We also analyse the boundary case, $\alpha =0$, when ${\overline{\Pi }}_{\alpha }$ is slowly varying at 0. When $\alpha \in (0,1)$, we show that ${\left(t{\overline{\Pi }}_{\alpha }\left(X_{\alpha }\left(t\right)\right)\right)}^{?1}$ converges in distribution, as $t\downarrow 0$, to the random variable ${\left(S_{\alpha }\left(1\right)\right)}^{\alpha }$. This latter random variable, as a function of $\alpha$, converges in distribution as $\alpha \downarrow 0$ to the inverse of an exponential random variable. We prove these convergences, also generalised to functional versions (convergence in $\mathbb{D}[0,1]$), and to trimmed versions, whereby a fixed number of its largest jumps up to a specified time are subtracted from the process. The $\alpha =0$ case produces convergence to an extremal process constructed from ordered jumps of a Cauchy subordinator. Our results generalise random walk and stable process results of Darling, Cressie, Kasahara, Kotani and Watanabe.     

Asymptotic results for renewal risk models with risky investments

We consider a renewal jump–diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin probabilities and related quantities, in models with light- or heavy-tailed jumps, whenever the distribution of the time between jumps has rational Laplace transform.     

低含量多元素物质的快速全反射X荧光分析

本文介绍了用全反射Ｘ荧光分析仪对样品量很少、元素含量很氏，多元素溶液的分析，测定了从含量最多的Ｎａ（２４３μｇ／ｍＬ）到含量最少的Ｃｕ（０．０６μｇ／ｍＬ）的１２种元素，同时也介绍了用累加法的多次快速测量以及逐差法处理数据以减少测量误差。     

Synthesis of stagonolide C from Mulzer epoxide

Total synthesis of stagonolide C using chiral pool strategy is described. The two key intermediates were prepared from l-glutamic acid and d-glucono-1,5-lactone, followed by Julia-Lythgoe olefination and Yamaguchi esterification to afford the target compound in an efficient way.     

Hydration Kinetics for Alkaline Activation of Slag from Color Variation Data

In this study, we explore a new method based on color variation data to derive the kinetics of the entire process of the hydration of alkali-activated slag (AAS). Using this image analysis technique, we can monitor the induction period that cannot be observed using conventional microcalorimetry techniques. Color variation was recorded across a sequence of 9999 images, which were processed via MATLAB software package. Further, an average pixel value (APV) was determined to represent the color in each image. Reaction parameters, such as color variation velocity v(t), reaction speed ε(t), and hydration degree α(t), that govern the entire hydration process were determined. On the basis of the reaction parameters and a Krstulovic–Dabic kinetic model, integral and differential equations were derived to simulate the three basic processes of AAS hydration. Equations describing the reaction kinetics of AAS with solutions of three different concentrations of NaOH were extracted using this method.     

A study of the parameters affecting the accuracy of the total pore blocking method

We report on a study wherein we investigate the different factors affecting the accuracy of the total pore blocking method to determine the interstitial volume of reversed-phase packed bed columns. Octane, nonane, decane and dodecane were all found to be suitable blocking agents, whereas heptane already dissolves too well in the applied fully aqueous buffers. The method of moments needs to be used to accurately determine the elution times, and a proper correction for the frit volume is needed. Failing to do so can lead to errors on the observed interstitial volume of the order of 2% or more. It has also been shown that the application of a high flow rate or a high pressure does not force the blocking agent out of the mesopores of the particles. The only potential source of loss of blocking agent is dissolution into the mobile phase (even though this is a buffered fully aqueous solution). This effect however only becomes significant after the elution of 400 geometrical column volumes, i.e., orders more than needed for a regular total pore blocking experiment.     

Total reflection X-ray fluorescence analysis of trace-elements in candies marketed in Mexico

Trace metals concentrations in food are significant for nutrition, due either to their nature or toxicity. Sweets, including chewing gum and candies, are not exactly a food, but they usually are unwearied consumed by children, the most vulnerable age-group to any kind of metal contamination in the food chain. The presence of relatively high concentrations of heavy metals such as Lead elicits concern since children are highly susceptible to heavy metals poisoning. Trace-metals concentrations were determined for six different flavors of a Mexican candy by means of Total X-ray Fluorescence Spectrometry. Triplicate samples of the various candy's flavours (strawberry, pineapple, lemon, blackberry, orange and chilli) were digested in 8 mL of a mix of supra-pure HNO₃ and H₂O₂ (6 mL: 2 mL) in a microwave oven MARS-X. Results show the presence of essential and toxic elements such as Ti, Cr, Mn, Fe, Ni, Cu, Zn, Br, Rb, Sr, and Pb. All metal concentrations were higher and significantly different (α = 0.05) in chilli candy, compared to other candy flavours. Lead concentration fluctuated in the range of 0.102 to 0.342 μg g^− 1. A discussion about risk consumption and concentration allowed by Mexican and International Norms is made. As a part of the Quality Control Program, a NIST standard of “Citrus Leaves” and a blank were treated in the same way.     

On the Size of the Plasma Region

AMS (MOS): 35J60, 35B40, 35J67     

Expedient synthesis of ialibinones A and B by manganese(III)-mediated oxidative free radical cyclisation

The tricyclic natural products ialibinone A and ialibinone B were prepared as a 41:59 mixture in four steps starting from phloroglucinol. The synthetic sequence involved (i) acylation of phloroglucinol under Friedel-Crafts conditions, (ii) double prenylation using phase-transfer methodology, (iii) dearomatising methylation, and (iv) oxidative free radical cyclisation using manganese(III) acetate.     

The calibration of volatility for option pricing models with jump diffusion processes

This paper is devoted to calibrate smooth local volatility surface under jump-diffusion processes. This calibration problem is posed as an inverse problem: given a finite set of observed European option prices, find a local volatility function such that the theoretical option prices matches the observed ones optimally with respect to a prescribed performance criterion. Firstly, we obtain an Euler-Lagrange equation for the calibration problem using Tikhonov regularization method. Then we solve the Euler–Lagrange equation using an iterative algorithm and obtain the volatility. Finally, numerical experiments show the effectiveness of the proposed method.