Ruin probabilities for a risk process with stochastic return on investments

In this paper, we consider a risk process with stochastic return on investments. The basic risk process is the classical risk process while the return on the investment generating process is a compound Poisson process plus a Brownian motion with positive drift. We obtain an integral equation for the ultimate ruin probability which is twice continuously differentiable under certain conditions. We then derive explicit expressions for the lower bound for the ruin probability. We also study a joint distribution related to exponential functionals of Brownian motion which is required in the derivations of the explicit expressions for the lower bound.     

带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质

本文考虑了带有某种相依重尾冲击的Poisson噪音过程尾的一致渐近性质.当冲击是二元上尾渐近独立的非负随机变量具有长尾和控制变化尾分布且噪音函数具有正的上下界时,得到了过程尾概率的一致渐近公式.进而,当冲击具有连续的一致变化尾分布时,去除了噪音函数具有正的下界的限制.对于噪音函数不一定具有正的上界的情形,当冲击具有两两负象限相依结构时,也得到了一致渐近性结果.     

Application of Löwdin's canonical orthogonalization method to the Slater‐type orbital configuration‐interaction basis set

We apply Löwdin's canonical orthogonalization method to investigate the linearly dependent problem arising from the variational calculation of atomic systems using Slater‐type orbital configuration‐interaction (STO‐CI) basis functions. With a specific arithmetic precision used in numerical computations, the nonorthogonal STO‐CI basis is easily linearly dependent when the number of basis functions is sufficiently large. We show that Löwdin's canonical orthogonalization method can successfully overcome such problem and simultaneously reduce the dimension of basis set. This is illustrated first through an S‐wave model He atom, and then the real two‐electron atoms in both the ground and excited states. In all of these calculations, the variational bound state energies of the two‐electron systems are obtained in reasonably high accuracy using over‐redundant STO‐CI bases, however, without using extended high‐precision technique. © 2015 Wiley Periodicals, Inc.     

On Ivády’s bounds for the gamma function and related results

Periodica Mathematica Hungarica - We prove that the inequality $$\begin{aligned} \Gamma (x+1)\le \frac{x^2+\beta }{x+\beta } \end{aligned}$$ holds for all $$x\in [0,1]$$ , $$\beta \ge {\beta...     

Photoluminescence of Y2O3:Eu thin film phosphors by sol-gel deposition and rapid thermal annealing

Y₂O₃:Eu³⁺ phosphor films have been developed by using the sol-gel process. Comprehensive characterization methods such as Photoluminescent (PL) spectroscopy, X-ray diffraction (XRD) and Fourier Transform Infrared (FTIR) spectroscopy were used to characterize the Y₂O₃:Eu³⁺ phosphor films. In this experiment, the XRD profiles show that the Y₂O₃:Eu³⁺ phosphor films crystallization temperature and optimum annealing temperature occur at about 650 and 750 °C, respectively. The optimum dopant concentration is 12 mol% Eu³⁺ and the critical transfer distance (R_c) among Eu³⁺ ions is calculated to be about 0.84 nm. Vacuum environment is more efficient than oxygen and nitrogen to eliminate the OH content and hence yields higher luminescent phosphor films. The PL emission intensity of Y₂O₃:Eu³⁺ phosphor films is also dependent on the annealing time. It was found that the H₂O impurities were effectively eliminated after annealing time of 25 s at 750 °C in vacuum environment. From the experiment results, the schematic energy band diagram of Y₂O₃:Eu³⁺ phosphor films is constructed.     

A study of the relationship between competitiveness and technological innovation capability based on DEA models

Researchers and managers have been searching for appropriate methods to explore the relationship between technological innovation capability and competitiveness in recent years. This study attempts to find a systematic quantitative methodology to tackle this problem. In a recent survey covering 182 industrial innovative firms in China, the traditional data envelopment analysis (DEA) model was employed to analyze the data collected. The research results show that only 16% of the enterprises operate on the best-practice frontier and there are some inconsistencies between organizational innovation capability and competitiveness in many enterprises. Decreasing returns to scale were found among about 70% of the inefficient enterprises and increasing returns to scale were found among the remaining 30% of the inefficient enterprises. Thus the internal innovation harmonizing process in these enterprises is considerably inefficient. Based on the restricted ranges of the input/output factors, a multi-objective DEA projection model has also been developed in this study to provide a benchmark for auditing competitiveness. Research results further indicate that there is still much room for enterprises to improve competitiveness in situations of confining score ranges of technological innovation capability and competitiveness.     

Pion-He scattering length

We present relativistic three-body calculations for the real part of the π-⁴He scattering length Re a. Nucleon binding, exclusion principle and Fermi motion are all included in a very careful manner. Because of our careful evaluation of the single-scattering process the remaining discrepancies with the experimental data can be attributed to higher-order mechanisms involving more than one nucleon. In particular for the πA S-wave interaction at threshold, one expects that these higher-order contributions arise largely from the absorption effect. We have performed our calculations for four current models of the input πN t-matrix. Using a πN t-matrix which reproduces the low energy πN phase shifts correctly leads to Re a_abs -Im a_abs, if we attribute the discrepancy of the calculated value with the accurately determined empirical value of Re a to pion absorption. We determine the strength parameter B₀ in a p² optical potential term from an adjustment to the π-⁴He scattering length. Finally some cross sections are calculated for T^lab_π = 10 MeV and T^lab_π = 15 MeV.     

Influence of electrolytic hydrogen on the etch pit density of iron (110) surfaces

Etch pit densities on iron (110) surfaces in sulphuric acid grow linearly with the interfacial hydrogen activity in excess of a critical activity. The hydrogen activity is approximately proportional to the square root of the cathodic current density. At constant cathodic current density the etch pit density increases with temperature and decreases with external stress. Dislocations at which the excess etch pits form penetrate into the iron at a rate proportional to the hydrogen activity and the square root of time. Effects of prior hydrogen deposition on the shape of etch pits are seen at depths greater than the penetration depth of hydrogen generated dislocations. Changes of etch pit shape similar to those produced by hydrogen are also found when external stress is applied.The results are compared to Prussin's theory in which the assumption is made that stresses accompanying diffusion of an impurity are fully relieved by plastic deformation and formation of dislocations for stresses exceeding a critical stress. While some of the predictions of the theory are met by the experiments, the dislocations penetrate into the iron much slower than diffusion of hydrogen, since dislocations cannot move fast enough, i.e. stresses are not fully relieved.     

Purification and determination of plant hormones auxin and abscisic acid using solid phase extraction and two-dimensional high performance liquid chromatography

A method for separation and purification of plant hormones auxin and abscisic acid based on mixed mode reversed-phase anion-exchange solid phase extraction and two-dimensional HPLC was developed. Two-dimensional HPLC in "heart cutting" mode was very efficient in the purification of these two hormones. Its purification power is high enough to allow reliable on-line quantification of both hormones even with non-selective detectors.