Limit theorems for sums of random exponentials

We study limiting distributions of exponential sums as t→∞, N→∞, where (X_i) are i.i.d. random variables. Two cases are considered: (A) ess sup X_i = 0 and (B) ess sup X_i = ∞. We assume that the function h(x)= -log P{X_i>x} (case B) or h(x) = -log P {X_i>-1/x} (case A) is regularly varying at ∞ with index 1 < ϱ <∞ (case B) or 0 < ϱ < ∞ (case A). The appropriate growth scale of N relative to t is of the form , where the rate function H₀(t) is a certain asymptotic version of the function (case B) or (case A). We have found two critical points, λ₁<λ₂, below which the Law of Large Numbers and the Central Limit Theorem, respectively, break down. For 0 < λ < λ₂, under the slightly stronger condition of normalized regular variation of h we prove that the limit laws are stable, with characteristic exponent α = α (ϱ, λ) ∈ (0,2) and skewness parameter β ≡ 1.Research supported in part by the DFG grants 436 RUS 113/534 and 436 RUS 113/722.Mathematics Subject Classification (2000): 60G50, 60F05, 60E07     

Some remarks on residually algebraic pairs of rings

In this paper we continue the study of residually algebraic pairs begun in [10], and we give other characterizations of such pairs. As a consequence, we study the interaction between residually algebraic pairs and pairs of rings when all intermediate domains satisfy some properties P {\cal P} .     

基于干涉条纹跟踪实现纳米级位移测量的方法研究

设计了一套干涉条纹图像实时采集处理系统。在分析迈克尔逊干涉条纹特征表象的基础上 ,给出了通过跟踪干涉条纹的移动量测量被测对象纳米级位移量的理论公式 ;提出了干涉条纹特征点的提取与跟踪算法 :分段线性变换、方形窗口中值滤波和门限化边缘提取 ,给出了基于统计学原理的通过计算多条干涉条纹移动量获得被测对象纳米级位移量的计算公式。实验结果表明了该方法的有效性和实用性     

Waves and energy in random elastic guided media through the stochastic wave finite element method

Energy propagation in random viscoelastic media is considered in this Letter. The forced response of uncertain waveguide subject to time harmonic loading is treated. This energy model is based on a spectral approach called the “Stochastic Wave Finite Element” (SWFE) method which is detailed in this Letter. Assuming that the random properties are spatially homogeneous in the media, the SWFE is a hybridization of the deterministic wave finite element and a parametric probabilistic approach. The proposed model is applicable in a wide frequency band with reduced time consumption. Numerical examples show the effectiveness of the proposed approach to predict the statistics of kinematic and quadratic variables of guided wave propagation. The results are compared to Monte Carlo simulations.     

Synthesis and vibrational analysis of N‐(2′‐Furyl)‐Imidazole

The N‐(2′‐furyl)‐imidazole ( 1 ) has been prepared and characterized using infrared, Raman and multidimensional nuclear magnetic resonance spectroscopies. Theoretical calculations have been carried out by employing the Density Functional Theory (DFT) method, in order to optimize the geometry of their two conformers in the gas phase and to support the assignments of the vibrational bands of 1 to their normal modes. For a complete assignment of the compound, DFT calculations were combined with Scaled Quamtum Mecanic Force Field (SQMFF) methodology in order to fit the theoretical wavenumber values to the experimental one. Furthermore, Natural Bond Orbital (NBO) and topological properties by Atoms In Molecules (AIM) calculations were performed to analyze the nature and magnitude of the intramolecular interactions. The result reveals that two conformers are expected in liquid phase. Copyright © 2009 John Wiley & Sons, Ltd.     

Using Bezier curves for the calculation of retention indices of polycyclic aromatic hydrocarbons in the so-called Lee's scale in temperature-programmed gas chromatography with mass spectrometry detection

The retention indices of some polycyclic aromatic hydrocarbons (PAHs) separated by temperature-programmed gas chromatography are computed by smoothing reference data with Bezier curves of orders 6 are more consistent with the scheme of this retention parameter, and they present standard deviations systematically smaller than those associated with classical retention indices. The Bezier curve possesses the property of local control, (i.e., their graphs are modified only in the neighbourhood of the displaced point). The values thus obtained were compared with the corresponding ones calculated in a classical way. Detailed statistical analysis is presented to describe the retention indices of PAHs expressed in the so-called Lee's scale as a function of retention temperatures (in degrees C). As a training set, experimental retention data of PAHs obtained on a PE-5 phase is used for correlation. As prediction sets, literature experimental retention indices expressed in the so-called Lee's scale obtained on a DB-5 slightly polar stationary phase are applied for comparison. The method developed is successfully used for estimating and predicting the capillary gas chromatography retention index of PAHs.     

Sequential Pd(II)-Pd(0) catalysis for the rapid synthesis of coumarins

Electrophilic palladium-catalyzed cycloisomerization of brominated aryl propiolates produces brominated coumarins. The brominated coumarins can be diversified by reduction of the Pd(II) catalyst to Pd(0) followed by Suzuki, Sonogashira, Heck, or Hartwig-Buchwald coupling. Thus, a single loading of precatalyst can be used to conduct sequential reactions, allowing the synthesis of functionalized coumarins. Extension of this methodology toward the synthesis of coumarin libraries is discussed.     

在线超临界流体色谱联用技术测定超临界二氧化碳中芘溶解度

设计了一种单阀外循环接口,采用静态溶解度测定方法,联用在线超临界流体色谱,准确测定了芘在超临界二氧化碳中的溶解度.通过釜内磁力搅拌和接口外循环的双重作用,促进芘在超临界二氧化碳中的溶解平衡过程,确保在测定芘溶解度时体系已达到溶解平衡状态,确定了溶解平衡时间,消除了联用体系中因芘的溶解度过高而产生的体系堵塞问题.     

Dynamic properties of epidemic spreading on finite size complex networks

The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS （susceptibleinfected-susceptible） model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.     

A study of the adsorption of bile salts onto model lecithin membranes

Bile salts play a central role in the promotion of cytotoxicity or cytoprotection. In this study, we examined the interaction of different bile salts with egg lecithin vesicles using 31P NMR spectroscopy. The effects of taurochenodeoxycholate (TCDC or 3alpha,7alpha,-dihydroxy-5beta-cholanoyl taurine, of tauroursodeoxycholate (TUDC) or 3alpha,7beta,-dihydroxy-5beta-cholanoyl taurine) and of taurobetamuricholate (TbetaMC or 3alpha,6beta,7beta,-trihydroxy-5beta-cholanoyl taurine), at various bile salt/lecithin ratios, were evaluated. From the percent 31P present in vesicles, the micellar capacity of bile salts to dissolve lecithin was determined. TCDC was incorporated into vesicles for bile salt/lecithin molar ratios lower than 0.62 while for TUDC and TbetaMC, the critical ratios were 0.94 and 1.1, respectively. The 31P chemical shift change was markedly larger with TCDC than that found with TUDC and TbetaMC. In order to specify the low interactions observed between hydrophilic bile salts and lecithin, we determined the intermixed micellar/vesicular bile salt concentrations (IMVC) of bile salt/lecithin solutions using rapid ultrafiltration-centrifugation for TUDC and lecithin solubility measurements for TUDC, TbetaMC and TCDC. The low IMVC obtained indicate that even hydrophilic bile salts were bound mostly to the mixed aggregates. In conclusion, the low disturbance in the arrangement of lecithin induced by TUDC and TbetaMC appears to be due to the interfacial location of these bile salts. TCDC (7alpha OH) penetrates more deeply in the membrane than the 7beta hydroxylated bile salts that may partly explain the distinct damaging effects of these bile salts.