On log-normal convolutions: An analytical–numerical method with applications to economic capital determination

We put forward an efficient algorithm for approximating the sums of independent and log-normally distributed random variables. Namely, by combining tools from probability theory and numerical analysis, we are able to compute the cumulative distribution functions of the just-mentioned sums to a high precision and in a relatively short computing time. We illustrate the effectiveness of the new method in the contexts of the individual and collective risk models, aggregate economic capital determination, and economic capital allocation.     

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

Polyhydroxyalkanoates (PHAs) are considered promising “green” alternatives to synthetic polymers because they are bio-derived, biodegradable and biocompatible. The properties of bacterial PHA copolymers depend on their microstructures, which can be modified with the use of different fermentation processes and feed materials. Thus, it is desirable to have an improved testing method for the determination of PHA microstructures. In this work, a detailed NMR analysis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) microstructure was made. Previously only two of the hydroxyvalerate ¹³C NMR peaks have been assigned at the triad level. In this work, three of the ¹³C hydroxyvalerate peaks and two of the hydroxybutyrate peaks were found to be split into four peaks each due to comonomer sequence effects. Using eight copolymer samples with a wide compositional range, we were able to assign all these peaks to B-centered and V-centered triad sequences. Through curve deconvolution, the triad intensities were determined. These triad sequence intensities can then be analyzed via both the first-order Markovian and two-component Bernoullian models to obtain more in-depth information on copolymer composition and comonomer reactivities.     

Engineering Carbon Distribution in Silicon-Based Anodes at Multiple Scales

The successful commercialization of promising silicon-based anode materials has been hampered by their poor cycling stability caused by the huge volume change. Integration of the carbon matrix with silicon-based (C/Si-based) anode materials has been demonstrated to be a powerful solution to achieve satisfactory electrochemical performance. This minireview aims to outline recent developments on C/Si-based composites, with the emphasis on the importance of carbon distribution at multiple scales. In addition, the forms of the carbon framework (carbon sources and doping of heteroatoms) have been summarized. Particularly, a novel C/Si-based hybrid with carbon distributed at the atomic scale has been highlighted.     

Pharmacokinetics and tissue distribution study of clevidipine and its primary metabolite H152/81 in rats

This present study was designed to investigate the pharmacokinetic profiles and tissue distribution characteristics of clevidipine and its primary metabolite H152/81 in rats following a single intravenous administration of clevidipine butyrate injectable emulsion. For this study, a sensitive and selective liquid chromatography–tandem mass spectrometry (LC–MS/MS) method was established and validated for the simultaneous quantitation of clevidipine and H152/81 in rat whole blood and various tissues. A Hedera ODS‐2 column with two gradient elution programs was employed for the troubleshooting of matrix effect on the detection of analytes among different biological samples. The experimental data showed that clevidipine represented quick elimination from blood with a half‐life of about 4.3 min and rapid distribution in all of the investigated tissues after administration; the highest concentration of clevidipine was found in the heart whereas the lowest concentration was detected in the liver. In addition, clevidipine was almost undetectable in most tissues except for heart and brain at 90 min post‐dosing, suggesting that there was no apparent long‐term accumulation in rat tissues. For H152/81, the peak concentration of 3714 ± 319 ng/mL occurred at 0.129 ± 0.048 h, the half‐life was 10.08 ± 1.45 h and area under the concentration–time curve was 42091 ± 3812 ng h/mL after drug administration. In addition, H152/81 was found at significant concentration levels in all tissues, in descending order of lung, kidney, heart, liver, spleen and brain at each time point. The results of current study offer useful clues for better understanding the distribution and metabolism of clevidipine butyrate injectable emulsion in vivo.     

Improved Model Selection Method for a Regression Function with Dependent Noise

This paper is devoted to nonparametric estimation, through the -risk, of a regression function based on observations with spherically symmetric errors, which are dependent random variables (except in the normal case). We apply a model selection approach using improved estimates. In a nonasymptotic setting, an upper bound for the risk is obtained (oracle inequality). Moreover asymptotic properties are given, such as upper and lower bounds for the risk, which provide optimal rate of convergence for penalized estimators.     

Fitting Height and Character Degree Graphs

Given a group G, Γ(G) is the graph whose vertices are the primes that divide the degree of some irreducible character and two vertices p and q are joined by an edge if pq divides the degree of some irreducible character of G. By a definition of Lewis, a graph Γ has bounded Fitting height if the Fitting height of any solvable group G with Γ(G)=Γ is bounded (in terms of Γ). In this note, we prove that there exists a universal constant C such that if Γ has bounded Fitting height and Γ(G)=Γ then h(G)≤C. This solves a problem raised by Lewis. Research supported by the Spanish Ministerio de Educación y Ciencia, MTM2004-06067-C02-01 and MTM2004-04665, the FEDER and Programa Ramón y Cajal.     

板翅式换热器物流分配研究综述

板翅式换热器由于具有紧凑高效等突出优点,在航空、化工、HVAC等领域具有重要地位。由多种因素引起换热器内部流动的不均匀分配,是造成换热效能的下降最主要原因之一。文中总结了国内外学者对于板翅式换热器物流分配不均匀的研究,详细阐述了各种流动分配模型及其对换热器效能的影响。     

Simulation of certain multivariate generalized Pareto distributions

The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms are available on the author’s home page .      

On the triple jump of the set of atoms of a Boolean algebra

We prove the following result concerning the degree spectrum of the atom relation on a computable Boolean algebra. Let be a computable Boolean algebra with infinitely many atoms and be the Turing degree of the atom relation of . If is a c.e. degree such that , then there is a computable copy of where the atom relation has degree . In particular, for every c.e. degree , any computable Boolean algebra with infinitely many atoms has a computable copy where the atom relation has degree .

     

二阶广义分布参数系统的谱分布

应用泛函分析算子理论的方法研究了Hilbert空间中二阶广义分布参数系统的谱分布问题,利用有界线性算子的广义逆给出了所讨论问题的解及解的构造性表达式。这对研究二阶广义分布参数系统的镇定及渐进稳定性问题都有重要的理论价值。