Moments of discounted aggregate claim costs until ruin in a Sparre Andersen risk model with general interclaim times

In the context of a Sparre Andersen risk model with arbitrary interclaim time distribution, the moments of discounted aggregate claim costs until ruin are studied. Our analysis relies on a novel generalization of the so-called discounted density which further involves a moment-based component. More specifically, while the usual discounted density contains a discount factor with respect to the time of ruin, we propose to incorporate powers of the sum until ruin of the discounted (and possibly transformed) claims into the density. Probabilistic arguments are applied to derive defective renewal equations satisfied by the moments of discounted aggregate claim costs until ruin. Detailed examples concerning the discounted aggregate claims and the number of claims until ruin are studied upon assumption on the claim severities. Numerical illustrations are also given at the end.     

Characterizations of counter-monotonicity and upper comonotonicity by (tail) convex order

In this paper, we characterize counter-monotonic and upper comonotonic random vectors by the optimality of the sum of their components in the senses of the convex order and tail convex order respectively. In the first part, we extend the characterization of comonotonicity by  Cheung (2010) and show that the sum of two random variables is minimal with respect to the convex order if and only if they are counter-monotonic. Three simple and illuminating proofs are provided. In the second part, we investigate upper comonotonicity by means of the tail convex order. By establishing some useful properties of this relatively new stochastic order, we prove that an upper comonotonic random vector must give rise to the maximal tail convex sum, thereby completing the gap in  Nam et al. (2011)’s characterization. The relationship between the tail convex order and risk measures along with conditions under which the additivity of risk measures is sufficient for upper comonotonicity is also explored.     

Some Discrete Nonlinear Inequalities and Applications to Boundary Value Problems for Difference Equations

In this paper, we establish some new discrete Gronwall–Bellman–Ou-Iang type inequalities over 2-dimensional lattices. These, on one hand, generalize some existing results in the literature and on the other hand, provide a handy tool for the study of qualitative properties of solutions of difference equations. We illustrate this by applying these new results to certain boundary value problem for difference equations.     

Crystal orientation dependence of ferromagnetism in Fe-implanted MgO single crystals

Single crystals of MgO with (100), (110) and (111) orientations were implanted with 64 keV Fe ions at a dose of 1.9×10¹⁷ ions/cm² by using metal-vapor vacuum arc ion source (MEVVA). The magnetic properties were investigated by a superconducting quantum interference device magnetometer and Rutherford backscattering spectrometry (RBS) was used to analyze the Fe concentration and distribution. The presence of Fe nanoparticles in MgO matrix was verified by magnetization measurements. Results show that all the samples behave with ferromagnetism at 5 K and 300 K, and the coercive field, H_C, follow well the relation: at measured temperatures. The orientation dependence of the coercive field may result from the different distribution of Fe nanoparticle size.     

Synthetic and mechanistic studies of indium-mediated allylation of imines in ionic liquids

Aldimines derived from aryl and non-enolizable aliphatic aldehydes were allylated with allyl bromide mediated by indium powder in [bpy][BF4] (bpy = N-butylpyridine) to give good yields of the corresponding homoallylic amines. Selective formation of monoallylated amines can be achieved by varying the amount of bromide ion additive in the form of [bpy][Br]. The transient organoindium intermediates, allylindium(I) and allylindium(III) dibromide formed in the reaction, were studied by NMR spectroscopy to explain the selectivity.     

CE methods applied to the analysis of micronutrients in foods

This article reviews the applications of CE that are relevant to the analysis of small molecules in foods. CE has been applied to a wide range of important areas of food analysis and is rapidly being established as an alternative technique to chromatographic methods including HPLC and GC within analytical food and research laboratories. In recent years the analysis of food by CE has become more frequent and important and as such a variety of compounds have been separated and quantified. Although many other analytes have been detected by CE, this review will highlight areas relating primarily to the rather broad chemical classes of free amino acids, carbohydrates, organic acids, vitamins and a variety of antioxidants. In addition, information relating to the analyte, sample matrix, mode of CE employed, scope of the methodology and the detection and derivatization of the small molecules are considered and discussed.     

Adsorption kinetics of bovine serum albumin on fused silica: population heterogeneities revealed by single-molecule fluorescence microscopy

The adsorption of bovine serum albumin (BSA) on fused silica at neutral pH was investigated at the single-molecule level by total internal reflection fluorescence microscopy. Dye-labeled BSA molecules that adsorbed on the quartz surface lit up as discrete, fluorescent dots which eventually disappeared upon desorption. Movies of these events offered unprecedented details for kinetics modeling. The results suggested that 99.3% of the BSA was not sticky, and even if adsorbed, it would desorb in minutes. In contrast, the remaining 0.7% was not only sticky, but would anchor in due course. Such population heterogeneity, otherwise masked in ensemble measurements, sheds new light on our understanding of protein adsorption. The methodology is also generally applicable to the studies of macromolecules at interfaces.     

Room-temperature copper-catalyzed alpha-arylation of malonates

An effective method in targeting alpha-aryl malonates is reported. In the presence of a catalytic amount of 2-picolinic acid and CuI, the coupling of aryl iodides with diethyl malonate proceeds smoothly even at room temperature. The high levels of functional group compatibility and exceptionally mild reaction conditions offer this an attractive protocol in accessing a variety of arylated malonates.     

Dewetting-induced membrane formation by adhesion of amphiphile-laden interfaces

We introduce an approach for forming bilayer polymer membranes by adhesion of amphiphile-laden interfaces. This adhesion is induced by a reduction of solvent quality for the amphiphilic diblock copolymers through selective evaporation of good solvent in the solvent mixture. By combining this membrane formation mechanism with a double-emulsion-templated approach for vesicle formation, we fabricate monodisperse polymersomes that exhibit excellent membrane uniformity, and structural stability, using a method that has high encapsulation efficiency. Moreover, we also show that the technique is versatile and can be applied to different block copolymers. The ability to direct the assembly of amphiphiles into a membrane creates new opportunities to engineer the structures of vesicles on the level of the individual bilayer leaflets.