On two families of bivariate distributions with exponential marginals: Aggregation and capital allocation

In this paper, we consider two main families of bivariate distributions with exponential marginals for a couple of random variables $(X_1,X_2)$. More specifically, we derive closed-form expressions for the distribution of the sum $S=X_1+X_2$, the TVaR of $S$ and the contributions of each risk under the TVaR-based allocation rule. The first family considered is a subset of the class of bivariate combinations of exponentials, more precisely, bivariate combinations of exponentials with exponential marginals. We show that several well-known bivariate exponential distributions are special cases of this family. The second family we investigate is a subset of the class of bivariate mixed Erlang distributions, namely bivariate mixed Erlang distributions with exponential marginals. For this second class of distributions, we propose a method based on the compound geometric representation of the exponential distribution to construct bivariate mixed Erlang distributions with exponential marginals. Notably, we show that this method not only leads to Moran–Downton’s bivariate exponential distribution, but also to a generalization of this bivariate distribution. Moreover, we also propose a method to construct bivariate mixed Erlang distributions with exponential marginals from any absolutely continuous bivariate distributions with exponential marginals. Inspired from Lee and Lin (2012), we show that the resulting bivariate distribution approximates the initial bivariate distribution and we highlight the advantages of such an approximation.     

Unified derivation of the limit shape for multiplicative ensembles of random integer partitions with equiweighted parts

We derive the limit shape of Young diagrams, associated with growing integer partitions, with respect to multiplicative probability measures underpinned by the generating functions of the form (which entails equal weighting among possible parts ). Under mild technical assumptions on the function , we show that the limit shape exists and is given by the equation , where . The wide class of partition measures covered by this result includes (but is not limited to) representatives of the three meta‐types of decomposable combinatorial structures — assemblies, multisets, and selections. Our method is based on the usual randomization and conditioning; to this end, a suitable local limit theorem is proved. The proofs are greatly facilitated by working with the cumulants of sums of the part counts rather than with their moments.Copyright © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 227–266, 2015     

Synthetic and NMR Studies on Calix[n]Arene (n = 4,6,8) Triflates,Mesylates, and Tosylates

Abstract

The synthesis and full characterization of eight new calix[n]arene sulfonate esters including their conformational analysis were carried out. While p-tBucalix[6]arene and p-tBu-calix[8]arene esters are conformationally labile in the temperature interval of 25–100°C, p-tBu-calix[4]arene mono-and diesters were isolated as stable conformers at ambient temperature. Two 1,3-functionalised compounds of these derivatives, p-tert-butylcalix[4]arene ditriflate (5) and dimesylate (6) were shown unexpectedly high conformational stability up to 100°C by dynamic NMR measurements. The NMR measurements confirm the pinched-cone conformation for both derivatives. For the dealkylated calix[4]arene derivatives the partial cone conformer of the triesters have been obtained as major products in all cases.     

Predicting skin permeability from complex chemical mixtures: incorporation of an expanded QSAR model

Quantitative structure–activity relationship (QSAR) models have been widely used to study the permeability of chemicals or solutes through skin. Among the various QSAR models, Abraham’s linear free-energy relationship (LFER) model is often employed. However, when the experimental conditions are complex, it is not always appropriate to use Abraham’s LFER model with a single set of regression coefficients. In this paper, we propose an expanded model in which one set of partial slopes is defined for each experimental condition, where conditions are defined according to solvent: water, synthetic oil, semi-synthetic oil, or soluble oil. This model not only accounts for experimental conditions but also improves the ability to conduct rigorous hypothesis testing. To more adequately evaluate the predictive power of the QSAR model, we modified the usual leave-one-out internal validation strategy to employ a leave-one-solute-out strategy and accordingly adjust the Q² _LOO statistic. Skin permeability was shown to have the rank order: water > synthetic > semi-synthetic > soluble oil. In addition, fitted relationships between permeability and solute characteristics differ according to solvents. We demonstrated that the expanded model (r² = 0.70) improved both the model fit and the predictive power when compared with the simple model (r² = 0.21).     

Ring-Opening Metathesis Polymerization Kinetics of Cyclooctene with Second Generation Grubbs’ Catalyst

A kinetic study of the ring-opening metathesis polymerization (ROMP) of cis-cyclooctene using the ruthenium initiator benzylidene [1,3-bis(2,4,6-trimethylphenyl)-4,5-dihydroimidazol-2-ylidene]-dichloro-(tricyclohexylphosphine) (second generation Grubbs’ catalyst) was carried out by ¹H-NMR. The dependence on the reaction rate with the temperature and the influence of the addition of a chain transfer agent were evaluated. Some kinetic constants are also reported for this system.     

Theoretical studies and NMR assay of coumarins and neoflavanones derivatives as potential inhibitors of acetylcholinesterase

Currently Alzheimer's disease (AD) is a devastating neurological disorder that mainly affects the elderly. The treatment of AD has as main objective to increase the levels of ACh in the synaptic cleft by inhibiting the cholinesterase enzymes, which are responsible for the degradation of ACh. Twenty one synthesized coumarins and neoflavanones (4-arylcoumarins) and theoretical studies were used to select the most promising ligands for in vitro experimental studies by Nuclear Magnetic Resonance. The eight compounds selected for the experimental study only 12b (effectiveness 68.54 ± 3.22%) was promising AChE inhibitor. This compound (12b) presents substituents at positions 4, 5, 6, 7 and 8 in a coumarin nucleus, being the most significant characteristic in comparison to the other studied compounds. These results can be used for the design and synthesis of other possible derivatives with inhibitory potential of AChE.     

Hypervalent iodine(III) catalyzed rapid and efficient access to benzimidazoles,benzothiazoles and quinoxalines: Biological evaluation of some new benzimidazole-imidazo[1,2-a]pyridine conjugates

A rapid, simple and highly efficient method for the synthesis of a variety of 2-aryl-benzimidazoles, 2-aryl-benzothiazoles and quinoxalines has been developed using Koser’s reagent [PhI(OH)OTs] as catalyst. The present work highlights the potential of Koser's reagent ([PhI(OH)OTs]) for the synthesis of benzimidazoles, benzothiazoles and quinoxalines, etc. Short reaction time, high yields, importantly low catalyst loading, broad substrate scope and scalability are the salient features of this methodology. Particularly, this method has been employed successfully to synthesize highly structured indole-benzimidazole and quinoxaline-6-carboxamide derivatives as well as biologically important benzimidazole-imidazo[1,2-a]pyridine conjugates in moderate to good yields. These remarkable features make the present methodology a valid contribution to the existing precedents for the synthesis of benzimidazoles, etc. In the MTT assay, benzimidazole-imidazo[1,2-a]pyridine conjugates 3s, 3t and 3v were found to be active on MCF-7 (IC₅₀ values of 5.10 ± 0.10, 8.23 ± 0.02, and 10.75 ± 0.03 µM, respectively) and MDA-MB-231 cell lines (IC₅₀ values of 10.83 ± 0.13, 7.68 ± 0.05, and 7.87 ± 0.24 µM, respectively). Flow-cytometry analysis revealed that the treatment of MCF-7 cells with compound 3s showed moderate effect on the progression of G0/G1 phase of the cell cycle.     

Finite-tight sets

We introduce two notions of tightness for a set of measurable functions — the finite-tightness and the Jordan finite-tightness with the aim to extend certain compactness results (as biting lemma or Saadoune-Valadier’s theorem of stable compactness) to the unbounded case. These compactness conditions highlight their utility when we look for some alternatives to Rellich-Kondrachov theorem or relaxed lower semicontinuity of multiple integrals. Finite-tightness locates the great growths of a set of measurable mappings on a finite family of sets of small measure. In the Euclidean case, the Jordan finite-tight sets form a subclass of finite-tight sets for which the finite family of sets of small measure is composed by d-dimensional intervals. The main result affirms that each tight set H ⊆ W ^1,1 for which the set of the gradients ∇H is a Jordan finite-tight set is relatively compact in measure. This result offers very good conditions to use fiber product lemma for obtaining a relaxed lower semicontinuity condition.      

用恒流源测金属丝的杨氏模量

介绍用恒流源测金属丝杨氏模量的实验原理和方法。