Characterizing compact Clifford semigroups that embed into convolution and functor-semigroups

We study algebraic and topological properties of the convolution semigroup of probability measures on a topological groups and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P(G) over some topological group G if and only if S embeds into the semigroup exp(G)\exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maximal semilattice. We also show that such a Clifford semigroup S embeds into the functor-semigroup F(G) over a suitable compact topological group G for each weakly normal monadic functor F in the category of compacta such that F(G) contains a G-invariant element (which is an analogue of the Haar measure on G).     

Center problem and bifurcation behavior for a class of quasi analytic systems

Results about the study of nonanalytic systems’ center-focus and bifurcations of limit cycles are hardly seen in published references up till now. In this paper, we investigated the problems of determining center or focus and bifurcations for a class of planar quasi cubic analytic systems. The recursive formula to figure out generalized focal values is given, ulteriorly the conditions for four limit cycles from the origin or the point at infinity are obtained and center problems are considered. What is worth pointing out is that we offer a kind of interesting phenomenon that the exponent parameter λ control the non-analyticity of studied system (3.8) in this paper. In terms of nonanalytic differential systems, our work is new.     

Error rates in classification of multivariate Gaussian random field observation

We consider the problem of supervised classifying the multivariate Gaussian random field (GRF) single observation into one of two populations in case of given training sample. The populations are specified by different regression mean models and by common factorized covariance function. For completely specified populations, we derive a formula for Bayes error rate. In the case of unknown regression parameters and feature covariance matrix, the plug-in Bayes discriminant function based on ML estimators of parameters is used for classification. We derive the actual error rate and the asymptotic expansion of the expected error rate associated with plug-in Bayes discriminant function. These results are multivariate generalizations of previous ones. Numerical analysis of the derived formulas is implemented for the bivariate GRF observations at locations belonging to the two-dimensional lattice with unit spacing.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

The Spectrum of Tetrahedral Quadruple Systems

An ordered analogue of quadruple systems is tetrahedral quadruple systems. A tetrahedral quadruple system of order v and index λ, TQS(v, λ), is a pair (S, T){(S, \mathcal{T})} where S is a finite set of v elements and T{\mathcal{T}} is a family of oriented tetrahedrons of elements of S called blocks, such that every directed 3-cycle on S is contained in exactly λ blocks of T{\mathcal{T}} . When λ = 1, the spectrum problem of TQS(v, 1) has been completely determined. It is proved that a TQS(v, λ) exists if and only if λ(v − 1)(v − 2) ≡ 0 (mod 3), λv(v − 1)(v − 2) ≡ 0 (mod 4) and v ≥ 4.     

交叉货币百慕大式互换期权的定价

本文首先研究了涉及两种货币市场的Hull-White随机利率模型.以此为基础,本文给出了交叉货币百慕大式互换期权的定价公式.由于无法得到显式定价公式,我们使用了Least Squared Monte-Carlo(LSM)算法来确定期权的最优执行时刻.最后本文给出了数值计算方面的结果.     

A diruthenium catalyst for selective, intramolecular allylic C-H amination: reaction development and mechanistic insight gained through experiment and theory

The mixed-valent paddlewheel complex tetrakis(2-oxypyridinato)diruthenium(II,III) chloride, [Ru(2)(hp)(4)Cl], catalyzes intramolecular allylic C-H amination with bis(homoallylic) sulfamate esters. These results stand in marked contrast to reactions performed with dirhodium catalysts, which favor aziridine products. The following discussion constitutes the first report of C-H amination using complexes such as [Ru(2)(hp)(4)Cl] and related diruthenium adducts. Computational and experimental studies implicate a mechanism for [Ru(2)(hp)(4)Cl]-promoted C-H amination involving hydrogen-atom abstraction/radical recombination and the intermediacy of a discrete, albeit short-lived, diradical species. The collective data offer a coherent model for understanding the preference of this catalyst to oxidize allylic (and benzylic) C-H bonds.     

Five-fold-symmetric macrocyclic aromatic pentamers: high-affinity cation recognition, ion-pair-induced columnar stacking, and nanofibrillation

Described in this study is a conceptually new class of five-fold-symmetric cavity-containing planar pentameric macrocycles with their interior decorated by five convergently aligned, properly spaced carbonyl oxygen atoms. These cation-binding oxygens enclose a hydrophilic lumen of 2.85 ? in radius and thus display high-affinity binding toward alkali metal cations, and possibly many other cations, too. Arising from their high-affinity recognition of metal ions, these planar macrocycles form cation- or ion-pair-induced one-dimensional columnar aggregates, and subsequently fascinating fibrillation results.     

Tailor-made dual pH-sensitive polymer-doxorubicin nanoparticles for efficient anticancer drug delivery

Efficient delivery of therapeutics into tumor cells to increase the intracellular drug concentration is a major challenge for cancer therapy due to drug resistance and inefficient cellular uptake. Herein, we have designed a tailor-made dual pH-sensitive polymer-drug conjugate nanoparticulate system to overcome the challenges. The nanoparticle is capable of reversing its surface charge from negative to positive at tumor extracellular pH (～6.8) to facilitate cell internalization. Subsequently, the significantly increased acidity in subcellular compartments such as the endosome (～5.0) further promotes doxorubicin release from the endocytosed drug carriers. This dual pH-sensitive nanoparticle has showed enhanced cytotoxicity in drug-resistant cancer stem cells, indicating its great potential for cancer therapy.