灰色GM(1,1)模型研究综述

GM(1,1)是灰色预测理论的核心模型和基础模型.从累加生成方法、初值优化、背景值优化、参数估计方法、模型性质和模型拓展的视角,梳理了GM(1,1)模型的研究进展.明确了有待进一步研究的问题,对GM(1,1)模型的未来研究方向提出了建议.     

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A Markov observation model with dividend is defined and the interpretation of the practical significance is given. We try to use an irreducible and homogeneous discrete-time Markov chain to modulate the inter-observation times and embed a dividend strategy. In the Markov observation model with dividend, a system of liner equations for the expected discounted value of dividends until ruin time is derived. Moreover, an explicit expression is obtained and proved. Finally, some interesting properties are illustrated by numerical analysis and by comparing with the complete compound binomial model with dividend.     

Anion and pH-regulated assembly of three Cd(II) coordination polymers based on 3,5-di(1H-benzo[d]imidazol-1-yl)benzoate

Three coordination polymers, {[CdI(DBBA)]?0.5H₂O}_n (1, DBBA = 3,5-di(1Hbenzo[d]imidazol-1-yl)benzoate), [Cd(DBBA)(CH₃COO)]_n (2) and [Cd(DBBA)₂]_n (3), were obtained through reactions between Cd(II) salts and 3,5-di(1H-benzo[d]imidazol-1-yl)benzoic acid under different pH conditions. Compounds 1 and 2 are 3-D frameworks with rtl topology based on different binuclear Cd(II) secondary building units. Compound 3 was formed at lower pH and showed a 1-D chain assembled with M₂L₂ ring units. Moreover, phase purities, thermal behaviors, and photoluminescent properties have also been investigated.     

Composition assessment of ferric oxide by accurate peak fitting of the Fe 2p photoemission spectrum

A quantitative study of the surface composition of ferric oxide employing photoemission spectra is presented. It was possible to accurately reproduce the expected composition (Fe_2.00±0.05O₃) by modeling the background as a combination of Shirley‐type (Shirley–Vegh–Salvi–Castle) and slope backgrounds through the active approach. The line‐shape employed to fit apparent peak asymmetries was the double‐Lorentzian. It was possible to resolve a previously unreported satellite located at ~729 eV. Copyright © 2016 John Wiley & Sons, Ltd.     

The Value Distribution and Normality Criteria of a Class of Meromorphic Functions

In this article, we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values, which improves some earlier related results.     

Shared Values of Certain Nonlinear Differential Polynomials of Meromorphic Functions

In this paper,by using the idea of truncated counting functions of meromorphic functions,we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one finite nonzero value.     

Capillary electrophoresis fingerprints combined with chemometric methods to evaluate the quality consistency and predict the antioxidant activity of Yinqiaojiedu tablet

The quality consistency of Yinqiaojiedu tablets (YQJDTs) was monitored by extracting their electrophoretic fingerprint and marker compound data that were obtained using capillary electrophoresis. To select the suitable background electrolyte, wing‐shape method was proposed. A background electrolyte composed of 103.1 mM boric acid, 51.6 mM sodium borate, 9.8 mM disodium hydrogen phosphate, and 15.6 mM sodium dihydrogen phosphate was used to separate compounds. Under the optimized conditions, the content of three marker compounds was determined in 25 YQJDT samples. The capillary electrophoresis fingerprints were developed simultaneously, then 25 samples from two manufacturers were clearly divided into two clusters based on the principal component analysis. In fingerprint assessments, systematic quantified fingerprint method was adopted for integrative quality discrimination of YQJDTs from both qualitative and quantitative perspectives, by which the qualities of 25 samples were well differentiated. In addition, partial least squares model was established to explore fingerprint–efficacy relationship between the fingerprints and the antioxidant activities in vitro, providing clinically useful information for quality control. The proposed method was reliable and comprehensive, which could be used for a valuable reference to monitor the quality consistency of traditional Chinese medicines.     

Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching ‘well posedness’ of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems.     

Capital allocation for portfolios with non-linear risk aggregation

Existing risk capital allocation methods, such as the Euler rule, work under the explicit assumption that portfolios are formed as linear combinations of random loss/profit variables, with the firm being able to choose the portfolio weights. This assumption is unrealistic in an insurance context, where arbitrary scaling of risks is generally not possible. Here, we model risks as being partially generated by Lévy processes, capturing the non-linear aggregation of risk. The model leads to non-homogeneous fuzzy games, for which the Euler rule is not applicable. For such games, we seek capital allocations that are in the core, that is, do not provide incentives for splitting portfolios. We show that the Euler rule of an auxiliary linearised fuzzy game (non-uniquely) satisfies the core property and, thus, provides a plausible and easily implemented capital allocation. In contrast, the Aumann–Shapley allocation does not generally belong to the core. For the non-homogeneous fuzzy games studied, Tasche’s (1999) criterion of suitability for performance measurement is adapted and it is shown that the proposed allocation method gives appropriate signals for improving the portfolio underwriting profit.