Determining the chromophore in the amylopectin–iodine complex by theoretical and experimental studies

A partial hydrolysis of amylose followed by the addition of iodine provides a spectrum almost identical to that of the amylopectin–iodine (API) complex suggesting the involvement of smaller “amylose-like” units in the API complex. Our theoretical studies on different polyiodine and polyiodide species suggest that a nearly linear I₄ unit stabilized within the cavity of a small “amylose-like” helix is responsible for the characteristic API spectrum. Since there are 2.75 anhydroglucose residues (AGU) for every iodine atom in the amylose–iodine (AI) complex and a structural similarity exists between the API and the AI (amylose–iodine) complexes, we identify (C₆H₁₀O₅)₁₁I₄ to be the chromophore in the API complex. © 1994 John Wiley & Sons, Inc.     

Organoelement Compounds with Al?Al,Ga?Ga,and In?In Bonds

In the attempt to synthesize compounds with aluminum in a low oxidation state and an Al Al bond, by the reduction of alkylaluminum halides with alkali metals, analogous to a Wurtz coupling, in general the deposition of elemental aluminum and the formation of the corresponding trialkylaluminum compounds is observed. Thus, tetrasubstituted dialuminum compounds R₂Al AlR₂, apart from a few poorly characterized examples, were for a long time considered part of an unverified class of substances. Only with the sterically very highly shielded tetrakis[bis(trimethylsilyl)methyl]dialuminum did we achieve the synthesis of the first completely characterized organoelement compound with unlimited stability, which shows aluminum in the oxidation state + II and has an Al Al bond. In the meantime, corresponding compounds for the elements gallium and indium have been obtained. With the simple access to tetrasubstituted dimetal compounds, a fascinating new research area has opened for preparative chemistry, in which the particular interest will naturally lie in the reactive properties of the metal-metal bond.     

Probing in vitro digestion at oil–water interfaces

Interfacial layers have been widely applied to study the formation and stability of emulsion-based systems. However, the application of isolated interfaces to address digestibility of emulsions is often limited because of the complexity of experimental methods and results. This review summarizes the latest developments in analytical methods and literature data on effects of digestion on interfacial layers. Particular emphasis is given to understand the changes on interfacial magnitudes during oral, gastric, and duodenal digestion, either applied separately or sequentially. Limitations of interfacial aspects and key factors that influence emulsion microstructure in bulk and lipid digestion are identified. Understanding the behavior of interfacial layers upon gastrointestinal digestion promotes an accurate tracking of the physiological fate of emulsions.     

Fermentation characteristics and the dynamic trend of chemical components during fermentation of Massa Medicata Fermentata

As a representative of traditionally fermented Chinese medicine, Massa Medicata Fermentata (MMF) shows the functions of invigorating the spleen and stomach and promoting digestion, which plays an important role in the treatment of gastrointestinal diseases. The fermentation mechanism and the key factors that affect the quality of MMF have not been revealed yet, which has become an urgent issue that limits its clinical application. This article aims to systematically and comprehensively reveal the transformation of physical properties and the dynamic trend of chemical components including substrate components, volatile components, and lactic acid as anaerobic fermentation product during MMF fermentation. Along with obvious hyphae growth observed for MMF, the weight of MMF decreased, and the moisture and temperature increased. Through the quantified 14 components from substrate, ferulic acid increased from 45.53 ± 6.94 to 141.89 ± 78.40 μg/g, while glycosides and phenolic acids declined except caffeic acid. Also, within the 66 volatile components analyzed, alcohols and acids increased, while aldehydes and ketones decreased. Lactic acid was not detected in the fermentation substrate, but an apparent increase in lactic acid content was observed along with the increased fermentation days, resulting in 2.54 ± 0.15 mg/g on day 8. Based on the tested components, the fermentation process of MMF was discriminated into three distinct stages by principal component analysis, and an optimal fermentation time of four days was proposed. The results of this study will be of great significance to clarify the characteristics of fermentation and conduce to improving quality standards of MMF.     

Integral Operators Between Fock Spaces∗

In this paper, the authors study the integral operator Sφf(z) = Z C φ(z, w)f(w)dλα(w) induced by a kernel function φ(z, ·) ∈ F ∞α between Fock spaces. For 1 ≤ p ≤ ∞, they prove that Sφ : F 1 α → F p α is bounded if and only if sup a∈C kSφkakp,α < ∞, (?) where ka is the normalized reproducing kernel of F 2 α; and, Sφ : F 1 α → F p α is compact if and only if lim |a|→∞ kSφkakp,α = 0. When 1 < q ≤ ∞, it is also proved that the condition (?) is not sufficient for boundedness of Sφ : F q α → F p α . In the particular case φ(z, w) = eαzw?(z ? w) with ? ∈ F 2 α, for 1 ≤ q < p < ∞, they show that Sφ : F p α → F q α is bounded if and only if ? = 0; for 1 < p ≤ q < ∞, they give sufficient conditions for the boundedness or compactness of the operator Sφ : F p α → F q α.     

基于新型核与灰度序列的时滞GM(1,N)模型及其应用

为了解决GM(1,N)模型在新型核与灰度的基础上,对驱动项的延迟作用机理不明确的问题,将时滞参数引入到GM(1,N)模型的驱动项中,构建了基于新型核与灰度的时滞GM(1,N)模型,分析了时滞参数的辨识方法,讨论了新模型的建模机理。为了更好地对该模型的有效性进行验证,将优化的时滞GM(1,N)模型对南京市的雾霾进行预测分析,选择GM(1,N)模型、一元回归模型与文中的优化模型进行对比。结果显示,优化模型对PM₁₀浓度的拟合精度更高,且误差均控制在5%之内,从而验证了提出的优化模型适用于具有时滞特征数据的模拟和预测。     

Qualitative properties of pulsating fronts for reaction–advection–diffusion equations in periodic excitable media

In this paper, we study the pulsating fronts of reaction–advection-diffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed is unique, monotone and decays exponentially at negative end, while the fronts of noncritical speeds decay to zero non-exponentially.     

Asymptotic stability of the Degasperis–Procesi antipeakon–peakon profile

The aim of this paper is to prove that the Degasperis–Procesi antipeakon–peakon profile is asymptotically stable for all time. We start by proving the asymptotic stability of a single Degasperis–Procesi peakon and antipeakon with respect to perturbations having a momentum density that is first negative and then positive. Then this result is extended towards a well-ordered trains of antipeakons–peakons under such perturbations. In particular, the asymptotic stability of the antipeakon–peakon profile holds.     

Minimax principles for elliptic mixed hemivariational–variational inequalities

In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent to a mixed hemivariational–variational inequality. While the minimax principle is of independent interest, it is employed in this paper to provide an elementary proof of the solution existence of the mixed hemivariational–variational inequality. Theoretical results are illustrated in the applications of two contact problems.     

Limit cycles of a class of Liénard systems derived from state-dependent impulses

Discontinuous phenomena, in which objects may behave continuously and sometimes discretely are not only found in nature and under laboratory conditions but also in simple, familiar contexts. For example, this phenomenon is skillfully incorporated into the internal structure of mechanical wristwatches. Unless an extremely small amount of state-dependent impulse is applied intermittently, the reciprocating rotational movement of the balance and hairspring, which is the heart of the mechanical wristwatch, cannot be maintained. The small amount of state-dependent impulse, which is often overlooked, can make a significant difference; however, very few studies have examined this subject. This study assumes the underlying cause of discontinuous behaviors as impulses generated when an object reaches a particular state, assuming that the continuous behavior follows the Liénard system, which is widely studied in the field of electrical circuits. The main theorem provides the conditions under which the effect of the impulses causes a stable limit cycle in the Liénard system, even if no limit cycle exists when there are no impulses. The Poincaré–Bendixson theorem for discontinuous dynamical systems and phase plane analysis are used to prove the main theorem. Several examples and their simulations are provided to illustrate the main theorem.