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.     

柠檬酸在D354树脂上的离子交换研究

研究了大孔型弱碱性阴离子交换树脂Ｄ３５４分离水中柠檬酸的相平衡和动力学。Ｌａｎｇｍｕｉｒ方程能够良好地关联等温线。建立了离子交换过程的孔扩散模型，并以正交配置法与Ｇｅａｒ法结合进行数据拟合。结果表明，液膜阻力对交换过程具有重大影响，简单线性推动力模型能够很好地描述液膜传质过程。     

Superized Troesch complexes and cohomology for strict polynomial superfunctors

We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Frobenius twists of the (super)symmetric power functors. We apply these complexes to construct injective resolutions of the even and odd Frobenius twist functors, to investigate the structure of the Yoneda algebra of the Frobenius twist functor, and to compute other extension groups between strict polynomial superfunctors. By an equivalence of categories, this also provides cohomology calculations in the category of left modules over Schur superalgebras.     

On Tutte polynomial expansion formulas in perspectives of matroids and oriented matroids

We introduce the active partition of the ground set of an oriented matroid perspective (or morphism, or quotient, or strong map) on a linearly ordered ground set. The reorientations obtained by arbitrarily reorienting parts of the active partition share the same active partition. This yields an equivalence relation for the set of reorientations of an oriented matroid perspective, whose classes are enumerated by coefficients of the Tutte polynomial, and a remarkable partition of the set of reorientations into Boolean lattices, from which we get a short direct proof of a 4-variable expansion formula for the Tutte polynomial in terms of orientation activities. This formula was given in the last unpublished preprint by Michel Las Vergnas; the above equivalence relation and notion of active partition generalize a former construction in oriented matroids by Michel Las Vergnas and the author; and the possibility of such a proof technique in perspectives was announced in the aforementioned preprint. We also briefly highlight how the 5-variable expansion of the Tutte polynomial in terms of subset activities in matroid perspectives comes in a similar way from the known partition of the power set of the ground set into Boolean lattices related to subset activities (and we complete the proof with a property which was missing in the literature). In particular, the paper applies to matroids and oriented matroids on a linearly ordered ground set, and applies to graph and directed graph homomorphisms on a linearly ordered edge-set.     

A Space-Time Polynomial Collocation Method for Solving 3D Burgers Equations北大核心CSCD

Burgers方程是一类应用广泛的非线性偏微分方程,方程中的非线性项难以处理。该文提出一种新的时空多项式配点法——多项式特解法求解三维Burgers方程。求解过程分为两步:第一步,对三维Burgers方程中的线性导数项(包括时间导数项),求出相应的多项式特解。第二步,将求出的多项式特解作为基函数,对三维Burgers方程中剩余的非线性项进行迭代求解。与时空多项式函数作为基函数对三维Burgers方程进行直接求解相比,该算法简单易行,得到的近似解精度非常高,算法极其稳定,对于教学过程中提高学生的编程能力,加深对高维Burgers方程的理解能力以及Burgers方程的实际应用具有重要意义。     

一类联图的距离谱半径以及盖理论（英文）

令X=(n₁,n₂,…,n_t),Y=(m₁,m₂,…,m_t)是两个t维递减序列.如果对所有的j,1≤j≤t,都有∑_i=1~j、n_i≥∑_i=1~j m_i以及∑_i=1~t n_i=∑_i=1~t m_i,则称X可盖Y,记作X■Y.如果X≠Y,则记作X■Y.本文考虑联图G(n₁,n₂,…,n_t;a)=(K_n1∪_n2∪…∪K_nt)∨K_a的谱半径,这里n₁+n₂+…+n_t+a=n,(n₁,n     

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators.     

Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.     

Certain bilateral generating relations for generalized hypergeometric functions

Recently, we introduced a class of generalized hypergeometric functionsI n:(b _q)/α:(a _p) (x, w) by using a difference operator Δ _x,w , where . In this paper an attempt has been made to obtain some bilateral generating relations associated withI _n ^ga (x, w). Each result is followed by its applications to the classical orthogonal polynomials.     

On Bahadur asymptotic efficiency in a semiparametric regression model

ＯＮＢＡＨＡＤＵＲＡＳＹＭＰＴＯＴＩＣＥＦＦＩＣＩＥＮＣＹＩＮＡＳＥＭＩＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＭＯＤＥＬＬＩＡＮＧＨＵＡ（梁华）;ＣＨＥＮＧＰＩＮＧ（成平）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ,ｔｈｅＣｈｉｎｅｓｅＡ...