Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

Chromatic Uniqueness of the Complement of T_m(l, 4, m - 6)

In the paper, we prove that the complement of Tm(1,4,m - 6)(m > 10) is chromatically unique if and only if m ≠5k(k ≥ 2).     

有消费或投资的华氏宏观经济模型

本文对华罗庚教授的宏观经济模型进行了推广 ,在原来模型的基础上 ,分别增加了消费、投资 ,得到两种不同的模型 ,并对模型具有经济意义的解进行了研究     

Regression quantiles for unstable autoregressive models

This paper investigates regression quantiles (RQ) for unstable autoregressive models. The uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit circle. It involves stochastic integrals in terms of a sequence of independent and identically distributed multivariate Brownian motions with correlated components. The related L-estimator is also discussed. The asymptotic distributions of the RQ and the L-estimator corresponding to the nonstationary componentwise arguments can be transformed into a function of a normal random variable and a sequence of i.i.d. univariate Brownian motions. This is different from the analysis based on the LSE in the literature. As an auxiliary theorem, a weak convergence of a randomly weighted residual empirical process to the stochastic integral of a Kiefer process is established. The results obtained in this paper provide an asymptotic theory for nonstationary time series processes, which can be used to construct robust unit root tests.     

Vector Lattices on a Set of Two Generators

It is proved that the center of an automorphism group Aut(FVL2) of a free vector lattice FVL2 on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice FVL2 has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in FVL2 are amply described. Similar results are obtained for a free vector lattice FVL2 _Q 2 generated by two elements over a field of rational numbers.     

表面活性剂增敏2.5次微分极谱测定香豆素

拟定了表面活性剂增敏、2 .5次微分极谱测定香豆素的方法。在含 6.0× 10 -6 mol·L-13 氯 2 羟丙基 三甲基氯化铵的 0 .1mol·L-1KH2 PO4 Na2 HPO4 (pH 6.8)缓冲液中 ,香豆素还原波 [峰电位Ep=- 1.60V(vs .SCE) ]的 2 .5次微分极谱峰峰电流e″p 与其浓度在 4 .0× 10 -7～ 6.0× 10 -5mol·L-1范围内呈良好线性关系 (r =0 .9998,n =10 ) ,检出限为 1.2× 10 -7mol·L-1。 13次平行测量 8.0× 10 -6 mol·L-1香豆素的峰电流 ,RSD为 1.5 %。该方法可用于中药白芷中香豆素的直接测定     

Study on Extraction Process of Root of Henry Wood Betony Polysaccharides and Their Antitumor Activity against S180

We optimized the hot water extraction of polysaccharides from the root of Henry wood betony (RHWPs) using a uniform test and explored their anti-tumor activities in vitro and in vivo. The optimal extraction conditions were as follows: 40 min extraction time, liquid/solid ratio 30 mL/g, 100 min soaking time, two extraction cycles, 100% ethanol concentration, and extraction temperature of 80 °C. The molecular weight distribution of RHWPs with MWs was 228,600 g/mol and 5001 g/mol. The IR spectrum further indicated that RHWPs are acidic polysaccharides containing pyranose and furan rings. The main monosaccharides found in RHWPs were mannose, ribose, l-rhamnose monohydrate, glucuronic acid, galacturonic acid, glucose, galactose, xylose, arabinose, and fucose. RHWPs inhibited the proliferation of S180 tumor cells and induced apoptosis in vitro. Oral administration of RHWPs to tumor-bearing mice significantly inhibited the growth of the S180 xenografts, accelerated apoptosis in tumor cells, and expanded the necrotic regions. Furthermore, RHWPs also markedly increased the levels of TNF-α, IFN-γ, and IL-2 in the sera of tumor-bearing mice, and activated immune cells such as lymphocytes, NK cells, and macrophages, thereby inducing tumor cell apoptosis. Taken together, RHWPs are a promising anti-tumor agent that ought to be explored further.     

Effect of the medium pH on the release of secondary metabolites from roots ofDatura stramonium,Catharanthus roseus,andTagetes patula cultured in vitro

The release of alkaloids from root culturesDatura stramonium andCatharanthus roseus and thiophenes from root cultures ofTagetes patula was found to increase when the pH of the culture media (ranging from 4.8 to 7.0) was reduced to 3.5. The extent of the effect was different in each type of culture. Increases ranged from 4- to 20-fold, which in some cases accounted for 75% of the total secondary metabolite pool produced per flask. When the release of individual metabolites was measured, even larger increases, were observed (nearly 400-fold for ajmalicine). Increased release of alkaloids fromC. roseus roots were also observed in cultures growing in a 14-L fermentor, when the medium pH was reduced. Reduction of the pH of the media did not affect growth of the root cultures in subsequent subcultures. The importance of this treatment as a stategy to improve the recovery of secondary metabolites from producing cultures is discussed.     

M-矩阵平方根的一类迭代法

矩阵平方根在数学的许多应用中起着重要的作用.本文研究M-矩阵平方根的计算问题,提出一种计算正则M-矩阵平方根的迭代方法.首先将这个问题转化为M-矩阵代数Riccati方程,进而提出一种有效的方法来求解这个特殊的MARE.理论分析表明,该方法在一定条件下是收敛的.数值实验表明该方法是可行的,且优于二项式迭代法.     

分裂的正则Hom-Leibniz-Rinehart代数

作为Hom-Leibniz代数胚的代数类比, 本文引入Hom-Leibniz-Rinehart代数的概念. 证明了分裂的正则Hom-Leibniz-Rinehart代数$L$写成$L=U+\sum_{\gamma}I_\gamma$, 其中$U$为极大交换子代数$H$的子空间和$I_\gamma$为$L$的理想, 若$[\gamma]\neq[d]$, 满足$[I_\gamma, I_d]=0$. 随后分别发展了分裂Hom-Leibniz-Rinehart代数的根和权的连通技术.最后研究了紧致的正则Hom-Leibniz-Rinehart代数的结构.