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。     

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.     

Characterization of the organization in shear layers via the Proper Orthogonal Decomposition

Experiments are performed in an incompressible plane turbulent mixing layer, using various hot wire rake configurations. From these experiments, the Proper Orthogonal Decomposition is applied for kernels where the space-time correlation tensor is evaluated over different spatial meshes and velocity components configurations. The resulting decompositions are then discussed in terms of characterization of the organization of the flow for various scalar or vectorial approaches of the POD. An incrtial range law is evidenced. The instantaneous contribution of the first modes of the POD to the organization of the flow is analyzed. A dynamical behavior for the organization of the flow is observed from the correlation between the first two modes contribution.     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

Parallel synthesis of multi-branched oligosaccharides related to elicitor active pentasaccharide in rice cell based on orthogonal deprotection and glycosylation strategy

We describe a parallel and efficient synthesis of multi-branched oligosaccharides 3a-g based upon the structure of the phytoalexin elicitor active branched pentasaccharide 2. One-pot sequential orthogonal deprotection of tetrasaccharide 5 with three different protecting groups provided each of seven glycosyl acceptors 4a-g. Glycosylation of the acceptors 4a-g, followed by deprotection provided branched oligosaccharides 3a-g. All the reaction processes from scaffold 5 to 3a-g except for final hydrogenolysis were achieved utilizing an automated synthesizer in a parallel fashion.     

Astragalus membranaceus ultrafine powder alleviates hyperuricemia by regulating the gut microbiome and reversing bile acid and adrenal hormone biosynthesis dysregulation

Ethnopharmacological relevanceMetabolic syndrome is closely related to the intestinal microbiota and disturbances in the host metabolome. Hyperuricemia (HUA), a manifestation of metabolic syndrome, can induce various cardiovascular diseases and gout, seriously affecting a patient’s quality of life. Astragalus membranaceus has a long history as a commonly used traditional Chinese medicine to treat kidney disease in China and East Asia.Materials and methodsWe compared the therapeutic effect of benzbromarone and two different doses Astragalus membranaceus ultrafine powder (AMUP) in rats with HUA. Ultra-performance liquid chromatography-mass spectrometer was used to analyze the AMUP metabolism in the plasma, urine, and feces. Further, 16S ribosome RNA sequencing and feces metabolomic were performed to capture the variation of the gut microbiota and metabolites changes before and after drug administration.ResultsAMUP had a notable impact on reducing blood uric acid levels while protecting the liver and kidney. Drug metabolism analysis demonstrated that effective constituent flavonoids are distributed in the blood, whereas saponins remain in the intestine. Gut microbiota analysis showed that low-dose AMUP ameliorated HUA-induced gut dysbiosis by reducing the abundance of harmful bacteria and increasing that of some beneficial bacteria with anti-inflammatory properties, such as Clostridia, Lachnospiraceae, and Muribaculaceae. In addition, HUA-induced changes in metabolite contents in bile acid and adrenal hormone biosynthesis pathways were restored after treatment with AMUP.ConclusionLow-dose AMUP exerts remarkable therapeutic effects on HUA by regulating the gut microbiome and mediating gut metabolism pathways associated with uric acid excretion.     

微波辐射下双(2-苯并咪唑基)丙烷的合成与结构表征

与传统加热相比较,微波辐射促进的有机合成反应具有加热时间短、节能、产率高、不使用或少使用溶剂而对环境友好和节约成本等优点[1]。苯并咪唑类化合物具有广泛的生物活性而被应用到仿生有机合成、遗传学染色体研究及单层膜合成与形态研究的领域[2～4]。苯并咪唑类化合物的传统合成方法是:在HC1、多聚磷酸(PPA)、H3BO3等酸性催化剂使用下加热回流有机酸与邻苯二胺的混合物,然而反应通常需要较高的压力、温度或较长的时间,副反应多[5]。本研究在微波辐射下,以戊二酸和邻苯二胺为原料、PPA为催化剂合成了双(2-苯并咪唑基)丙烷,用正交试…     

Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

胆汁酸的薄层层析——数理统计法用于层析溶剂系统的选择

本文选择氯仿、乙醇、乙酸乙酯、醋酸和水等五种溶剂作为胆汁酸薄层层析的展开剂,采用正交设计法[L_(16)(4~5)]安排实验,对胆固醇、胆酸、脱氧胆酸、甘氨胆酸、甘氨脱氧胆酸、牛磺胆酸、牛磺脱氧胆酸和卵磷脂等八种化合物的R_f值及层析谱斑点的集中情况,用直观分析和方差分析法处理,得到了单向一次薄层层析全部分离胆汁的溶剂系统,较文献报道方法为佳。     

茉莉醛相转移催化合成法的改良

茉莉醛又称2-戊基肉桂醛,具有优雅的茉莉花香,是一种深受调香师喜爱的合成香料。目前已广泛应用于各种日用化学品中。