The simplified methodology for obtaining the Lie algebra structures of nonlinear evolution equations

The technique for obtaining the prolongation structure of differential equations is simplified. This new simplified method is used to obtain the Lie algebra structure of the Burgers–KdV equation.     

Representation for the Lagrangian numerical differentiation formula involving elementary symmetric functions

By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29-52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes.     

Incomplete Gröbner basis as a preconditioner for polynomial systems

Precondition plays a critical role in the numerical methods for large and sparse linear systems. It is also true for nonlinear algebraic systems. In this paper incomplete Gröbner basis (IGB) is proposed as a preconditioner of homotopy methods for polynomial systems of equations, which transforms a deficient system into a system with the same finite solutions, but smaller degree. The reduced system can thus be solved faster. Numerical results show the efficiency of the preconditioner.     

Error-correcting pooling designs associated with some distance-regular graphs

Motivated by the pooling designs over the incidence matrices of matchings with various sizes of the complete graph K_2n considered by Ngo and Du [Ngo and Du, Discrete Math. 243 (2003) 167–170], two families of pooling designs over the incidence matrices oft-cliques (resp. strongly t-cliques) with various sizes of the Johnson graph J(n,t) (resp. the Grassmann graph J_q(n,t)) are considered. Their performances as pooling designs are better than those given by Ngo and Du. Moreover, pooling designs associated with other special distance-regular graphs are also considered.     

一个求解半正定规划问题的新原始-对偶内点算法

在原始对偶内点算法的设计和分析中,障碍函数对算法的搜索方法和复杂性起着重要的作用.本文由核函数来确定障碍函数,设计了一个求解半正定规划问题的原始-对偶内点算法.这个障碍函数即可以定义算法新的搜索方向,又度量迭代点与中心路径的距离,同时对算法的复杂性分析起着关键的作用.我们计算了算法的迭代界,得出了关于大步校正法和小步校正法的迭代界,它们分别是O(√n log n 10g n/ε)和O(√n log n/ε),这里n是半正定规划问题的维数.最后,我们根据一个算例,说明了算法的有效性以及对核函数的参数的敏感性.     

A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms

Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large- and small-update methods.     

Similarity mass and approximate reasoning

It can reflect the nature of approximate reasoning and meet more application expectations to design the approximate reasoning matching schemes and the corresponding algorithms with similarity relation Q instead of equivalence relation R. In this paper, based on similarity relation Q, we introduce type V matching scheme and corresponding approximate reasoning type V Q-algorithm with the given input A* and knowledge A → B. Besides, we present completeness of type V and its perfection on knowledge base K in Q-logic ℂ _Q in this paper.     

Cimicifuga species identification by high performance liquid chromatography-photodiode array/mass spectrometric/evaporative light scattering detection for quality control of black cohosh products

Black cohosh has become one of the most important herbal products in the US dietary supplements market. It is manufactured from roots and rhizomes of Cimicifuga racemosa (Ranunculaceae). Botanical identification of the raw starting material is a key step in the quality control of black cohosh preparations. The present report summarizes a fingerprinting approach based on high performance liquid chromatography-photodiode array/mass spectrometric/evaporative light scattering detection (HPLC-PDA/MS/ELSD) that has been developed and validated using a total of 10 Cimicifuga species. These include three North American species, Cimicifuga racemosa, Cimicifuga americana, Cimicifuga rubifolia, and seven Asian species, Cimicifuga acerina, Cimicifuga biternat, Cimicifuga dahurica, Cimicifuga heracleifolia, Cimicifuga japonica, Cimicifuga foetida, and Cimicifuga simplex. The chemotaxonomic distinctiveness of the HPLC fingerprints allows identification of all 10 Cimicifuga species. The triterpene glycoside cimigenol-3-O-arabinoside (3), cimifugin (12), and cimifugin-3-O-glucoside (18) were determined to be suitable species-specific markers for the distinction of C. racemosa from the other Cimicifuga species. In addition to identification, the fingerprint method provided insight into chemical interconversion processes occurring between the diverse triterpene glycosides contained in black cohosh. The reported method has proven its usefulness in the botanical standardization and quality control of black cohosh products.     

Coexistence of magnetization relaxation and dielectric relaxation in a single-chain magnet

A novel single-chain magnet, [MnIII3O(Meppz)3(EtOH)4(OAc)] (1), has been successfully synthesized from a secondary building block [MnIII3O(Meppz)3(EtOH)5Cl] (2) with an S = 1 ground state. SCM 1 exhibits both magnetization relaxation and dielectric relaxation properties.