A counterexample to subexponential growth of orthogonal polynomials

We construct an example of polynomialsp _n orthonormal with respect to a measure such that the sequencep _n (x) has an exponential lower bound for a pointx in the support of .Communicated by Paul Nevai.     

On Lipschitz property of solutions of functional equations

In this work it is proved that under certain conditions the continuous vector-valued solutionsf of the functional equation

Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis

We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH ₀ (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH ₀. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :

Convex polynomial and spline approximation in C[−1, 1]

We prove that a convex functionf C[–1, 1] can be approximated by convex polynomialsp _n of degreen at the rate of ₃(f, 1/n). We show this by proving that the error in approximatingf by C² convex cubic splines withn knots is bounded by ₃(f, 1/n) and that such a spline approximant has anL third derivative which is bounded by n³₃(f, 1/n). Also we prove that iff C²[–1, 1], then it is approximable at the rate ofn ^–2 (f, 1/n) and the two estimates yield the desired result.Communicated by Ronald A. DeVore.     

Orientation-reversing involutions on handlebodies

The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.

     

Universal system for liquid stationary phase classification on the basis of thermodynamical data

Summary Equations modifying Rohrschneider's relationship between I and thermodynamical characteristics values are derived. Polarity in chromatography is discussed as a possibility of stationary phases or absorbents to enter into intermolecular interactions and is determined on the basis of the partial molar free energies of solution (G) of six test substances. A simple method for the calculation of stationary phase polarity in terms of G from retention indices and McReynolds constants is given. Equations are presented for the calculation of stationary phase selectivity utilizing G data tabulated for selected test substances. The thermodynamical basis of selecting a reference phase for a unified system expressing the selectivity of stationary phases which can also be applied for adsorbents is suggested. The energy equivalent to an index unit, G_i.u., is discussed.     

磷脂酶A2家族的功能性分类研究

采用“结合强度指纹图谱分析”方法, 通过对多重分子对接得到的作用强度数据进行聚类矩阵分析对蛋白质进行功能分类. 着重研究了磷脂酶A₂家族基于抑制剂作用强度的功能分类, 并且与基于序列的聚类结果进行比较, 成功地解决了序列比对方法不能处理的远源蛋白(cPLA₂)的分类问题.     

西松烷型二萜内酯的全合成进展

按照内酯环的大小综述了西松烷二萜的合成方法。     

Protein family classification and functional annotation

With the accelerated accumulation of genomic sequence data, there is a pressing need to develop computational methods and advanced bioinformatics infrastructure for reliable and large-scale protein annotation and biological knowledge discovery. The Protein Information Resource (PIR) provides an integrated public resource of protein informatics to support genomic and proteomic research. PIR produces the Protein Sequence Database of functionally annotated protein sequences. The annotation problems are addressed by a classification-driven and rule-based method with evidence attribution, coupled with an integrated knowledge base system being developed. The approach allows sensitive identification, consistent and rich annotation, and systematic detection of annotation errors, as well as distinction of experimentally verified and computationally predicted features. The knowledge base consists of two new databases, sequence analysis tools, and graphical interfaces. PIR-NREF, a non-redundant reference database, provides a timely and comprehensive collection of all protein sequences, totaling more than 1,000,000 entries. iProClass, an integrated database of protein family, function, and structure information, provides extensive value-added features for about 830,000 proteins with rich links to over 50 molecular databases. This paper describes our approach to protein functional annotation with case studies and examines common identification errors. It also illustrates that data integration in PIR supports exploration of protein relationships and may reveal protein functional associations beyond sequence homology.