Application of variational inequalities to the moving-boundary problem in a fluid model for biofilm growth

We consider a moving-boundary problem associated with the fluid model for biofilm growth proposed by J. Dockery and I. Klapper, Finger formation in biofilm layers, SIAM J. Appl. Math. 62 (3) (2001) 853–869. Notions of classical, weak, and variational solutions for this problem are introduced. Classical solutions with radial symmetry are constructed, and estimates for their growth given. Using a weighted Baiocchi transform, the problem is reformulated as a family of variational inequalities, allowing us to show that, for any initial biofilm configuration at time t=0$t=0$ (any bounded open set), there exists a unique weak solution defined for all t≥0$t\ge 0$.     

Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel

In this paper, we introduce and investigate a fractional calculus with an integral operator which contains the following family of generalized Mittag-Leffler functions:

     

Carrier Method for the General Evaluation and Control of Pose, Molecular Conformation, Tracking, and the Like

The four basic geometric objects of points, point pairs, circles and spheres correspond to outer product null-spaces constructed by conformal points in conformal geometric algebra. Wedging with the infinity point we get four flat objects: finite-infinity point pairs, lines, planes and the whole 5D space. We show that all these basic geometric objects have the same algebraic structure. We then develop a single general algebraic method to quantify and interpolate the relative pose of the eight different classes of objects. As an explicit example we finally apply our framework to the conformation of organic macromolecules. Received: November, 2007. Accepted: February, 2008.     

H—103大孔吸附剂分离纯化抗生素LY—92的研究

本文研究了用非离子型大孔网状吸附树脂从ＬＹ－９２原液中分离并纯化抗生素ＬＹ－９２，摸索了最佳吸附剂，动态吸附的最佳ＰＨ，流速，解吸剂的选择及粗品的精制，实验结果表明，选用国产（南开大学）Ｈ－１０３树脂作吸附剂，吸附最适ＰＨ为６．５，最佳流速１／３ｍｌ／ｍｉｏｎ，以丙酮，流速为１／７ｍｌ／ｍｉｎ进行解吸，吸附率为８４．２％，解吸率为８２．３％，采用Ｈ－１０３大孔吸附剂进一步纯化粗品，能使效价由４８６     

Efficient 1H NMR chiral discrimination of sulfoxides caused by the dynamic nature of (R,R)-3′,3″-biBINOL

A chiral BINOL dimer, (R,R)-3′,3″-BiBINOL, which possesses both rigid (atropos) and dynamic (tropos) axial chiralities, was found to work as an effective NMR chiral solvating reagent for the determination of the enantiomeric purities of various chiral sulfoxides. The unique chiral discrimination mechanism was also revealed by using DFT calculations and X-ray crystallographic analysis.