When does the subadditivity theorem for multiplier ideals hold?

Demailly, Ein and Lazarsfeld proved the subadditivity theorem for multiplier ideals on nonsingular varieties, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals. We prove that, in the two-dimensional case, the subadditivity theorem holds on log terminal singularities. However, in the higher dimensional case, we have several counterexamples. We consider the subadditivity theorem for monomial ideals on toric rings and construct a counterexample on a three-dimensional toric ring.

     

双奇核188Au的准粒子带结构研究

利用在束γ谱学实验技术, 通过¹⁷³Yb(¹⁹F,4nγ)反应 布居了¹⁸⁸Au的高自旋态, 并对其准粒子带结构进行了研究. 基于实验测量结果, 对原有的双奇核¹⁸⁸Au能级纲图做了较大的修改. 通过系统性比较, 对15⁺以上的能级结构进行了讨论.     

Generalized Airy Functions and the Cohomological Intersection Numbers

We compute explicitly the cohomological intersection numbers for the basis and extend the result of Iwasaki and Matsumoto. To this end, we establish the exterior power structure for the polynomial twisted de Rham cohomology group associated with the generalized Airy functions at a point of extended Veronese variety. Using this structure, we introduce a natural basis of the twisted de Rham cohomology group coming from that of the one-dimensional case, which is considered as an analogue of a flat basis of the Jacobi ring of A-type simple singularity.     

Temperature and velocity measurement of a 3-D thermal flow field using thermo-sensitive liquid crystals

It is an important challenge to analyze a three-dimensional thermal flow field in engineering, science, and agriculture. For such an analysis, it is essential to measure physical quantities such as temperature and velocity over the entire thermal flow field. This paper presents a measurement system based on color image processing for temperature and velocity vector distributions in a three-dimensional thermal flow field. Flow visualization is accomplished by the use of thermo-sensitive liquid crystal tracers. An algorithm for the color-to-temperature transformation using a multi-layer feed-forward neural network is applied to three-dimensional natural convection in a rotating cylindrical cell. Two-dimensional temperature distributions in a slit plane are obtained by using the algorithm. A three-dimensional temperature distribution is consequently constructed by interpolating the two-dimensional distributions using the B-spline function. In addition, the Spatio-Temporal correlation method is applied to the natural convection to obtain a three-dimensional velocity vector distribution.     

A Genus-3 Topological Recursion Relation

In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof of this formula is a new relation in the tautological ring of the moduli space of 1-pointed genus-3 stable curves. Research of the first author was partially supported by NSF grant DMS-0204824 Research of the second author was partially supported by NSF grant DMS-0505835     

Keratinized epithelial transport of beta-blocking agents. I. Relationship between physicochemical properties of drugs and the flux across rat skin and hamster cheek pouch.

The maximum fluxes (Jmax) of beta-blockers through keratinized membranes were determined in vitro and compared with their physiochemical parameters such as lipophilicity (log k'0) and melting point (mp). Rat abdominal skin and hamster cheek pouch mucosa were used as the model membranes. Propranolol, metoprolol, timolol, pindolol, nadolol and agenolol were used as beta-blockers with a variety of physicochemical characters. Linear relations of Jmax with either log k'0 or mp were observed both in intact rat skin and in intact hamster cheek pouch, suggesting that the lipophilicity and thermodynamic activity of a drug in the crystal state primarily affect the drug's permeation through these membranes. However, the slope, dJmax/d(log k'0), for cheek pouch mucosa was greater than that for rat skin, corresponding to the lack of appendigeal shunt pathways in cheek pouch. Penetration studies using the delipidized membranes and the isolated stratum corneum sheet of hamster cheek pouch mucosa clarified that the primary rate-limiting barrier function might exist in the lipid layer of the stratum corneum. Jmax values for the tape-stripped and delipidized skins correlated with both the solubilities of drugs in the vehicle and with the mp, suggesting the polar porous characteristics of both model membranes. However, a theoretical approach confirmed that the contribution of an intracellular or aqueous pore route in the intact membrane to the permeation of drugs with positive lipophilic indexes is negligible.     

Synthesis and orientation study of a magnetically aligned liquid‐crystalline chitin/poly(acrylic acid) composite

A high magnetic field of 5 T was used to fabricate a magnetically aligned, optically anisotropic, liquid‐crystalline chitin/poly(acrylic acid) composite. The aligned mesophase was fixed by photoinitiated free‐radical polymerization. From an examination of polarized optical micrographs and an X‐ray diffraction study, a high degree of orientation of 0.70 was observed for the composite with a higher liquid‐crystalline chitin concentration (10.70 wt %); the orientation was reduced with a decreased chitin concentration at a given acrylic acid concentration. The X‐ray data for the developed composite showed a uniplanar orientation for the chitin crystallites, with its molecular long axes perpendicular to the direction of the magnetic field. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 711–714, 2003