Two-photon dyes containing heterocyclic rings with enhanced photostability

A series of donor-pi-donor derivatives containing phenyl, naphthyl, and anthryl groups as the pi-center and heterocyclic rings as the conjugation bridge have been synthesized and their one- and two-photon spectroscopic properties and photostability were determined. These compounds show bathochromic shifts in the absorption and emission spectra, larger two-photon cross-section, and enhanced photostability in comparison to their open-chain analogues. In addition, a convenient method for the qualitative photostability measurement is proposed.     

A simplified homology‐model builder toward highly protein‐like structures: An inspection of restraining potentials

A homology model builder using simple restraining potentials based on spline‐interpolated quadratic functions is developed and interfaced with CHARMM package. The continuity and stability of the potential function were validated, and the parameters were optimized using the CASP7 targets. The performance of the model builder was benchmarked to the Modeller program using the template‐based modeling targets in CASP9. The benchmark results show that, while our builder yields the structures with slightly lower packing, backbone, and template modeling scores, our models show much better protein‐like scores in terms of normalized discrete optimized protein energy, dipolar distance‐scaled finite‐ideal gas reference, Molprobity clash, Ramachandran appearance Z‐score, and rotamer Z‐score. As our model builder is interfaced with CHARMM, it is advantageous to directly use other CHARMM functionality and energy functions to refine the model structures or to use the models for other computational studies using CHARMM. © 2012 Wiley Periodicals, Inc.     

Growth rate of the functions in Bergman type spaces

For 0<p,α<∞, let ‖f‖_p,α be the L^p-norm with respect the weighted measure . We define the weighted Bergman space A_α^p(D) consisting of holomorphic functions f with ‖f‖_p,α<∞. For any σ>0, let A^−σ(D) be the space consisting of holomorphic functions f in D with . If D has C² boundary, then we have the embedding A_α^p(D)⊂A^−(n+α)/p(D). We show that the condition of C²-smoothness of the boundary of D is necessary by giving a counter-example of a convex domain with C^1,λ-smooth boundary for 0<λ<1 which does not satisfy the embedding.     

Optimal Sobolev estimates for ¯∂ on convex domains of finite type

We prove that solutions for ¯ get 1/M-derivatives more than the data in L^p-Sobolev spaces on a bounded convex domain of finite type M by means of the integral kernel method. Also we prove that the Bergman projection is invariant under the L^p-Sobolev spaces of fractional orders by different methods from McNeal-Stein's. By using these results, we can get L^p-Sobolev estimates of order 1/M for the canonical solution for ¯. The author was supported by grant No. R01-2000-000-00001-0 from the Basic Research Program of the Korea Science&Engineering Foundation.     

Estimates on the mean growth of functions in convex domains of finite type

Let be a bounded convex domain of finite type in with smooth boundary. In this paper, we prove the following inequality:

where , and . This is a generalization of some classical result of Hardy-Littlewood for the case of the unit disc. Using this inequality, we can embed the space into a weighted Bergman space in a convex domain of finite type.