可加稳定过程的自相交局部时

本文研究了可加稳定过程的自相交局部时的问题.利用Borel–Canteil引理等方法,得到可加稳定过程的自相交局部时的Hlder上界,推广了文献[5]中的结果.     

Du Fort-Frankel格式及DFF-I并行格式的稳定性

 本文对抛物型方程的Du Fort-Frankel(DFF)格式以及基于该格式构造的并行差分格式(DFF-I)进行了稳定性分析。采用矩阵分析方法, 证明了其无条件(LR)稳定性, 给出了DFF格式的稳定性系数的最小值的上界估计, 结果表明其与网格比有关, 从而DFF格式并非绝对稳定。本文改进了并行差分格式(DFF-I)的稳定性分析结果, 证明了其增长矩阵的谱半径严格小于1, 从而具有长时间稳定性。数值算例验证了DFF-I格式具有空间二阶精度, 且有很好的稳定性。     

Context-free grammars for triangular arrays

We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.     

A strict topology on Orlicz spaces

Let φ be a Young function, Ω be a locally compact space, and μ be a positive Radon measure on Ω. We consider a strict topology (in the sense of Sentilles‐Taylor) on the Orlicz function space and investigate various properties of this locally convex topology. We also study the Orlicz space of a locally compact group G with a left Haar measure under the strict topology and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators on under the topology and other natural ones.     

Desch‐Schappacher perturbation of one‐parameter semigroups on locally convex spaces

We prove a Desch‐Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one‐parameter semigroups which are defined on a sequentially complete locally convex space.     

Air‐Stable Oxyallyl Patterns and a Switchable N‐Heterocyclic Carbene

Oxyallyl derivatives are typically elusive compounds. Even recently reported “stabilized” 1,3‐diaminooxyallyl species are still highly reactive and have short lifetimes at room temperature. Herein, we report the synthesis and preliminary study of mesoionic pyrimidine derivatives that feature 1,3‐bis(dimethylamino)oxyallyl patterns with an unprecedented level of stabilization. The latter are not only insensitive towards air and moisture, but they are also compatible with the formation of an ancillary stable N‐heterocyclic carbene moiety. As the oxyallyl pattern is proton‐responsive, it allows the reversible switching of the electronic properties of the carbene, as a ligand.     

Aromatic 19F–13C TROSY—[19F, 13C]‐Pyrimidine Labeling for NMR Spectroscopy of RNA

We present the access to [5‐¹⁹F, 5‐¹³C]‐uridine and ‐cytidine phosphoramidites for the production of site‐specifically modified RNAs up to 65 nucleotides (nts). The amidites were used to introduce [5‐¹⁹F, 5‐¹³C]‐pyrimidine labels into five RNAs—the 30 nt human immunodeficiency virus trans activation response (HIV TAR) 2 RNA, the 61 nt human hepatitis B virus ? (hHBV ?) RNA, the 49 nt SAM VI riboswitch aptamer domain from B. angulatum, the 29 nt apical stem loop of the pre‐microRNA (miRNA) 21 and the 59 nt full length pre‐miRNA 21. The main stimulus to introduce the aromatic ¹⁹F–¹³C‐spin topology into RNA comes from a work of Boeszoermenyi et al., in which the dipole‐dipole interaction and the chemical shift anisotropy relaxation mechanisms cancel each other leading to advantageous TROSY properties shown for aromatic protein sidechains. This aromatic ¹³C–¹⁹F labeling scheme is now transferred to RNA. We provide a protocol for the resonance assignment by solid phase synthesis based on diluted [5‐¹⁹F, 5‐¹³C]/[5‐¹⁹F] pyrimidine labeling. For the 61 nt hHBV ? we find a beneficial ¹⁹F–¹³C TROSY enhancement, which should be even more pronounced in larger RNAs and will facilitate the NMR studies of larger RNAs. The [¹⁹F, ¹³C]‐labeling of the SAM VI aptamer domain and the pre‐miRNA 21 further opens the possibility to use the biorthogonal stable isotope reporter nuclei in in vivo NMR to observe ligand binding and microRNA processing in a biological relevant setting.     

超重现毛细管电泳的理论与例证

毛细管电泳经常遭受结果不稳定、不重现的困扰。该文从理论上推导了一些新模式并以例证说明,这些模式能在一定条件下抵抗条件变化,获得超重现电泳谱图。它们是加权淌度谱、迁移电量谱、电荷密度谱、摩尔电荷密度谱、扩散系数谱、液相质量谱,以及它们各自的比例谱等,其中前4种为实时测量模式,其余的为实验后模式。这些模式需要发展新的仪器或算法,但都有发展潜力,值得深入研究。