Subword complexes in Coxeter groups

Let (Π,Σ) be a Coxeter system. An ordered list of elements in Σ and an element in Π determine a subword complex, as introduced in Knutson and Miller (Ann. of Math. (2) (2003), to appear). Subword complexes are demonstrated here to be homeomorphic to balls or spheres, and their Hilbert series are shown to reflect combinatorial properties of reduced expressions in Coxeter groups. Two formulae for double Grothendieck polynomials, one of which appeared in Fomin and Kirillov (Proceedings of the Sixth Conference in Formal Power Series and Algebraic Combinatorics, DIMACS, 1994, pp. 183-190), are recovered in the context of simplicial topology for subword complexes. Some open questions related to subword complexes are presented.     

Tuning the band gap in hybrid tin iodide perovskite semiconductors using structural templating

Structural distortions within the extensive family of organic/inorganic hybrid tin iodide perovskite semiconductors are correlated with their experimental exciton energies and calculated band gaps. The extent of the in- and out-of-plane angular distortion of the SnI4(2-) perovskite sheets is largely determined by the relative charge density and steric requirements of the organic cations. Variation of the in-plane Sn-I-Sn bond angle was demonstrated to have the greatest impact on the tuning of the band gap, and the equatorial Sn-I bond distances have a significant secondary influence. Extended Hückel tight-binding band calculations are employed to decipher the crystal orbital origins of the structural effects that fine-tune the band structure. The calculations suggest that it may be possible to tune the band gap by as much as 1 eV using the templating influence of the organic cation.     

Elongated silica nanoparticles with a mesh phase mesopore structure by fluorosurfactant templating

Mesoporous silica materials with pore structures such as 2D hexagonal close packed, bicontinuous cubic, lamellar, sponge, wormhole-like, and rectangular have been made by using surfactant templating sol-gel processes. However, there are still some "intermediate" phases, in particular mesh phases, that are formed by surfactants but which have not been made into analogous silica pore structures. Here, we describe the one-step synthesis of mesoporous silica with a mesh phase pore structure. The cationic fluorinated surfactant 1,1,2,2-tetrahydroperfluorodecylpyridinium chloride (HFDePC) is used as the template. Like many fluorinated surfactants, HFDePC forms intermediate phases in water (including a mesh phase) over a wider range of compositions than do hydrocarbon surfactants. The materials produced by this technique are novel elongated particles in which the layers of the mesh phase are oriented orthogonal to the main axis of the particles.     

Ultrafast Fluorescence Spectroscopy via Upconversion and Its Applications in Biophysics

In this review, the experimental set-up and functional characteristics of single-wavelength and broad-band femtosecond upconversion spectrophotofluorometers developed in our laboratory are described. We discuss applications of this technique to biophysical problems, such as ultrafast fluorescence quenching and solvation dynamics of tryptophan, peptides, proteins, reduced nicotinamide adenine dinucleotide (NADH), and nucleic acids. In the tryptophan dynamics field, especially for proteins, two types of solvation dynamics on different time scales have been well explored: ~1 ps for bulk water, and tens of picoseconds for “biological water”, a term that combines effects of water and macromolecule dynamics. In addition, some proteins also show quasi-static self-quenching (QSSQ) phenomena. Interestingly, in our more recent work, we also find that similar mixtures of quenching and solvation dynamics occur for the metabolic cofactor NADH. In this review, we add a brief overview of the emerging development of fluorescent RNA aptamers and their potential application to live cell imaging, while noting how ultrafast measurement may speed their optimization.     

微乳液的热力学性质 I: 芳烃类的侧链链长对微乳液热力学函数影响

本文研究以非离子型表面活性剂-正辛醇-水-芳烃类所组成的微乳液, 探讨醇从油相转移到界面相时的自由能变化, 以及温度对自由能的影响。计算出熵和焓的变化, 发现在实验范围内, 上述热力学函数的对数值与芳烃侧链的碳原子数(n)呈线性关系。这些关系式对微乳液的构成和稳定性的讨论是重要的, 还对几种芳烃异构体所构成的微乳液的热力学函数进行了实验和讨论。     

Unusual dependence of particle architecture on surfactant concentration in partially fluorinated decylpyridinium templated silica

A series of porous silica particles is prepared with different concentrations of the fluorinated cationic surfactant 1-(3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,10)-heptadecafluorodecyl)pyridinium chloride (HFDePC) to trace the changes in pore structure and particle morphology as the surfactant concentration increases. At the lowest concentration studied (1.5 mmol/L), the product consists of small round particles with close-packed cylindrical mesopores. As the HFDePC concentration increases, macroporous voids are introduced to create multi-chambered hollow particles with mesoporous walls. With a still higher concentration of HFDePC the macropore volume decreases, and elongated, tactoid-like nanoparticles are formed with random mesh-phase pores oriented with silica layers perpendicular to the main axis of the particles. Further increasing the concentration of HFDePC eventually leads to the formation of round particles with disordered pores. These changes are consistent with increasing HFDePC concentration favoring increasingly oblate or disklike micelles. The process of forming the elongated particles with random mesh-phase structure is investigated by TEM of chilled and dried samples. The results indicate that the oriented tactoid-like structure forms spontaneously within 2 min by co-assembly of silica and HFDePC rather than by preferred growth perpendicular to the layers. The particle shape and layer orientation are consistent with what would be expected for a liquid-crystal particle with orientation-dependent surface tension. Finally, we compare samples prepared with a high HFDePC and with good or poor mixing. With inadequate mixing, a gel layer forms at the top of the sample which is composed of elongated mesoporous particles with a thick coating of microporous silica. The lower particulate phase contains small disordered particles similar to those obtained in a well-mixed sample. Presumably, the structure of the upper layer results from initial immiscibility of the precursor and slow diffusion of silicates out of the gel.     

抗坏血酸和尿酸在甘氨酸-壳聚糖修饰玻碳电极上的电化学行为及测定

制备了甘氨酸-壳聚糖复合膜修饰玻碳电极(Gly-CTS/GCE),研究了抗坏血酸(AA)和尿酸(UA)在该修饰电极上的电化学行为。结果表明在pH=5.59的磷酸盐缓冲溶液中,AA、UA在Gly-CTS/GCE上均产生灵敏的不可逆氧化峰,其峰电流与浓度在一定范围内呈良好的线性关系。对AA和UA混合溶液平行测定7次,相对标准偏差分别为4.6%、2.9%,表明该电极重现性和稳定性良好。AA、UA在Gly-CTS/GCE电极上的氧化峰峰电位相差340mV,据此可实现对二者的同时检测,并可应用于实际样品测定。