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.     

Additions of enantiopure alpha-sulfinyl carbanions to (S)-N-sulfinimines: asymmetric synthesis of beta-amino sulfoxides and beta-alphamino alcohols

The addition of the lithium anions derived from (R)- and (S)-methyl and -ethyl p-tolyl sulfoxides to (S)-N-benzylidene-p-toluenesulfinamide provides an easy access route to enantiomerically pure beta-(N-sulfinyl)amino sulfoxides. Stereoselectivity can be achieved when the configurations at the sulfur atoms of the two reagents are opposite (matched pair), thus resulting in only one diastereoisomer, even for the case in which two new chiral centers are created. The N-sulfinyl group primarily controls the configuration of the carbon bonded to the nitrogen, whereas the configuration of the alpha-sulfinyl carbanion seems to be responsible for the level of asymmetric induction, as well as for the configuration of the new stereogenic C-SO carbon in the reactions with ethyl p-tolyl sulfoxides. An efficient method for transforming the obtained beta-(N-sulfinyl)amino sulfoxides into optically pure beta-amino alcohols, based on the stereoselective non-oxidative Pummerer reaction, is also reported.     

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.     

(Z)-3-p-tolylsulfinylacrylonitrile as a chiral dienophile: diels-alder reactions with furan and acyclic dienes

The behavior of (Z)-3-p-tolylsulfinylacrylonitrile (1) as a chiral dienophile has been evaluated from its reactions with furan and acyclic dienes. Electrostatic interactions of the cyano group with the sulfinyl one restrict the conformational mobility around the C-S bond, thus controlling the pi-facial selectivity, which is almost complete in all cases, the approach of the diene from the less-hindered face of the dienophile (that bearing the lone electron pair) in the predominant rotamer being the favored one. The regioselectivity is also completely controlled by the cyano group. Additionally, the reactivity of compound 1 as well as its endo-selectivity are both higher than those observed for the corresponding (Z)-3-sulfinylacrylates, thus proving the potential of sulfinylnitriles as chiral dienophiles.     

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.     

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.