Amphoteric refraction exhibited by anisotropic crystals

Amphoteric refraction of light ray at the interface between isotropic materials and anisotropic materials is analyzed. Depending on the incident angle, the refractive light ray can either refract positively or negatively. This amphoteric refraction phenomenon can be quite prevalent when the difference of the two principal refractive indices is large. The reflectance under various incident angles has also been calculated, and an experimental demonstration with a calcite crystal in air is presented.     

Bulk universality for Wigner matrices

We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e^?U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson sine kernel provided that U ∈ C⁶( \input amssym $\Bbb R$ ) with at most polynomially growing derivatives and ν(x) ≥ Ce^?C|x| for x large. The proof is based upon an approximate time reversal of the Dyson Brownian motion combined with the convergence of the eigenvalue density to the Wigner semicircle law on short scales. © 2010 Wiley Periodicals, Inc.     

Mutually pumped phase conjugator using a BaTiO3 crystal having two inclined faces

A pentagon-shaped undoped BaTiO₃ crystal was used to construct a high-quality mutually pumped phase conjugator. It yields two very stable phase-conjugate outputs (ǃ.7% fluctuation in intensity) with high reflectivity (the highest ᅝ%) when the two incident beams are of equal intensities. The response time of the conjugator is rather fast (ƻ s) and the tolerance of the acceptance angle is large too (걄°). Fine structures (35 7m) in an image, after passing through a phase aberrator, can be recovered by the conjugate waves yielded by this conjugator.     

Fundamentals of Computational Conformal Geometry

Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.     

Early cure behavior of a liquid dicyanate ester resin

The early cure behavior of 4,4‐dicyanato 1,1‐diphenolethane resin with and without incorporating Cr(acac)₃, Co(acac)₃, and Cu(acac)₂, respectively, as catalysts was investigated by gel permeation chromatography. The curing intermediates were separated by the column elution method and characterized by Fourier transform infrared, ¹H, and ³C NMR spectroscopies. The results indicated that the formed dimer in the early cure stage is a straight chain containing a primary amino group. The formed triazine ring in the trimer has a strong catalytic effect on the remaining cyanate groups so that the reactivity of the trimers was significantly increased. The reactivities of the curing intermediates decreased with molecular size until 7‐mer was reached. The initial monomer consumption is described by second‐order‐rate kinetics. In the presence of metal acetylacetonates, the curing reactions may be accelerated, but they did not change the reaction path and preceding sequence of reactivities. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3085–3092, 2001     

Geometric aspects of the moduli space of Riemann surfaces

We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore, the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford.     

Hydrogen‐Bonding Induced Cooperative Effect on the Energy Transfer in Helical Polynorbornenes Appended with Porphyrin‐Containing Amidic Alanine Linkers

Polynorbornenes appended with porphyrins containing a range of different linkers are synthesized. The use of bisamidic chiral alanine linkers between the pending porphyrins and the polymeric backbone has been shown to bring the adjacent porphyrin chromophores to more suitable orientation for exciton coupling owing to hydrogen bonding between the adjacent linkers. The hydrogen bonding between the adjacent pendants in these polymers may induce a cooperative effect and therefore render single‐handed helical structures for these polymers. Such a cooperative effect is reflected in the enhancement of FRET efficiencies between zinc–porphyrin and free base porphyrin in random copolymers.     

Selection of aptamers for signal transduction proteins by capillary electrophoresis

High‐affinity aptamers for important signal transduction proteins, i.e. Cdc42‐GTP, p21‐activated kinase1 (PAK1) and MRCK (myotonic dystrophy kinase‐related Cdc42‐binding kinase) α were successfully selected in the low micro‐ to nanomolar range using non‐systematic evolution of ligands by exponential enrichment (SELEX) with at least three orders of magnitude enhancement from their respective bulk affinity of naïve DNA library. In the non‐SELEX procedure, CE was used as a highly efficient affinity method to select aptamers for the desired molecular target through a process that involved repetitive steps of partitioning, known as non‐equilibrium CE of equilibrium mixtures with no PCR amplification between successive steps. Various non‐SELEX conditions including the type, concentration and pH of the run buffer were optimized. Other considerations such as salt composition of selection buffer, protein concentration and sample injection size were also studied for high stringency during selection. After identifying the best enriched aptamer pool, randomly selected clones from the aptamer pool were sequenced to obtain the individual DNA sequences. The dissociation constants (K_d) of these sequences were in the low micromolar to nanomolar range, indicating high affinity to the respective proteins. The best binders were also subjected to sequence alignment to generate a phylogenetic tree. No significant consensus region based on approximately 50 sequences for each protein was observed, suggesting the high efficiency of non‐SELEX for the selection of numerous unique sequences with high selectivity.