Orientational ordering of a ferroelectric liquid crystal with high spontaneous polarization

The orientational ordering of the liquid crystal, 3M2CPHOB ((2S, 3S)-3-methyl-2-chloropentanoic acid-4′,4″-hexyloxybiphenyl ester) in its smectic A and chiral smectic C phases has been studied by carbon-13 2D N.M.R. The technique used is separated local-field spectroscopy, which produces a first-order splitting for each carbon signal, from which carbon-proton dipolar constants can be determined. The order parameters for different molecular segments of the liquid crystal can then be calculated. The C-H bond order parameter at the chiral centre with a chlorine atom is unusually large, which is a strong indication of hindered rotation of the molecular segment at the chiral centre. The carbon-13 chemical shifts of 3M2CPHOB were also measured as a function of temperature, and the relation between the chemical shifts and the order parameters is discussed.     

Double-notch-shaped microdisk resonator devices with gapless coupling on a silicon chip Invited Paper

We propose novel double-notch-shaped microdisk resonator-based devices with gapless waveguide-to- microdisk and inter-cavity coupling via the two notches of the microdisk. Both finite-difference time- domain simulations and experimental demonstrations reveal the high-quality-factor multimode resonances in such microdisks. Using such double-notch microdisk resonators, we experimentally demonstrate the many-element linearly cascaded-microdisk resonator devices with up to 50 elements on a silicon chip.     

Twin-image elimination in optical scanning holography

We propose a novel multiplexing technique to solve the twin image problem in optical scanning holography without the use of a spatial carrier, as commonly used in conventional off-axis holography. The technique involves simultaneously acquiring sine and cosine Fresnel zone-lens plate coded images by optical scanning. A complex addition of the two coded images will then be performed and decoded to give a twin-image rejection reconstruction. Computer simulations will be presented to demonstrate the validity of the idea.     

Torus symmetry of compact self-dual manifolds

We classify compact anti-self-dual Hermitian surfaces and compact four-dimensional conformally flat manifolds for which the group of orientation preserving conformal transformations contains a two-dimensional torus. As a corollary, we derive a topological classification of compact self-dual manifolds for which the group of conformal transformations contains a two-dimensional torus.Partially supported by the National Science Foundation grant DMS-9306950.     

Classification of homogeneous copolymers of propylene and 1‐octene based on comonomer content

The solid‐state structure and properties of homogeneous copolymers of propylene and 1‐octene were examined. Based on the combined observations from melting behavior, dynamic mechanical response, morphology with primarily atomic force microscopy, X‐ray diffraction, and tensile deformation, a classification scheme with four distinct categories is proposed. The homopolymer constitutes Type IV. It is characterized by large α‐positive spherulites with thick lamellae, good lamellar organization, and considerable secondary crystallization. Copolymers with up to 5 mol % octene, with at least 28 wt % crystallinity, are classified as Type III. Like the homopolymer, these copolymers crystallize as α‐positive spherulites, however, they have smaller spherulites and thinner lamellae. Both Type IV and Type III materials exhibit thermoplastic behavior characterized by yielding with formation of a sharp neck, cold drawing, strong strain hardening, and small recovery. Copolymers classified as Type II have between 5 and 10 mol % octene with crystallinity in the range of 15–28%. Type II materials have smaller impinging spherulites and thinner lamellae than Type III copolymers. Moreover, the spherulites are α‐negative, meaning that they exhibit very little crystallographic branching. These copolymers also contain predominately α‐phase crystallinity. The materials in this category have plastomeric behavior. They form a diffuse neck upon yielding and exhibit some recovery. Type I copolymers have more than 10 mol % octene and less than 15% crystallinity. They exhibit a granular texture with the granules often assembled into beaded strings that resemble poorly developed lamellae. Type I copolymers crystallize predominantly in the mesophase. Materials belonging to this class deform with a very diffuse neck and also exhibit some recovery. They are identified as elastoplastomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4357–4370, 2004     

Cycle Cover Ratio of Regular Matroids

A cycle in a matroid is a disjoint union of circuits. This paper proves that every regular matroidM without coloops has a set S of cycles whose union is E(M) such that every element is in at most three of the cycles in S. It follows immediately from this that, on average, each element of M is in at most three members of the cycle cover S. This improves on a 1989 result of Jamshy and Tarsi who proved that there is a cycle cover for which this average is at most 4, and conjectured that a cycle cover exists for which the average is at most 2.     

Proteomics investigation on aristolochic acid nephropathy: a case study on rat kidney tissues

Prolonged intake of aristolochic acid (AA) has been shown to be associated with the development of certain renal disorders. Renal tubular atrophy and interstitial fibrosis are the early symptoms of AA nephropathy. The symptoms were observed in rats that were dosed with AA at a dosage of 10 mg/kg/day for 1 month. Apart from the renal tubular atrophy and interstitial fibrosis, AA–DNA adducts were detected in the rat kidney tissue. Differentiated proteins were identified in the kidney tissues from proteomics investigations. The upregulated proteins identified included ornithine aminotransferase, sorbitol dehydrogenase, actin, aspartoacylase, 3-hydroxyisobutyrate dehydrogenase, and peroxiredoxin-1. Downregulated proteins such as ATP synthase subunit β, glutamate dehydrogenase 1, regucalcin, glutamate–cysteine ligase regulatory subunit, dihydropteridine reductase, hydroxyacyl-coenzyme A dehydrogenase, voltage-dependent anion-selective channel protein 1, prohibitin, and adenylate kinase isoenzyme 4 were also identified. Several identified protein markers were found to have biological and medical significance.     

Guanine-rich RNAs and DNAs that bind heme robustly catalyze oxygen transfer reactions

Diverse guanine-rich RNAs and DNAs that fold to form guanine quadruplexes are known to form tight complexes with Fe(III) heme. We show here that a wide variety of such complexes robustly catalyze two-electron oxidations, transferring oxygen from hydrogen peroxide to thioanisole, indole, and styrene substrates. Use of (18)O-labeled hydrogen peroxide reveals the source of the oxygen transferred to form thioanisole sulfoxide and styrene oxide to be the activated ferryl moiety within these systems. Hammett analysis of the kinetics of thioanisole sulfoxide formation is unable to distinguish between a one-step, direct oxygen transfer and a two-step, oxygen rebound mechanism for this catalysis. Oxygen transfer to indole produces a range of products, including indigo and related dyes. Docking of heme onto a high-resolution structure of the G-quadruplex fold of Bcl-2 promoter DNA, which both binds heme and transfers oxygen, suggests a relatively open active site for this class of ribozymes and deoxyribozymes. That heme-dependent catalysis of oxygen transfer is a property of many RNAs and DNAs has ramifications for primordial evolution, enzyme design, cellular oxidative disease, and anticancer therapeutics.     

Does gravity cause load-bearing bridges in colloidal and granular systems?

We study structures which can bear loads, "bridges", in particulate packings. To investigate the relationship between bridges and gravity, we experimentally determine bridge statistics in colloidal packings. We vary the effective magnitude and direction of gravity, volume fraction, and interactions, and find that the bridge size distributions depend only on the mean number of neighbors. We identify a universal distribution, in agreement with simulation results for granulars, suggesting that applied loads merely exploit preexisting bridges, which are inherent in dense packings.     

On the Dirichlet's box principle

In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in Hong Kong.