Row and Column Removal Theorems for Homomorphisms of Specht Modules and Weyl Modules

We prove a q-analogue of the row and column removal theorems for homomorphisms between Specht modules proved by Fayers and the first author [16]. These results can be considered as complements to James and Donkin’s row and column removal theorems for decomposition numbers of the symmetric and general linear groups. In this paper we consider homomorphisms between the Specht modules of the Hecke algebras of type A and between the Weyl modules of the q-Schur algebra.This research was supported by ARC grant DP0343023. The first author was also supported by a Sesqui Research Fellowship at the University of Sydney.     

A highly sensitive fluorescent immunoassay based on avidin-labeled nanocrystals

Nanocrystals of the fluorogenic precursor fluorescein diacetate (FDA) were applied as labels in order to improve on the assay sensitivity achieved in our previous studies. Each FDA nanocrystal can be converted into ∼2.6×10⁶ fluorescein molecules, which is useful for improving immunoassay sensitivity and limits of detection. NeutrAvidin was simply adsorbed onto the surface of the FDA nanocrystals, which were coated with distearoylglycerophosphoethanolamine (DSPE) modified with amino(poly(ethylene glycol))(PEG(2000)-Amine) as an interface for coupling biomolecules. This can be applied to detect different kinds of analytes that are captured by corresponding biotinylated biomolecules in different bioanalytical applications. The applicability of the NeutrAvidin-labeled nanocrystals was demonstrated in an immunoassay using the labeled avidin–biotin technique. Biotinylated antibody and FDA-labeled avidin were applied to the assay sequentially. The performance was compared with the traditional sandwich-type assay for mouse immunoglobulin G detection. Following the immunoreaction, the nanocrystals were released by hydrolysis and dissolution instigated by adding a large volume of organic solvent/sodium hydroxide mixture. The limit of detection was lower (by a factor of 2.5–21) and the sensitivity was (3.5–30-fold) higher than immunoassays using commercial labeling systems (FITC and peroxidase). This study shows that using fluorescent nanocrystals in combination with the avidin–biotin technique can enhance assay sensitivity and provide a lower limit of detection without requiring long incubation times as in enzyme-based labels.     

Couette flow of viscoelastic fluid with constitutive relation involving general Caputo-type fractional derivative

In this paper, the general Caputo-type fractional differential operator introduced by Pr. Anatoly N. Kochubei is applied to the linear theory of viscoelasticity. Firstly, using the general Caputo-type derivative, a generalized linear viscoelastic constitutive equation is proposed for the first time. Secondly, the momentum equation for the plane Couette flow of viscoelastic fluid with the constitutive relation is given as an integrodifferential equation and the analytical solution of the equation is established by employing the separation of variables method. Lastly, for special cases of the general constitutive relation, the analytical solutions are obtained in terms of the Mittag-Leffler functions.     

Incidence modules for symplectic spaces in characteristic two

We study the permutation action of a finite symplectic group of characteristic 2 on the set of subspaces of its standard module which are either totally isotropic or else complementary to totally isotropic subspaces with respect to the alternating form. A general formula is obtained for the 2-rank of the incidence matrix for the inclusion of one-dimensional subspaces in the distinguished subspaces of a fixed dimension.     

Some Results Obtained by Application of the LLT Algorithm

We determine the v-decomposition numbers d _μλ(v) for μ a partition with at most three parts. We use this information to compute the composition factors of the Specht modules of the Hecke algebra ?₀ = ?_{?, ω}( _n ) which correspond to partitions with at most three parts.     

Hemoglobin as a Diagnosing Molecule for Biological Effects of Atmospheric-Pressure Plasma

The studies with proteins are necessary to understand the biological effects of atmospheric pressure plasma (APP). Among proteins, those with transient metal ions play key roles in many biological events and they are very sensitive to environmental redox states. Iron-containing hemoglobin (Hb) is investigated in this study, after APP treatments under two environmental gas conditions of pure N₂ and N₂?+?O₂ mixture. Monitoring the intensity change for absorption spectra could lead to a quantitative assessment of the effect of discharge plasma on Hb. Redox states of Hb are classified into five states including O₂-bound Hb (oxy-Hb), deoxy-Hb, met-Hb, NO-bound Hb (NO-Hb), and hemichrome. Chemically generated reactive species and some scavengers are applied to understand the chemical reactions. Our experimental results confirm the complex chemical reactions of APP and suggest the possible use of Hb as a model protein for the visualization of APP biological effects.     

Dynamic kinetic resolution of 2-methyl-2-nitrocyclohexanol: Combining the intramolecular nitroaldol (Henry) reaction & lipase-catalysed resolution

Efforts to combine the intramolecular nitroaldol reaction with lipase-catalysed resolution of the resulting nitroaldol adduct in a one-pot dynamic kinetic resolution (DKR) are described. Significant challenges were encountered in the combination of the two systems. trans-2-Methyl-2-nitrocyclohexyl acetate (±)-3b was isolated in excellent enantiopurity (>98% ee) via a sequential DKR sequence where the lipase-mediated resolution and base-mediated interconversion of 2-methyl-2-nitrocyclohexanol 2 were effected alternately, demonstrating the feasibility of this approach initially. Further work showed, for the first time, evidence that a DKR-type system is possible for 2. Reaction engineering allowed the design of a sequential one-pot reaction system which furnished the products with excellent enantioselectivity, and good diastereoselectivity.     

Benzofurans and sterol from the seeds of <Emphasis Type="Italic">styrax obassia</Emphasis>

Two benzofurans (1, 2) along with five known compounds (3.7) were isolated from the seeds of S. obassia. Their structures were elucidated as methyl 3-[7-methoxy-2-(3′,4′-methylenedioxyphenyl)-5-benzofuranyl]-propionate (1), methyl 3-[2-(3′,4′-methylenedioxyphenyl)-5-benzofuranyl]-propionate (2), egonol (3), egonolacetate (4), egonol-2-methylbutanoate (5), 7-demethoxyegonol-2-methylbutanoate (6), and stigmasterol (7) on the basis of their comprehensive spectroscopic analysis including 2D NMR data. Compounds 1, 2 are obtained for the first time from nature, while this is the first record of compound 7 from the Styrax species. Published in Khimiya Prirodnykh Soedinenii, No. 4, pp. 350-353, July-August, 2008. Original article submitted May 4, 2007.