Jucys–Murphy elements,orthogonal matrix integrals,and Jack measures

We study symmetric polynomials whose variables are odd-numbered Jucys–Murphy elements. They define elements of the Hecke algebra associated to the Gelfand pair of the symmetric group with the hyperoctahedral group. We evaluate their expansions in zonal spherical functions and in double coset sums. These evaluations are related to integrals of polynomial functions over orthogonal groups. Furthermore, we give their extension based on Jack polynomials.     

On spherical designs obtained from Q‐polynomial association schemes

We characterize that the image of the embedding of the Q ‐polynomial association scheme into the first eigenspace by primitive idempotent E ₁ is a spherical t‐design in terms of the Krein numbers. Furthermore, we show that the strengths of P‐ and Q‐polynomial schemes as spherical designs are bounded by a constant. Copyright © 2011 John Wiley & Sons, Ltd. 19:167‐177, 2011     

Boron adsorption mechanism on polyvinyl alcohol

Recently, an increase in the use of boron compounds has led to an increase in boron emissions, and concern has grown regarding its detrimental effects on the human body. An adsorbent that adsorbs boron selectively has been developed as a countermeasure. Although certain commercially available boron selective adsorbents can be used to remove boron from aqueous solutions by utilizing the strong affinity between boron and hydroxyl groups, the adsorption capacity appears to be insufficient. So, we adopted polyvinyl alcohol (PVA), which contains many hydroxyl groups, as a model adsorbent. We investigated the boron adsorption characteristics of PVA, and then studied the relationship between the number of adsorption sites and actual adsorption amounts. We assessed the adsorption result by using adsorption site availability (ASA) as an indicator of the ratio of effectively functioning hydroxyl groups from the many hydroxyl groups in PVA. ASA was expressed as a percentage of the experimental equilibrium adsorbed amount in relation to the theoretical equilibrium adsorbed amount. We also compared the adsorption isotherms and ASA obtained with PVA, commercially available N-methylglucamine-type resin (CRB03 and CRB05) and the adsorbent we synthesized from polyallylamine (PAA) and glucose (PAA-Glu). Although PVA has many hydroxyl groups in a molecule, ASA analysis revealed that only 6% of the hydroxyl groups in PVA was used for boron adsorption. On the other hand, CRBs and PAA-Glu exhibited higher ASA values (about 15% and 35% respectively) and adsorption amounts, suggesting that the sterically congested adsorbent structure had a great influence on boron adsorption and ASA.     

A Light/Ketone/Copper System for Carboxylation of Allylic C−H Bonds of Alkenes with CO2

A photo‐induced carboxylation reaction of allylic C?H bonds of simple alkenes with CO₂ is prompted by means of a ketone and a copper complex. The unique carboxylation reaction proceeds through a sequence of an endergonic photoreaction of ketones with alkenes forming homoallyl alcohol intermediates and a thermal copper‐catalyzed allyl transfer reaction from the homoallyl alcohols to CO₂ through C?C bond cleavage.     

Unbiased orthogonal designs

The notion of unbiased orthogonal designs is introduced as a generalization of unbiased Hadamard matrices, unbiased weighing matrices and quasi-unbiased weighing matrices. We provide upper bounds and several methods of construction for mutually unbiased orthogonal designs. As an application, mutually quasi-unbiased weighing matrices for various parameters are obtained.     

Use of Highly Purified and Mixed Antibodies for Simultaneous Detection of Multiple Protein Species Released from Mitochondria upon Induction of the Permeability Transition

Concomitant with the induction of the mitochondrial permeability transition (PT), cytochrome c is released from mitochondria into the cytosol where it triggers subsequent steps of cellular apoptosis. Thus, inducers of the mitochondrial PT would become “seed compounds” of regulators of apoptosis. However, when we examine the actions of certain chemicals on the release of mitochondrial cytochrome c, the behaviors of not only cytochrome c but also multiple mitochondrial protein species must be carefully examined because the mitochondrial PT and release of proteins from mitochondria occur in diverse manners. In the present study, we examined whether it is possible to measure the behaviors of multiple protein species in a single experiment using purified and mixed antibodies. The results obtained clearly indicate that this procedure would be applicable for high-throughput screening of regulators of apoptosis. Further requirements necessary for the establishment of a useful screening system for apoptosis regulators are discussed.     

Fabrication and placement of a ring structure of nanoparticles by a laser-induced micronanobubble on a gold surface

We have developed a new fabrication method for a ring structure of assembled nanoparticles on a gold surface by the use of continuous Nd:YAG laser light. A micronanobubble on a gold surface, created by laser local heating, acts as a template for the formation of the ring structure. Both Marangoni convection flow and capillary flow around the micronanobubble are responsible for the driving force to assemble nanoparticles such as CdSe Q-dots into the ring structure from the solution. Because a single micronanobubble was generated by the Nd:YAG laser focusing point, the precise positioning of the ring structure was feasible directly on the gold surface, which makes it possible to fabricate various patterns of rings such as arrays and letters and even a double-ring structure without any photomasks or any templates.