A classification of sharp tridiagonal pairs

Let F denote a field and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A:V→V and A^∗:V→V that satisfy the following conditions: (i) each of A,A^∗ is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A^∗V_i⊆V_i-1+V_i+V_i+1 for 0?i?d, where V_-1=0 and V_d+1=0; (iii) there exists an ordering of the eigenspaces of A^∗ such that for 0?i?δ, where and ; (iv) there is no subspace W of V such that AW⊆W, A^∗W⊆W, W≠0, W≠V. We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0?i?d the dimensions of coincide. The pair A,A^∗ is called sharp whenever . It is known that if F is algebraically closed then A,A^∗ is sharp. In this paper we classify up to isomorphism the sharp tridiagonal pairs. As a corollary, we classify up to isomorphism the tridiagonal pairs over an algebraically closed field. We obtain these classifications by proving the μ-conjecture.     

Chromatographic separation of neodymium isotopes by using chemical exchange process

The neodymium isotope effects were investigated in Nd–malate ligand exchange system using the highly porous cation exchange resin SQS-6. The temperature of the chromatographic columns was kept constant at 50 °C by temperature controlled water passed through the columns jackets. The separation coefficient of neodymium isotopes, ?’s, was calculated from the isotopic ratios precisely measured by means of an ICP mass spectrometer equipped with nine collectors as ion detectors. The separation coefficient, ? × 10⁵, were calculated and found to be 1.4, 4.8, 5.4, 10.6, 16.8 and 20.2 for ¹⁴³Nd, ¹⁴⁴Nd, ¹⁴⁵Nd, ¹⁴⁶Nd, ¹⁴⁸Nd and ¹⁵⁰Nd, respectively.     

Surface-modified lead–zirconium-titanate system for solution-processed ferroelectric-gate thin-film transistors

We propose the use of a La₂O₃ (LO) film as the capping layer for improvement of a semiconductor/insulator interface in a solution-processed indium–tin–oxide (ITO) ferroelectric-gate thin-film transistor (FGT) device. It is demonstrated that the LO layer acts as a good barrier film not only for preventing the interdiffusion between the ITO semiconductor and lead–zirconium-titanate (PZT) insulator layers, but also for stabilizing the PZT surface structure. The fabricated FGT device exhibited high I _on/I _off, large M _w, high μ _FE and improved retention time of about 10⁹, 3.5 V, 7.94 cm²?V^?1?s^?1 and 1 day, respectively, which are comparable to or better than those obtained with FGTs fabricated by means of conventional vacuum processes. We also point out that the key origin of the interface improvement is likely due to the incorporation of La into the PZT system, forming a La surface-modified PZT system which is more stable than the pure PZT in terms of Pb volatility and formation of oxygen vacancies.     

Laser ablation synthesis of monodispersed magnetic alloy nanoparticles

Monodispersed CoPt alloy nanoparticles were synthesized by a pulsed laser ablation (PLA) technique coupled with a low-pressure operating differential mobility analyzer (LP-DMA). The CoPt alloy nanoparticles were generated by laser ablating a solid Co–Pt target. In CoPt alloy nanoparticles synthesized from a target with a Co composition of 75 at%, the nanoparticle surfaces were covered by an oxide layer and exhibited a core-shell structure. In contrast, no shell was observed in particles generated from a target with a Co:Pt ratio of 50:50 at%. According to an EDX analysis, the compositions of the individual nanoparticles were almost the same as that of the target material. Finally, the magnetic hysteresis loops of the CoPt alloy nanoparticles exhibited ferromagnetism.     

Two Beam Coupling in Semi-Insulating GaN Film Using Electroabsorption Effect

The photorefractive effect was observed in He-ion-implanted semi-insulating GaN film in the UV spectral region. The photorefractive grating is induced by the electroabsorption effect near the band-edge. Two beam coupling experiments were performed at a wavelength of 363.8 nm. The experimental results indicate that absorption grating mainly contributes to the beam coupling.     

Adsorption behavior of metal ions onto a bovine serum albumin (BSA) membrane monitored by means of an electrode-separated piezoelectric quartz crystal.

The interaction between metal ions and bovine serum albumin (BSA) was studied by using a piezoelectric quartz crystal (PQC) arranged in the electrode-separated configuration. A silanized surface of the PQC was coated with a BSA membrane via a coupling reaction with glutaraldehyde. The frequency shifts obtained from PQC coated with a BSA membrane suggested that various kinds of metal ions could be adsorbed onto the BSA membrane from aqueous solutions containing a low concentration of metal ions (2 or 10 micromol dm(-3)), only when the BSA was denatured with an alkaline solution. Anionic species of Pt(IV) and Au(III) were adsorbed onto the denatured BSA membrane from an acetic acid solution at pH 2.2, and cationic species of Cd(II), Zn(II), Co(II), Ni(II), Cu(II), and Ag(I), and cations, such as Ca2+, Ba2+, and Mg2+, were adsorbed from ammonia buffer at pH 9.5, whereas Al(III), Cr(III), Fe(III), Hg(II), and Pb(II) were hardly adsorbed. The adsorption mechanisms of these metal ions are discussed, based on the electrostatic interaction between the metal ions and the denatured BSA membrane, and complex formation between the metal ions and amino acid residues of the denatured BSA. Further, the PQC coated with a denatured BSA membrane was applied to the determination of Pt and Cd, using large frequency shifts for Pt(IV) and Cd(II).