Completely Entangled State and Simultaneous Eigenstate in a Finite Dimensional Space

It is shown that a completely entangled state belonging to a finite dimensional Hilbert space is equivalent to a simultaneous eigenstate of two unitary operators. These operators are exponentials of sum and difference of two Hermitian operators of a two-mode system that are complementary with each other.     

Uniqueness of maximum planar five-distance sets

A subset X in the Euclidean plane is called a k-distance set if there are exactly k distances between two distinct points in X. We denote the largest possible cardinality of k-distance sets by g(k). Erdős and Fishburn proved that g(5)=12 and also conjectured that 12-point five-distance sets are unique up to similar transformations. We classify 8-point four-distance sets and prove the uniqueness of the 12-point five-distance sets given in their paper. We also introduce diameter graphs of planar sets and characterize these graphs.     

Synthesis and properties of amino acid esters of hydroxypropyl cellulose

The amino acid esters of hydroxypropyl cellulose (HPC) [R′ = H ( 2a ), CH₃ ( 2b ), CH₂CH(CH₃)₂ ( 2c ), CH₂CONH₂ ( 2d ), CH₂CH₂CONH₂ ( 2e ), CH₂CH₂CH₂CH₂ NHOCOC(CH₃)₃ ( 2f )] were synthesized in good yield by the reaction of t‐butoxycarbonyl (t‐Boc)‐protected amino acids with hydroxy groups of HPC ( 1 ; molar substitution (MS), 4.61). The amino acid functionalities displaying varied chemical nature, shape, and bulk were utilized and the bulk of the substituent on the α‐carbon of amino acids was elucidated to be of vital significance for the observed degree of incorporation (DS_Est). The ¹H NMR spectra and elemental analysis were employed to determine the degree of incorporation of amino acid moiety (DS_Est) and almost complete substitution of the hydroxy protons was revealed for 2a , 2b , and 2f . The presence of the peaks characteristic of the carbonyl group in the FTIR spectra furnished further evidence for the successful esterification of HPC. The starting as well as the resulting polymers ( 1 and 2a – f ) were soluble in polar organic solvents; however, the esterification of 1 with bulky organic moieties resulted in an increased hydrophobicity as all of the amino acid‐functionalized polymers ( 2a – f ) were insoluble in water. The onset temperatures of weight loss of 2a – f were 175–230 °C, indicating fair thermal stability. The amino acid functionalization led to the enhanced polymer chain stiffness, and the glass transition temperatures of the derivatized polymers were 30–40 °C higher than that of 1 (T_g 3.9 °C; cf. T_g of 2a – f , 35.1–43.3 °C). © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2326–2334, 2008     

Evaluation of an ODS column modified with zwitterionic/nonionic mixed surfactants and its application to direct injection determination of inorganic anions.

An octadecylsilica (ODS) column modified with zwitterionic/nonionic mixed surfactants was evaluated for the direct injection determination of inorganic anions in biological fluids by ion chromatography. A zwitterionic surfactant (sulfobetaine-type) and a nonionic surfactant (polyoxyethylene-type) were used for a stationary-phase modification. When aqueous electrolyte solutions with concentrations of sub-mM to several mM were used as a mobile phase, the zwitterionic surfactant coated on the ODS surface exhibited unique separation selectivity for ionic species, while the nonionic surfactant coated on the ODS might have formed a hydrophilic network over the ODS surface and restricted matrix proteins from adsorbing on the stationary phase. Consequently, the mixed surfactant-modified column system allowed an efficient ion chromatographic separation of inorganic anions as well as a size-exclusive removal of column-fouling proteins. This separation system was applied to the direct injection determination of UV-absorbing anions in human saliva. The detection limits for nitrite, nitrate, iodide and thiocyanate were 3.1, 2.7, 4.5 and 25 microM, respectively, with UV detection at 210 nm (injection volume; 20 microl), and their relative standard deviations for 5 replicate measurements of saliva samples spiked with 100 microM each of those anions were 1.4, 0.9, 2.2 and 5.5%, respectively.     

Unprecedented alkylation of silicon enolates with alcohols via carbenium ion formations catalyzed by tin hydroxide-embedded montmorillonite

The solid acid, tin hydroxide-embedded montmorillonite, catalyzes the unprecedented alkylation of various silicon enolates with primary, secondary and tertiary benzylic alcohols as well as secondary allylic alcohols. The acid catalysis of Sn-Mont was not only higher than that of the other ion-exchanged montmorillonites (M-Mont; M = H, Ti, Fe and Al), but also higher than that of the typical homogeneous acid catalysts such as BF₃·OEt₂, TMSOTf and TfOH.     

Dissipative crystallization of aqueous solutions of hydroxypropyl cellulose

Drying dissipative structures of aqueous solutions of hydroxypropyl cellulose, their viscosities of 2 wt.% solutions ranging from 2 to 2,000 mPa.s were studied on a cover glass, a watch glass, and a Petri glass dish. The thickness profile of the dried film shows the coexistence of a low round hill and a high broad ring on a cover glass. The broad ring size increased as molecular weight and/or concentration of the polymers increased on a cover glass and a watch glass. Microscopic drying crystal patterns of HPC changed as a function of the distance from the film center, which is one of the typical results of the dissipative crystallization. Rod-like microscopic drying patterns originated in the cholesteric liquid crystalline structures were observed. The rods oriented mainly parallel and in some case perpendicularly to the radial direction of the dried film except the central area, where the rods distributed at random. These orientation effects were significant for low molecular weight samples and in a watch glass.     

Microscopic phase behavior of supercritical carbon dioxide + non-ionic surfactant + water systems at elevated pressures

The microscopic phase behavior of the supercritical carbon dioxide (scCO₂) + polyethylene oxide-2,6,8-trimethyl-4-nonyl ether (TMN) + water systems at about 3 wt% of TMN were investigated using a synthetic method with a microscope. The two types of TMN (TMN-3 and TMN-10) used in this work had molecular weight distributions caused by the distribution of the number of ethylene oxide groups. Two different types of phase transition were observed when pressure was decreased gradually at a constant temperature from the high pressure at which the transparent phase was observed to the low pressure at which the separate vapor–liquid phases were observed for the scCO₂ + TMN-3 + water system at 3 wt% of TMN-3. The transparent phase was colorless under all experimental conditions and the phase transition from a transparent phase to a turbidity phase with small, dispersed droplets was observed at the higher side phase transition (higher phase transition pressure). As the pressure continued to decrease, another phase transition was observed from the phase with small droplets to a state with an accelerating aggregation of droplets (lower phase transition pressure). In the turbidity phase between the higher and the lower phase transition, the degree of turbidity became higher with decreasing pressure. On the other hand, in the phase observed below the lower phase transition, a new liquid phase adhered to the sapphire windows and the wall inside the optical cell.     

Dissipative crystallization of sodium salt of deoxyribonucleic acid

Drying patterns of aqueous solutions of sodium salt of deoxyribonucleic acid (NaDNA) were studied on a cover glass, a watch glass, and a Petri glass dish at room temperature. Orientation of the rod-like single crystals of NaDNA molecules in the radial direction was observed especially at low polymer concentrations. The ratios of the size of the broad ring against initial size of the liquid on a cover glass and a watch glass were very small between 0.05 and 0.1 compared with those of the typical polyelectrolytes. Main cause is the compact conformation of NaDNA forming single or double stranded helix structures in the dried film. Microscopic drying patterns were long rods accompanied with the many short rods especially on a cover glass. Thick and short rods and dendritic crystals were fogrmed at the inward and outward areas of the dried films, respectively, on a watch glass and a Petri glass dish. Rod-like and dendritic crystals resembled the distorted hedrite and/or spherulite structures. Dissipative crystallization such as the orientation and accumulation of the single crystals of NaDNA were observed and the importance of the convectional and sedimentation processes was demonstrated during the course of crystallization.