A Relaxation of a Min-Cut Problem in an Anisotropic Continuous Network

Strang [18] introduced optimization problems on a Euclidean domain which are closely related with problems in mechanics and noted that the problems are regarded as continuous versions of famous max-flow and min-cut problems. In [15] we generalized the problems and called the generalized problems max-flow and min-cut problems of Strang's type. In this paper we formulate a relaxed version of the min-cut problem of Strang's type and prove the existence of optimal solutions under some suitable conditions. The conditions are essential. In fact, there is an example of the relaxed version which has no optimal solutions if the conditions are not fulfilled. We give such an example in the final section. Accepted 8 October 1998     

Conformation and dynamics of polymer chains in condensed systems

A Stockmayer's type-A chain such as cis-polyisoprene (PI) having dipole components parallel to the chain contour exhibits slow dielectric response, reflecting fluctuation of its end-to-end vector ( dielectric normal modes ). This article reviews our own work on dielectric spectroscopy for studying dynamics and conformational properties of probe PI chains in binary blends with PI or polybutadiene (PB) that does not exhibit normal modes. Through such studies we were able to see the crossover of the probe-chain dynamics from Rouse behaviour in low-molecular-weight (lmw) matrices to pure reptation behaviour in high-molecular-weight (hmw) matrices. We were also able to confirm experimentally Flory's earlier prediction on excluded volumes in dilute blends of hmw probe chains in lmw matrices, for which a proof has never been given before.     

New trend of radiation application to polymer modification — irradiation in oxygen free atmosphere and at elevated temperature

Polycarbosilane (PCS) fiber as a precursor for ceramic fiber of silicon carbide was cured by electron beam (EB) irradiation under oxygen free atmosphere. Oxygen content in the cured PCS fiber was scarce and the obtained silicon carbide (SiC) fiber with low oxygen content showed high heat resistance up to 1973 K and tensile strength of 3 GPa. Also, the EB cured PCS fiber with very low oxygen content could be converted to silicon nitride (Si₃N₄) fiber by the pyrolysis in NH₃ gas atmosphere, which was the new processing to produce Si₃N₄ fiber. The process of SiC fiber synthesis was developed to the commercial plant.

The other application was the crosslinking of polytetrafluoroethylene (PTFE). PTFE, which had been recognized to be a typical chain scission polymer, could be induced to crosslinking by irradiation at the molten state in oxygen free atmosphere. The physical properties such as crystallinity, mechanical properties, etc. changed much by crosslinking, and the radiation resistance was much improved.     

Rheology of heterophase polymer systems

This lecture attempts to elucidate rheological behavior of multiphase polymer systems through a comparison with our studies on much simpler systems such as suspensions of (a) non-aggregating and (b) aggregating monodisperse spheres in viscoelastic media, (c) polymer latex in the same polymer liquids, and (d) emulsions or blends of two polymers with or without an emulsifying block copolymer. For the system (a) not only the viscosity η but also the modulus obey the known simple dependence on volume fraction ϕ of hard-sphere suspensions, while for the system (b) the flow induced-aggregation and dissociation of the particles govern the rheology. In the system (c), relaxations of entanglements of the adsorbed chains as well as the spatial distribution of the latexes are essential. For the emulsion (d) of a biased composition range (e.g., ϕ₁ > ϕ₂) the matrix phase 1 dominates, unless η₁ << η₂. When η₁ ≥ η₂, deformation and/or bursting of the dispersed phase 2 take place. For those of an even composition, the viscosity is additive of those of the components and is enhanced by adding the emulsifying block copolymer component.     

ESR study on chemical crosslinking reaction mechanisms of polyethylene using a chemical agent—II. The effect of phenolic antioxidants

The effect of antioxidant on the reaction mechanism of chemical crosslinking of polyethylene (PE) with dicumyl peroxide (DCP) at high temperatures was investigated by electron spin resonance (ESR). The antioxidant reacts with the alkyl radicals in PE formed by the thermal decomposition of DCP above 120°C, and disturbs the crosslinking. A phenolic type antioxidant produced the phenoxy radical by the reaction with alkyl radicals formed in PE. It is suggested that the selection of a suitable antioxidant for PE crosslinking can be made by ESR analysis. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2431–2439, 1997     

A Quantum Algorithm for a FULL Adder Operation Based on Registers of the CPU in a Quantum-gated Computer

International Journal of Theoretical Physics - So far, the world of quantum-gated computing has been exploited, aimed at the limited applications based upon the Deutsch algorithm in 1985 and a few...     

Insight into chemical mechanisms of sepal color development and variation in hydrangea

Hydrangea (Hydrangea macrophylla) is a unique flower because it is composed of sepals rather than true petals that have the ability to change color. In the early 20th century, it was known that soil acidity and Al³⁺ content could intensify the blue hue of the sepals. In the mid-20th century, the anthocyanin component 3-O-glucosyldelphinidin (1) and the copigment components 5-O-caffeoylquinic, 5-O-p-coumaroylquinic, and 3-O-caffeoylquinic acids (2–4) were reported. Interestingly, all hydrangea colors from red to purple to blue are produced by the same organic components. We were interested in this phenomenon and the chemical mechanisms underlying hydrangea color variation. In this review, we summarize our recent studies on the chemical mechanisms underlying hydrangea sepal color development, including the structure of the blue complex, transporters involved in accumulation of aluminum ion (Al³⁺), and distribution of the blue complex and aluminum ions in living sepal tissue.     

Using Inequalities as Tests for the Kochen-Specker Theorem for Multiparticle States

The Kochen-Specker theorem is investigated for n spin-1/2 systems by using an inequality proposed in Nagata (J. Math. Phys. 46, 102101, 2005) on the basis on binary logic. A measurement theory based on the truth values (binary logic), i.e., the truth T (1) for true and the falsity F (0) for false is used. The values of measurement outcome are either + 1 or 0 (in \(\hbar /2\) unit). The quantum predictions by n-multipartite states violate the inequality by an amount that grows exponentially with n. The measurement theory based on the binary logic provides an exponentially stronger refutation of the existence of hidden-variable when the number of parties of the state increases more. It turns out that the Kochen-Specker theorem becomes a quite strong theorem when the dimension of the multipartite state highly increases, regardless of entanglement properties.

     

Sterically congested, "roofed" β-iminodisulfides as new chiral ligands for palladium-catalyzed, asymmetric allylic alkylation

The preparation of a new class of "roofed" β-iminodisulfides from sterically congested, conformationally rigid chiral 2-thiazolidinones is described. A functional survey of palladium-catalyzed asymmetric allylic alkylation of 1,3-diphenyl-2-propenyl acetate with dimethyl malonate proved that symmetrical "roofed" β-iminodisulfides are efficient chiral ligands, showing enantioselectivity opposite that associated with chiral "roofed" β-iminothioether ligands.     

A Pretreatment Method for GC–MS Determination of Endocrine Disrupting Chemicals in Mollusk Tissues

Automatic soxhlet extraction followed by silica gel cartridge cleanup process was developed as a pretreatment method for GC–MS determination of seven endocrine disrupting chemicals in mollusk tissues. Operation parameters including extraction time, adsorption flow rate and elution flow rate were optimized as 140 min, 2 mL min^?1 and 2 mL min^?1, respectively. Thirty percent dichloromethane in n-hexane and 70% dichloromethane in n-hexane were used as elution solvents in turn. Recovery rates were 93.7, 91.7, 84.5, 83.3, 88.4, 81.2, and 79.7% for nonylphenols (NPs), bisphenol A (BPA), 17α-ethynylestradiol (EE2), estrone (E1), 17α-estradiol (17α-E2), 17β-estradiol (E2), and estriol (E3), respectively. Acceptable relative standard derivations ranged from 8.5 to 12.1%. Method detection limits ranged from 0.27 to 0.68 ng g^?1 dry weight (dw), and quantitative detection limits ranged from 0.62 to 1.26 ng g^?1 dw. The method was successfully applied to five mollusk species in Dapeng Bay of China to verify its practicability, and NPs, BPA, EE2, E1 and 17α-E2 were detected in the range from 1.6 to 131.5 ng g^?1 dw.