Arrangements of n Points whose Incident-Line-Numbers are at most n/2

We consider a set X of n noncollinear points in the Euclidean plane, and the set of lines spanned by X, where n is an integer with n ≥ 3. Let t(X) be the maximum number of lines incident with a point of X. We consider the problem of finding a set X of n noncollinear points in the Euclidean plane with t(X) ￡ ?n/2 ?{t(X) \le \lfloor n/2 \rfloor}, for every integer n ≥ 8. In this paper, we settle the problem for every integer n except n = 12k + 11 (k ≥ 4). The latter case remains open.     

Planar-chiral pillar[5]arene: chiral switches induced by multiexternal stimulus of temperature, solvents, and addition of achiral guest molecule

We synthesized chiral-substituents modified pillar[5]arene for the first time. The chiral-substituents modified pillar[5]arene showed planar chirality and interconversion between (pS) and (pR) forms took place quickly. The planar chirality was switched by temperature, solvents, and addition of achiral guest. As the measurement temperature increased, the diastereomeric excess was decreased. The diastereomeric excesses were high in low-permittivity solvents, while a low diastereomeric excess was observed in high-permittivity solvents. Addition of achiral guest induced an increase of negative CD intensities.     

Formation and coordination modes of the C4E4 moiety (E = COOMe) bound to two palladium(II) moieties

The transmetallation of the palladacyclopentadiene complex Pd{C(COOMe)C(COOMe)C(COOMe)C(COOMe)}(bipy) with the dicationic Pd(II) complex [Pd(bipy)(CH(3)CN)(2)][BF(4)](2) afforded a terminally σ-palladated diene complex [Pd(2){μ-η(1):η(1)-C(COOMe)C(COOMe)C(COOMe)C(COOMe)}(bipy)(2)(CH(3)CN)(2)][BF(4)](2). It was revealed by X-ray crystallographic analysis that replacement of the acetonitrile ligands in a terminally σ-palladated diene complex with PPh(3) ligands resulted in the conformation change of the σ-palladated diene moiety from skewed s-cis to planar s-trans. Treatment of a bis-triphenylphosphine dipalladium complex [Pd(2)(PPh(3))(2)(CH(3)CN)(4)][PF(6)](2) with dimethoxyacetylene dicarboxylate (DMAD) (1 equiv.) in acetonitrile resulted in the insertion of DMAD to the Pd-Pd bond to afford [Pd(2){μ-η(1):η(1)-C(COOMe)C(COOMe)}(PPh(3))(2)(CH(3)CN)(4)][PF(6)](2). Addition of the second DMAD gave the ylide-type complex [Pd(2){μ-η(2):η(3)-C(COOMe)C(COOMe)C(COOMe)C(COOMe)(PPh(3))}(PPh(3))(2)(CH(3)CN)(3)][PF(6)](2) of which the structure was determined by X-ray crystallographic analysis.     

Selective complexation of n-alkanes with pillar[5]arene dimers in organic media

A pillar[5]arene dimer was synthesized by linking a mono-hydroxylated pillar[5]arene with 1,4-bis(bromomethyl)benzene. The pillar[5]arene dimer formed stronger complexes with n-alkanes than did a monomeric pillar[5]arene.     

Improvement of texture and palatability of chicken breast: effect of high hydrostatic pressure and sodium hydrogen carbonate

Chicken breast is not preferred in Japan because it is not juicy. In this study, the effect of combined high pressure and sodium hydrogen carbonate (NaHCO₃) treatment on the texture and palatability of chicken breast was investigated. The sample used was broiler chicken breast. Meat samples were soaked in.0–.4 M NaHCO₃ solution and then pressurized at 100–400 MPa. After pressurization, the samples were heated for 30 min at 80°C and cooled down in ice-cold water. High pressure and NaHCO₃ treatment of broiler chicken breast resulted in increased water content, and decreased weight reduction and rupture stress. Moreover, meat exposed to 200 MPa pressurization and.3 M NaHCO₃ treatment was judged tender, juicy and of good taste by sensory evaluation. The combination of high pressure and NaHCO₃ treatment can be effectively used for broiler chicken breast production.     

Helly Numbers of Polyominoes

We define the Helly number of a polyomino P as the smallest number h such that the h-Helly property holds for the family of symmetric and translated copies of P on the integer grid. We prove the following: (i) the only polyominoes with Helly number 2 are the rectangles, (ii) there does not exist any polyomino with Helly number 3, (iii) there exist polyominoes of Helly number k for any k ≠ 1, 3.     

Reversibly tunable lower critical solution temperature utilizing host-guest complexation of pillar[5]arene with triethylene oxide substituents

A thermoresponsive macromolecule consisting of 10 outer triethylene oxide groups and a pillar[5]arene core was prepared. The macromolecule showed lower critical solution temperature behavior. Moreover, its clouding point can be reversibly tuned based on the addition of guest and host compounds; the clouding point increased upon addition of a guest didecylviologen salt and decreased when the competitive host cucurbit[7]uril was added.