The Green–Kubo Formula for Locally Interacting Fermionic Open Systems

We consider a model describing finitely many free Fermi gas reservoirs coupled by local interactions and prove the Green–Kubo formulas and the Onsager reciprocity relations for heat and charge fluxes generated by temperature and chemical potential differentials. Submitted: September 2, 2006. Accepted: November 21, 2006.     

Physical properties and structure of silk. II. Dynamic mechanical and dielectric properties of silk fibroin

Dynamic mechanical and dielectric properties of amorphous regenerated films of silk fibroin were studied as a function of temperature. A mechanical loss tangent peak at about 175°C may be due to the segmental motion of the main chains in the amorphous silk fibroin film. The dynamic modulus of the amorphous silk fibroin increased at 185°C due to the crystallization of the silk fibroin. Dielectric loss tangent peaks were observed at about ?40°C and 175°C at 1 kHz. The former is ascribed to the local motion of the amorphous silk fibroin with absorbed water, while the latter seems to originate from the segmental motion of the main chains and the crystallization of silk fibroin.     

Selective cleavage of polycyclic cyclopropanes by electrochemical oxidation

Anodic oxidation in acetic acid of polycyclic cyclopropanes, namely tricyclene, cyclofenchene, and longicyclene, followed by hydrolysis brought about stereo- and regioselective formation of the corresponding homoallylic alcohols as the main product in good yields.     

Hydrogenolysis of tertiary phosphines coordinated on transition metals by hydrogen transfer from amines

Considerable amounts of benzene were formed by heating triphenylphosphine complexes of transition metals in several types of organic compounds, especially in amines; in the case of a tributylphosphine complex, n-butane was detected. In the reactions with indoline, tetrahydroquinoline or dioxane, the hydrogen consumed for the hydrogenolysis was proved to arise from the amines or the ether.     

Syntheses and structures of bowl-shaped triarylphosphines and their palladium(II) complexes

Novel bowl-shaped triarylphosphines, tris(2,2″,6,6″-tetraalkyl[1,1′:3′,1″-terphenyl]-5′-yl)phosphines (TRMP: alkyl = methyl; TRIP: alkyl = isopropyl), were prepared by lithiation of the corresponding m-terphenyl bromides followed by reaction with PCl₃. X-ray crystallographic analysis revealed that the phosphorus center of TRMP is embedded in the shallow bowl-shaped cavity of 16 Å diameter and 2.1 Å depth formed by three radially extended m-terphenyl units. Its cone angle was estimated to be as large as 174°. In the crystal structure of TRIP, the depth of the cavity and cone angle increased to 3.3 Å and 206°, respectively, because of the different arrangement of the m-terphenyl units. In contrast with TRMP, which can form the mononuclear complex, PdCl₂(TRMP)₂ (6), in the reaction with PdCl₂, treatment of TRIP (1 or 3 eq.) with PdCl₂ produced the trinuclear palladium(II) chloride complex, [(PdCl₂)₃(TRIP)₂] (8), as a single product. X-ray crystallography established the structure of 8, where the trimer of PdCl₂ is terminated by two TRIP ligands. The formation of the different types of PdCl₂ complexes was explained in terms of the difference in the cavity shape of TRMP and TRIP.     

Determination of reducing sugars with 3:6-dinitrophthalic acid

Reducing sugars are determined in the concentration range 10 ˜ 100 μg/ml using 3:6-dinitrophthalic acid as a colour developing agent. Individual pentoses, hexoses, and disaccharides give the same calibration curves, respectively. Sucrose is also determined in the presence of glucose or fructose.     

Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a ₀ + a ₁ x ₁ + . . . + a _n x _n subject to certain constraints to solve the problem of minimizing a rational function of the form (a ₀ + a ₁ x ₁ + . . . + a _n x _n )/(b ₀ + b ₁ x ₁ + . . . + b _n x _n ) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo’s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo’s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an α-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an α-approximation (1/α-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.