Sorption and diffusion of toluene in isotropic and oriented linear polyethylene

Sorption and diffusion of toluene vapor in linear polyethylene with mass-fraction crystallinity between 0.48 and 0.82 and draw ratios λ up to 10 have been studied at 30°C. The sorbed concentration in the amorphous phase C_a is little affected by crystallinity, indicating that the free-volume fraction is roughly the same for all isotropic samples. However, the diffusion path becomes more tortuous with increasing crystalline content, thereby leading to a sixfold drop in the zero-concentration diffusion coefficient D₀. Drawing has more drastic effects, reducing C_a and D₀ by factors of 4 and 60, respectively, as λ increases to 10. These large changes result from the transformation of the initially spherulitic material into a fibrous structure, which is composed of aligned microfibrils with taut tie molecules lying on the outer boundaries. The effects of crystallinity and orientation on the concentration dependence of the diffusion coefficient are also discussed.     

A stereoselective cyclization to carbafuranose derivatives starting from 1,4-bis-epoxides

[reactions: see text] A concise synthesis of highly functionalized cyclopentane derivatives via a Brook rearrangement mediated stereoselective linchpin cyclization reaction involving tert-butyldimethylsilyl-1,3-dithianyllithium and homochiral 1,4-bis-epoxides is described.     

Probing the interior of neutron stars with gravitational waves

We show here how the internal structure of a neutron star can be inferred from its gravitational wave spectrum. Under the premise that the frequencies and damping rates of a few w-mode oscillations are found, we apply an inversion scheme to determine its mass, radius, and density distribution. In addition, an accurate equation of state of nuclear matter can also be determined.     

High-resolution angular measurement using surface-plasmon-resonance via phase interrogation at optimal incident wavelengths

It is demonstrated that ultrahigh-resolution angular measurement can be achieved via surface-plasmon-resonance excitation in which the phase difference between p- and s-polarized reflected waves is monitored as a function of the incidence angle. Resolutions down to 1.9 x 10(-6) deg are obtained by performing the measurements at optimal incident wavelengths. This represents an order of magnitude improvement compared with previously reported values.     

Nonexistence of abelian difference sets: Lander's conjecture for prime power orders

In 1963 Ryser conjectured that there are no circulant Hadamard matrices of order 4$"> and no cyclic difference sets whose order is not coprime to the group order. These conjectures are special cases of Lander's conjecture which asserts that there is no abelian group with a cyclic Sylow -subgroup containing a difference set of order divisible by . We verify Lander's conjecture for all difference sets whose order is a power of a prime greater than 3.

     

Nuclear hyperfine coupling interactions in the rotational spectra of the linear and bent isomers of HF-N2O

The rotational spectra of six isotopomers of the linear and bent isomers of HF-N₂O have been collected in the 7-18 GHz region with a Fourier transform microwave spectrometer. The nuclear hyperfine structure in the spectra produced by HF spin-spin coupling interaction and nuclear quadrupole coupling interactions due to the D nucleus of DF and the nuclei of N₂O have been resolved and analyzed. In the linear isomer, H in HF is bonded to the terminal N in N₂O. The NF bond lengths are 2.9808(2) Å for the HF-containing isotopomers and 2.9732(2) Å for the DF-containing isotopomers. The zero point angles are 23.1° for HF and 31-34° for N₂O. The hyperfine constants suggest that the HF bond is lengthened by 0.0105 Å upon complexation and that the electric field gradients of the two nitrogen nuclei in N₂O are perturbed differently in the complex. In the bent isomer, the hydrogen bond is formed between HF and O in N₂O. The intermolecular distances are 3.4942(2) Å for the HF-containing isotopomers and 3.4436(2) Å for the DF-containing isotopomers, with HF and N₂O forming angles of 34° and 46°, respectively, with the intermolecular axis. The nuclear quadrupole coupling constants of the two nitrogen nuclei do not indicate electric field gradient perturbation in this isomer.     

Low-energy spectra in t-J-type models at low doping levels

Based on a variational approach, we propose that there are two kinds of low-energy states in the t-J-type models at low doping. In a quasiparticle state an unpaired spin bound to a hole with a well-defined momentum can be excited with spin waves. The resulting state shows a suppression of antiferromagnetic order around the hole with the profile of a spin bag. These spin-bag states with spin and charge or hole separated form a continuum of low-energy excitations. Very different properties predicted by these two kinds of states explain a number of anomalous results observed in the exact diagonalization studies on small clusters up to 32 sites.     

Manufacturer’s revenue-sharing contract and retail competition

This paper investigates a revenue-sharing contract for coordinating a supply chain comprising one manufacturer and two competing retailers. The manufacturer, as a Stackelberg leader, offers a revenue-sharing contract to two competing retailers who face stochastic demand before the selling season. Under the offered contract terms, the competing retailers are to determine the quantities to be ordered from the manufacturer, prior to the season, and the retail price at which to sell the items during the season. The process of pricing and ordering is expected to result in an equilibrium as in the Bayesian Nash game. On the basis of anticipated responses and actions of the retailers, the manufacturer designs the revenue-sharing contract. Adopting the classic newsvendor problem model framework and using numerical methods, the study finds that the provision of revenue-sharing in the contract can obtain better performance than a price-only contract. However, the benefits earned under the revenue-sharing contract by different supply chain partners differ because of the impact of demand variability and price-sensitivity factors. The paper also analyses the impact of demand variability on decisions about optimal retail price, order quantity and profit sharing between the manufacturer and the retailers. Lastly, it investigates how the competition (between retailers) factor influences the decision-making of supply chain members in response to uncertain demand and profit variability.     

Reactivity of dioxoruthenium(VI) porphyrins toward amines. Synthesis and characterization of bis(arylamine)ruthenium(II), bis(arylamido)- and bis(diphenylamido)ruthenium(IV), and oxo(tert-butylimido)ruthenium(VI) porphyrins

Reactions of dioxoruthenium(VI) porphyrins, [Ru(VI)O2(Por)], with p-chloroaniline, trimethylamine, tert-butylamine, p-nitroaniline, and diphenylamine afforded bis(amine)ruthenium(II) porphyrins, [Ru(II)(Por)(L)2] (L-p-ClC6H4NH2, Me3N, Por=TTP, 4-Cl-TPP; L=tBuNH2, Por = TPP, 3,4,5-MeO-TPP, TTP, 4-Cl-TPP, 3,5-Cl-TPP) and bis(amido)ruthenium(IV) porphyrins, [Ru(IV)(Por)(X)2] (X=p-NO2C6H4NH, Por=TTP, 4-Cl-TPP; X = Ph2N, Por = 3,4,5-MeO-TPP, 3,5-Cl-TPP), respectively. Oxidative deprotonation of [Ru(II)(Por)(NH2-p-C6H4Cl)2] in chloroform by air generated bis(arylamido)ruthenium(IV) porphyrins, [RuIV(Por)(NH-p-C6H4Cl)2] (Por=TTP. 4-Cl-TPP). Oxidation of [RuII(Por)-(NH2tBu)2] by bromine in dichloromethane in the presence of tert-butylamine and traces of water produced oxo(imido)ruthenium(VI) porphyrins, [RuVI-O(Por)(NtBu)] (Por=TPP, 3,4,5-MeO-TPP, TTP, 4-Cl-TPP, 3,5-Cl-TPP). These new classes of ruthenium complexes were characterized by 1H NMR, IR, and UV/visible spectroscopy, mass spectrometry, and elemental analysis. The structure of [Ru(IV)(TTP)(NH-p-C6H4Cl)2 . CH2Cl2 was determined by X-ray crystallography. The Ru-N bond length and the Ru-N-C angle of the Ru-NHAr moiety are 1.956(7) A and 135.8(6) degrees, respectively.     

Periodic optimal control for parabolic Volterra-Lotka type equations

This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with L^∞ periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.