A remark on the ring of algebraic integers in $$\mathbb{Q}(\sqrt { - d} )$$

It is well-known that the rings O_d of algebraic integers in \(\mathbb{Q}(\sqrt { - d} )\) for d = 19, 43, 67, and 163 are principal ideal domains but not Euclidean. In this article we shall provide a method, based on a result of P. M. Cohn, to construct explicitly pairs (b, a) of integers in O_d for d = 19, 43, 67, and 163 such that, in O_d, there exists no terminating division chain of finite length starting from the pairs (b, a). That is, a greatest common divisor of the pairs (b, a) exists in O_d but it can not be obtained by applying a terminating division chain of finite length starting from (b, a). Furthermore, for squarefree positive integer d ? {1, 2, 3, 7, 11, 19, 43, 67, 163}, we shall also construct pairs (b, a) of integers in O_d which generate O_d but have no terminating division chain of finite length. It is of interest to note that our construction provides a short alternative proof of a theorem of Cohn which is related to the concept of GE₂-rings.     

Effective results on compositions of nonexpansive mappings

This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the setting of (r,δ)$(r,\delta )$-convex spaces, a class of geodesic spaces which generalizes metric spaces with a convex geodesic bicombing.     

An application of proof mining to nonlinear iterations

In this paper we apply methods of proof mining to obtain a highly uniform effective rate of asymptotic regularity for the Ishikawa iteration associated with nonexpansive self-mappings of convex subsets of a class of uniformly convex geodesic spaces. Moreover, we show that these results are guaranteed by a combination of logical metatheorems for classical and semi-intuitionistic systems.     

Water dynamics in a lithium chloride aqueous solution probed by Brillouin neutron and x-ray scattering

We studied the collective excitations in an aqueous solution of lithium chloride over the temperature range of 270-205 K using neutron and x-ray Brillouin scattering. Both neutron and x-ray experiments revealed the presence of low- and high-frequency excitations, similar to the low- and high-frequency excitations in pure water. These two excitations were detectable through the entire temperature range of the experiment, at all probed values of the scattering momentum transfer (0.2 ?(-1) < Q < 1.8 ?(-1)). A wider temperature range was investigated using elastic intensity neutron and x-ray scans. Clear evidence of the crossover in the dynamics of the water molecules in the solution was observed in the single-particle relaxational dynamics on the μeV (nanosecond) time scale, but not in the collective dynamics on the meV (picosecond) time scale.     

Constituents from the leaves of Phellodendron amurense and their antioxidant activity

Three new coumarins, phellodenols F-H (1-3) and a new glutaric acid derivative, phellodendric acid-A (4) were isolated from the leaves of Phellodendron amurense together with twenty-nine known compounds. Extensive 1D and 2D NMR experiments and other spectroscopic studies were employed to determine the structures of 1-4. The isolated compounds were screened for their antioxidant activity through DPPH (alpha,alpha-diphenyl-beta-picrylhydrazyl) radical scavenging assay. Compounds quercetin, quercetin-3-O-beta-D-glucoside, quercetin-3-O-beta-D-galactoside and kaempferol-3-O-beta-D-glucoside demonstrated significant radical scavenging activity comparable to vitamin E.     

Synthesis and properties of novel aromatic poly(ester-imide)s bearing 1,5-bis(benzoyloxy)naphthalene units

Two series of new aromatic poly(ester-imide)s were prepared from 1,5-bis(4-aminobenzoyloxy)naphthalene (p-1) and 1,5-bis(3-aminobenzoyloxy)naphthalene (m-1), respectively, with six commercially available aromatic tetracarboxylic dianhydrides via a conventional two-stage synthesis that included ring-opening polyaddition to give poly(amic acid)s followed by chemical imidization to polyimides. The intermediate poly(amic acid)s obtained in the first stage had inherent viscosities of 0.41-0.84 and 0.66-1.37 dl/g, respectively. All the para-series and most of the meta-series poly(ester-imide)s were semicrystalline and showed less solubility. Two of the meta-series poly(ester-imide)s derived from less rigid dianhydrides were amorphous and readily soluble in polar aprotic solvents, and they could be solution-cast into transparent and tough films with good mechanical properties. The meta-series polymers derived from rigid dianhydrides were generally semicrystalline and showed less solubility. Except for one example, the meta-series poly(ester-imide)s displayed discernible T_gs in the range 239-273 °C by DSC. All of these two series poly(ester-imide)s did not show significant decomposition below 450 °C in nitrogen or in air.     

Synthesis of well-aligned carbon nanotubes by inductively coupled plasma chemical vapor deposition

Uniform and well-aligned carbon nanotubes (CNTs) have been grown using a high density inductively coupled plasma chemical vapor deposition (ICP-CVD) system. A gas mixture of methane-hydrogen was used as the source and Ni as the catalyst for the CNT growth. The effect of process parameters, such as inductive RF power, DC bias voltage and CH₄/H₂ ratio, on the growth characteristics of CNTs was investigated. It was found that both plasma intensity and ion flux to the substrate, as controlled by the inductive RF power and DC bias voltage, respectively, can greatly affect the growth of CNTs. The relative importance of the generation of ions and the subsequent transport of ions to the substrate as serial process steps are considered as the two underlying factors in determining the growth characteristics of CNTs. PACS 81.05.Uw; 81.07.De; 81.15.Gh     

Bond energies, reaction volumes, and kinetics for σ- and π-complexes of MoCO5L

The photosubstitution reactions of molybdenum hexacarbonyl with σ and π donor ligands were investigated using photoacoustic calorimetry and computational methods in a series of linear alkane solvents (pentane, hexane, heptane, octane, decane, and dodecane). The results show that reaction volumes make a significant contribution to the photoacoustic signal and must be considered during thermodynamic calculations based on photoacoustic measurements. The enthalpies of CO substitution by an alkane solvent and subsequent substitution by each Lewis base were determined. Corresponding Mo-L bond energies (kcal mol(-1)) were calculated: L = linear alkanes (13), triethylsilane (26), 1-hexyne (27), 1-hexene (27), and benzene (17). The relative energies are in agreement with computational results. The experimental reaction volume for CO substitution by alkane was positive (15 mL mol(-1)) and negative or close to zero for alkane substitution by a Lewis base (for example, -11 mL mol(-1) for triethylsilane and 3.6 mL mol(-1) for benzene). The errors in the experimental and computational reaction volumes are large and often comparable to the reaction volumes. An improved calibration of the methods as well as a better understanding of the underlying physics involved is needed. For the Lewis bases reported in this study, the second-order rate constants for the displacement of a coordinated alkane are less than diffusion control (5 × 10(6)-4 × 10(7) M(-1) s(-1)) and decrease monotonically with the alkane chain length. The rate constants correlate better with steric effects than with bond energies. An interchange mechanism is consistent with the results.