A new explicit three-level difference scheme for the solution of the heat flow equation

A new explicit three-level difference scheme for the numerical solution of the heat flow equation is proposed. The main features of the new scheme are: i) it is unconditionally stable, ii) it is very highly accurate from the point of view of the truncation error, and iii) its solution converges to the solution of the heat equation even if the time and the distance increments tend to zero independently.     

Optimal p--cyclic SOR

Summary. Our purpose in this paper is to extend --cyclic SOR theory to consistent singular systems and to apply the results to the solution of large scale systems arising, {\em e.g.,} in queueing network problems in Markov analysis. Markov chains and queueing models lead to structured singular linear systems and are playing an increasing role in the understanding of complex phenomena arising in computer, communication and transportation systems. For certain important classes of singular problems, we develop a convergence theory for --cyclic SOR, and show how to repartition for optimal convergence. Results by Kontovasilis, Plemmons and Stewart on the concept of convergence of SOR in an {\em extended} sense are rigorously analyzed and applied to the solution of periodic Markov chains with period . Received October 20, 1992 / Revised version received September 14, 1993     

Concise synthesis of enantiopure erythro-saccharinic acid lactone and potassium (2R,3R)-2,3,4-trihydroxy-2-methylbutanoate

A short and efficient approach was applied to the total synthesis of erythro-saccharinic acid lactone and the leaf-closing substance potassium (2R,3R)-2,3,4-trihydroxy-2-methylbutanoate from a 2-C-hydroxymethyl-d-erythrose derivative, using a combined strategy.     

Nanocomposites of polystyrene-b-polyisoprene copolymer with layered silicates and carbon nanotubes

Nanocomposites of polystyrene-b-polyisoprene (PS-b-PI) copolymer with layered-smectite clays (organically modified montmorillonite) and nanostructured clay-carbon nanotube hybrids were prepared. The diblock copolymer was synthesized by anionic polymerization using high-vacuum techniques and was molecularly characterized by size exclusion chromatography. Carbon nanotubes were developed on clay-supported nickel nanoparticles by the CCVD method. Nanotubes attached on the clay platelets were then chemically modified to create ester groups on their surfaces. PS-b-PI nanocomposites at various polymer to reinforcement loadings were prepared by solution intercalation. The final nanocomposites were characterized by powder X-ray diffraction, FT-IR spectroscopy, thermal analysis, and scanning electron microscopy. The experiments complemented with viscometry measurements reveal the successful incorporation of the reinforcements in the polymer mass.     

Singular integral equations — The convergence of the Nyström interpolant of the Gauss-Chebyshev method

Nyström's interpolation formula is applied to the numerical solution of singular integral equations. For the Gauss-Chebyshev method, it is shown that this approximation converges uniformly, provided that the kernel and the input functions possess a continuous derivative. Moreover, the error of the Nyström interpolant is bounded from above by the Gaussian quadrature errors and thus convergence is fast, especially for smooth functions. ForC input functions, a sharp upper bound for the error is obtained. Finally numerical examples are considered. It is found that the actual computational error agrees well with the theoretical derived bounds.This research has been partially supported by a grant from the Rutgers Research Council.     

The lead tetraacetate oxidation of bisacetylhydrazones of α-dicarbonyl compounds

The oxidative cyclization of the title compounds results in generally two different kinds of products. The first, 1-(N,N-bisacetylamino)-1,2,3-triazole 7 (R³ = CH₃) is the primary product, while the second, 1-N-acetylamino-1,2,3-triazole 8 (R³ = CH₃), when observed, is obtained via hydrolysis from the former during work-up and separation of the reaction mixture. The primary products are considered as resulting from intramolecular nucleophilic attack on the acetyl group, of the presumed zwitterionic intermediate 5 (R³ = CH₃), by the N of the ambident N-acetylimine site of 5 .     

Ligands that enforce unnatural stereospinomers

Computational evidence is provided for the existence of combinations of a stereoisomer and a spin state not previously observed in d(4) and d(8) complexes, achieved by means of encapsulating ligands that enforce a tetrahedral coordination.     

Optimization of apodization functions in terahertz transient spectrometry

A quadratic programming optimization procedure for designing asymmetric apodization windows tailored to the shape of time-domain sample waveforms recorded using a terahertz transient spectrometer is proposed. By artificially degrading the waveforms, the performance of the designed window in both the time and the frequency domains is compared with that of conventional rectangular, triangular (Mertz), and Hamming windows. Examples of window optimization assuming Gaussian functions as the building elements of the apodization window are provided. The formulation is sufficiently general to accommodate other basis functions.     

Electronic structure and bonding of ozone

The ground and low-lying states of ozone (O(3)) have been studied by multireference variational methods and large basis sets. We have constructed potential energy curves along the bending coordinate for (1,2) (1)A('), (1,2) (1)A("), (1,2) (3)A('), and (1,2) (3)A(") symmetries, optimizing at the same time the symmetric stretching coordinate. Thirteen minima have been located whose geometrical and energetic characteristics are in very good agreement with existing experimental data. Special emphasis has been given to the interpretation of the chemical bond through valence-bond-Lewis diagrams; their appropriate use captures admirably the bonding nature of the O(3) molecule. The biradical character of its ground state, adopted long ago by the scientific community, does not follow from a careful analysis of its wave function.     

Dielectric studies of chain dynamics in homogeneous semi‐interpenetrating polymer networks

Semi‐interpenetrating polymer networks (semi‐IPNs) were prepared from linear polyurethane (PUR) and polycyanurate (PCN) networks. Wide‐angle X‐ray scattering measurements showed that the IPNs were amorphous, and differential scanning calorimetry and small‐angle X‐ray scattering measurements suggested that they were macroscopically homogeneous. Here we report the results of detailed studies of the molecular mobility in IPNs with PUR contents greater than or equal to 50% via broadband dielectric relaxation spectroscopy (10⁻²–10⁹ Hz, 210–420 K) and thermally stimulated depolarization current techniques (77–320 K). Both techniques gave a single α relaxation in the IPNs, shifting to higher temperatures in isochronal plots with increasing PCN content, and provided measures for the glass‐transition temperature (T_g) close to and following the calorimetric T_g. The dielectric response in the IPNs was dominated by PUR. The segmental α relaxation, associated with the glass transition and, to a lesser extent, the local secondary β and γ relaxations were analyzed in detail with respect to the timescale, the shape of the response, and the relaxation strength. The α relaxation became broader with increasing PCN content, the broadening being attributed to concentration fluctuations. Fragility decreased in the IPNs in comparison with PUR, the kinetic free volume at T_g increased, and the relaxation strength of the α relaxation, normalized to the same PUR content, increased. The results are discussed in terms of the formation of chemical bonds between the components, as confirmed by IR, and the reduced packing density of PUR chains in the IPNs. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3070–3087, 2000