Evaluation of the Electrophilicites and Band Gaps of Conductive Polymers: A New Model

It is shown that the obtained hardness and electrophilicity values of the short length oligomers for a heterocyclic conductive polymer from density functional theory method are quadraticly correlated to those obtained from semiempirical method. Therefore these quantities for all oligomers (up to 15 repeating units) are predicted using the obtained quadratic relations. Both of these predicted quantities for different oligomers are fitted to a new exponential model (Y = Y_∞ e^d/n) to estimate the electronic properties for the considered conjugated polymers. The calculated band gaps from this model show better agreement with the reported experimental data than those predicted by the previous models. Because of a wide range of variations, the electrophilicity could be a better index for investigating the doping effect in polymers than the hardness.

     

Computing latest starting times of activities in interval-valued networks with minimal time lags

This paper deals with problems of determining possible values of earliest and latest starting times of an activity in networks with minimal time lags and imprecise durations that are represented by means of interval or fuzzy numbers. Although minimal time lags are practical in different projects, former researchers have not considered these problems.After proposing propositions which reduce the search space, a novel polynomial algorithm is presented to compute intervals of possible values of latest starting times in interval-valued networks with minimal time lags. Then, the results are extended to networks with fuzzy durations.     

Stanley decompositions and partitionable simplicial complexes

We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen–Macaulay simplicial complexes. We also prove these conjectures for all Cohen–Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3. Dedicated to Takayuki Hibi on the occasion of his fiftieth birthday.     

A Critical Evaluation and Modification of the Padé–Laplace Method for Deconvolution of Viscoelastic Spectra

This paper shows that using the Padé–Laplace (PL) method for deconvolution of multi-exponential functions (stress relaxation of polymers) can produce ill-conditioned systems of equations. Analysis of different sets of generated data points from known multi-exponential functions indicates that by increasing the level of Padé approximants, the condition number of a matrix whose entries are coefficients of a Taylor series in the Laplace space grows rapidly. When higher levels of Padé approximants need to be computed to achieve stable modes for separation of exponentials, the problem of generating matrices with large condition numbers becomes more pronounced. The analysis in this paper discusses the origin of ill-posedness of the PL method and it was shown that ill-posedness may be regularized by reconstructing the system of equations and using singular value decomposition (SVD) for computation of the Padé table. Moreover, it is shown that after regularization, the PL method can deconvolute the exponential decays even when the input parameter of the method is out of its optimal range.     

Synthesis of multi-wall carbon nanotubes by copper vapor laser

Synthesis of multi-wall carbon nanotubes in a 1473 K furnace using a copper vapor laser (CVL) is reported. The operating parameters of this laser, i.e. a high fluence at the focal point and an extremely high frequency of 10 kHz, distinguished it from common laser sources in the synthesis of CNTs. Therefore, the unexpected experimental findings, the formation of MWNTs instead of the generally reported SWNTs, would be verified by these two notable parameters. Electron microscopy beside Raman spectroscopy illustrates the presence of multi-wall carbon nanotubes in the resulting product.     

Formation of a percolating cluster in films prepared by cathodic electrodeposition of a mixture of lower and higher molecular weight epoxy-amine adducts

The electrodeposition behavior of blends of primary dispersions of a lower and a higher molecular weight epoxy-amine adduct has been investigated. The throwing power of the above-mentioned blends showed a voltage-dependent critical composition at which the throwing power dropped to a much lower value. This was assigned to the formation of an infinite conducting cluster, the extension of which is dependent on the rate of the electrocoagulation process at the cathode boundary. The random resistor network approach of Stauffer (RRNS) and the random resistor network approach of Miller and Abrahams (RRNMA) were applied to the experimental data with high correlations (r2=0.9314 and 0.9699). The percolating cluster formed within the film, however, gave a critical exponent of conductivity equal to 1.1028, much less than expected from a classical three-dimensional lattice (i.e., 1.5-2.0). This discrepancy was explained in terms of the changed behavior of the film resulting from the bubbles formed near the cathode and its effect on the infinite conducting cluster.     

Syzygy and Torsionless Modules with Respect to a Semidualizing Module

This paper aims at generalizing the notions of “Auslander dual”, “k-torsionless” and “k-th syzygy” modules to the relative setting with respect to a semidualizing module. It is shown that the “relative” Auslander dual shares many nice properties with the Auslander dual originally introduced by Auslander and Bridger. It is also shown the interplay between the “relative” version of “k-torsionless” and “k-th syzygy” modules parallels that of k-torsionless and k-th syzygy modules.     

A direct variable step block multistep method for solving general third-order ODEs

This paper discusses a direct three-point implicit block multistep method for direct solution of the general third-order initial value problems of ordinary differential equations using variable step size. The method is based on a pair of explicit and implicit of Adams type formulas which are implemented in PE(CE) ^t mode and in order to avoid calculating divided difference and integration coefficients all the coefficients are stored in the code. The method approximates the numerical solution at three equally spaced points simultaneously. The Gauss Seidel approach is used for the implementation of the proposed method. The local truncation error of the proposed scheme is studied. Numerical examples are given to illustrate the efficiency of the method.     

Stabilizing the pull-in instability of an electro-statically actuated micro-beam using piezoelectric actuation

In the present article an investigation is presented into the stability of an electro-statically deflected clamped–clamped micro-beam sandwiched by two piezoelectric layers undergoing a parametric excitation applying an AC voltage to these layers. Applying an electrostatic actuation not only deflects the micro-beam but also decreases the bending stiffness of the structure, which can lead the structure to an unstable position by undergoing a saddle node bifurcation. Utilizing an appropriate AC actuation voltage to the piezoelectric layers produces a time varying axial force, which can play the role of a stabilizer exciting the system parameter. The governing equation of the motion is a nonlinear electro-mechanically coupled type PDE, which is derived using variational principle and discretized, applying Eigen-function expansion method. The resultant is a Mathieu type equation in its damped form. Using Floquet theory for single degree of freedom system the stable and unstable regions of the problem are investigated. The effects of viscous damping and electrostatic actuation on the stable regions of the problem are also studied.