Non-contractible edges in a 3-connected graph

An edgee in a 3-connected graphG is contractible if the contraction ofe inG results in a 3-connected graph; otherwisee is non-contractible. In this paper, we prove that the number of non-contractible edges in a 3-connected graph of orderp≥5 is at most $$3p - \left[ {\frac{3}{2}(\sqrt {24p + 25} - 5} \right],$$ and show that this upper bound is the best possible for infinitely many values ofp.     

Optimization of ETV-ICP-MS conditions for the determination of multi-elements in semiconductor grade acids

The performance of an electro thermal vaporization (ETV) unit as a sample introduction device for an inductively coupled plasma mass spectrometer (quadrupole-ICP-MS) was evaluated. The technique was found to have several advantages over the conventional nebulization method. Some features of ETV-ICP-MS for single element determination have been investigated. Attempts were made to optimize the experimental parameters such as vaporization temperature, vaporization interval and carrier gas flow rate. The study highlights on the determination of Cr, Mn, Al and Na. A compromise condition for multi-element determination was suggested and tested from single-element optimum conditions obtained. 25 L solution was used for the analysis. Results obtained for the analysis of conc. HCl samples are also reported.     

Emulsion polymerization of vinyl acetate using iodine‐transfer and RAFT radical polymerizations

This study deals with control of the molecular weight and molecular weight distribution of poly(vinyl acetate) by iodine‐transfer radical polymerization and reversible addition‐fragmentation transfer (RAFT) emulsion polymerizations as the first example. Emulsion polymerization using ethyl iodoacetate as the chain transfer agent more closely approximated the theoretical molecular weights than did the free radical polymerization. Although ¹H NMR spectra indicated that the peaks of α‐ and ω‐terminal groups were observed, the molecular weight distributions show a relatively broad range (M_w/M_n = 2.2–4.0). On the other hand, RAFT polymerizations revealed that the dithiocarbamate 7 is an excellent candidate to control the polymer molecular weight (M_n = 9.1 × 10³, M_w/M_n = 1.48), more so than xanthate 1 (M_n = 10.0 × 10³, M_w/M_n = 1.89) under same condition, with accompanied stable emulsions produced. In the M_n versus conversion plot, M_n increased linearly as a function of conversion. We also performed seed‐emulsion polymerization using poly(nonamethylene L ‐tartrate) as the chiral polyester seed to fabricate emulsions with core‐shell structures. The control of polymer molecular weight and emulsion stability, as well as stereoregularity, is also discussed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

A siloxane polymer lightwave circuit on ceramic substrate applicable to ultrafast optoelectronic multi-chip-modules

Technique for integrating optical waveguide circuits on electrical circuits is developed toward the application to opto-electronic multi-chip modules (O/E-MCM), which enables one to handle ultrafast lightwave pulses and electrical signals on a common circuit board. We use ceramic material as the substrate of O/E-MCM having a multi-layer structure. A siloxane polymer is utilized to form low loss optical waveguides on ceramic substrates by low temperature processes. The waveguide has shown high transparency around 1310 nm. The group velocity dispersion has been measured and shown to become almost zero at wavelength of 1310 nm and about 0.4 fs/cm nm at 1550 nm. An optical circuit has been formed on simple electrical circuit consisting of a thermometer film resistance layer. A Mach–Zehnder interferometer optical switch exhibiting the waveguide extinction ratio of 30 dB, control power of 5 mW, and switching speed of 6 ms has been demonstrated. Thermal management characteristics also have been demonstrated successfully. This single-mode optical waveguide can thus be formed readily on ceramic substrates involving electrical circuit layers; this result confirms its applicability to O/E-MCM.     

Small‐angle x‐ray scattering study of thermoreversible poly(vinyl chloride) gels

Poly(vinyl chloride) (PVC)/bis(2‐ethylhexyl)phthalate (DOP) gels were prepared at room temperature from tetrahydrofuran solutions of PVC and DOP. PVC/DOP gels of different molecular weights at various PVC concentrations (c) were investigated with small‐angle X‐ray scattering (SAXS). The mean distance between two neighboring inhomogeneities (D) and two characteristic lengths, the intrainhomogeneity distance (d₁) and interinhomogeneity distance (d₂), were evaluated from Bragg's law and the distance distribution function, respectively. Both D and d₂ can be expressed by a power‐law relation (e.g., D and d₂ ∝ c^?0.5). After a period of rapid cooling to 25 °C from the sol state, the structural evolution was examined with time‐resolved SAXS measurements. An Avrami analysis with the SAXS invariant data revealed that the growth kinetics of PVC/DOP gels was one‐dimensional growth from predetermined nuclei, regardless of c. These results suggest that the PVC/DOP gels are constructed from a fibrillar structure that forms gel structures at high concentrations or low temperatures. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2340–2350, 2001     

Phase Separation in a Bidirectional Two-Lane Asymmetric Exclusion Process

This paper studies a bidirectional two-lane asymmetric exclusion process, in which particles move in opposite direction on the two lanes. Interaction between the two lanes is implemented as follows: particle hops with rate p when there is a particle at the same site in the other lane, otherwise it hops with rate 1. It is shown that under periodic boundary conditions, a plateau will form on the fundamental diagram if p<1. This plateau corresponds to a phase separation phenomenon. We have compared the phase separation with those reported in previous works, and it is shown that the mechanism of phase separation in our model is different from previous ones. A possible phase separation mechanism is proposed, i.e., the system always tries to maximize the probability that particles could hop with rate 1. A simple mean field approximation and a 2-cluster mean field approach have been applied to calculate the steady current. It is shown that the results of the 2-cluster mean field approach are much closer to the simulations.     

Synthesis, properties, and reactions of a series of stable dialkyl-substituted silicon-chalcogen doubly bonded compounds

The first dialkyl-substituted silicon-chalcogen doubly bonded compounds [R2Si=X; R2=1,1,4,4-tetrakis(trimethylsilyl)butane-1,4-diyl, X = S (4), Se (5), and Te (6)]were synthesized by the reactions of an isolable dialkylsilylene R2Si: (3) with phosphine sulfide, elemental selenium, and elemental tellurium, respectively. Systematic changes of characteristics of silicon-chalcogen double bonds are elucidated by X-ray analysis, UV-vis spectroscopy, and DFT calculations. In the solid state, the unsaturated silicon atom in 4-6 adopts planar geometry and the extent of the shortening of Si=X double bonds from the corresponding Si-X single bonds decreases in the order 4 > 5 > 6. In the absorption spectra of 4-6, pi -->pi* transition bands are observed distinctly in addition to n -->pi* transition bands. Both the n -->pi* and pi -->pi* transitions are red-shifted in the order 4 < 5 < 6, and the difference between the energies of the two transitions is kept almost constant among 4-6. The tendency is explained using the qualitative perturbation theory and is reproduced by the DFT calculations for model silanechalcogenones. Addition reactions of water, methanol, and isoprene to 4-6 are reported.     

A chromophore-labeled poly(N-propargylamide): a new strategy for a stimuli-responsive conjugated polymer

A new stimuli-responsive conjugated polymer was synthesized, where, following the change of secondary conformation from helical to disordered state, the fluorescence property of the side chain chromophore changes upon sensing external stimuli.