On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Raman spectroscopic characteristics of phthalocyanine and naphthalocyanine in sandwich-type phthalocyaninato and porphyrinato rare earth complexes Part 5. – Raman spectroscopic characteristics of naphthalocyanine in mixed [tetrakis(4-tert-butylphenyl)porphyrinato]-(naphthalocyaninato) rare earth double-deckers

Raman spectra were recorded in the range 400–1800 cm−1 for a series of 15 mixed \[tetrakis(4-tert-butylphenyl)porphyrinato](2,3-naphthalocyaninato) rare earth double-deckers M(TBPP)(Nc) (M = Y; La–Lu except Pm) using laser excitation at 632.8 and 785 nm. Comparisons with bis(naphthalocyaninato) rare earth counterparts reveal that the vibrations of the metallonaphthalocyanine M(Nc) fragment dominate the Raman features of M(TBPP)(Nc). When excited with radiation of 632.8 nm, the most intense vibration appears at about 1595 cm−1, due to the naphthalene stretching. These complexes exhibit the marker Raman band for Nc•− as a medium-intense band in the range 1496–1507 cm−1, attributed to the coupling of pyrrole and aza stretching, while the marker Raman band of Nc2− in intermediate-valence Ce(TBPP)(Nc) appears as a strong band at 1493 cm−1 and is due to the isoindole stretchings. By contrast, when excited with radiation of 785 nm that is in close resonance with the main Q absorption band of the naphthalocyanine ligand, the ring radial vibrations at ca 680 and 735 cm−1 for MIII(TBPP)(Nc) are selectively intensified and are the most intense bands. For the cerium double-decker, the most intense vibration also acting as the marker Raman band of Nc2− appears at 1497 cm−1 with contributions from both pyrrole CC and aza CN stretches. The same vibrational modes show weak to medium intensity scattering at 1506–1509 cm−1 for MIII(TBPP)(Nc) and this is the marker Raman band of Nc•− when thus excited. The scatterings due to the Nc breathings, ring radial vibration, aza group stretchings, naphthalene stretchings, benzoisoindole stretchings and the coupling of pyrrole CC and aza CN stretchings in MIII(TBPP)(Nc) are all slightly blue shifted along with the decrease in rare earth ionic radius, confirming the effects of increased ring–ring interactions on the Raman characteristics of naphthalocyanine in the mixed ring double-deckers.

Study on microwave dielectric properties of epoxy resin mixtures used for rapid product development

This paper presents a preliminary study on the dielectric properties and curing of three different types of epoxy resins mixed at various stichiometric mixture of hardener, flydust and aluminium powder under microwave energy. In this work, the curing process of thin layers of epoxy resins using microwave radiation was investigated as an alternative technique that can be implemented to develop a new rapid product development technique. In this study it was observed that the curing time and temperature were a function of the percentage of hardener and fillers presence in the epoxy resins. Initially dielectric properties of epoxy resins with hardener were measured which was directly correlated to the curing process in order to understand the properties of cured specimen. Tensile tests were conducted on the three different types of epoxy resins with hardener and fillers. Modifying dielectric properties of the mixtures a significant decrease in curing time was observed. In order to study the microstructural changes of cured specimen the morphology of the fracture surface was carried out by using scanning electron microscopy.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Administrative Placement of the Information Systems Discipline in Universities - A SWOT Analysis of Queensland University of Technology

In some Queensland universities, Information Systems academics have moved out of Business Faculties. This study uses a pilot SWOT analysis to examine the ramifications of Information Systems academics being located within or outside of the Business Faculty. The analysis provides a useful basis for decision makers in the School studied, to exploit opportunities and minimise external threats. For Information Systems academics contemplating administrative relocation of their group, the study also offers useful insights. The study presages a series of further SWOT analyses to provide a range of perspectives on the relative merits of having Information Systems academics administratively located inside versus outside Business faculties.