Oscillation of Systems of Neutral Equations with Variable Coefficients

Consider the system of the neutral delay differential equations (1) $ \frac{d}{{dt}}\left[{Y\left(t \right) - R\left(T \right)Y\left({T - \varrho } \right)} \right] + P\left(t \right)Y\left({t - \tau } \right) - Q\left(t \right)Y\left({t - \sigma } \right) = 0 $ where P(t) = (p_ij(t)), Q(t) = (q_ij(t)) and R(t) = (r_ij(t)) are n x n matrices for t ≧ 0 and the delays τ, σ and ? are nonnegative numbers. We obtain sufficient conditions for the oscillation of all solutions of (1) under the following hypotheses:      

Messing about in transformations: Structured systemic planning for systemic solutions to systemic problems

The literature on multimethodology indicates that cognitive mapping is relevant to enriching the preliminary, information-gathering phase of Soft Systems Methodology (SSM), and especially the rich picture. By noting the structural complementarity evidenced between SSM’s transformations and the bipolar constructs used in the cognitive mapping methodology known as Strategic Options Development and Analysis (SODA), this paper shows how SODA can be applied beyond SSM’s initial stage, and much more analytically within the heart of SSM, to guide the manner in which a systemic resolution to a problematic situation may be approached. It is proposed, and illustrated through examples, that a SODA map of large numbers of transformations, resulting from an exercise in SSM, offers a methodological means for structuring what might otherwise be perceived as a mess. The paper discusses how in such cases ‘strategic options development and analysis’ of transformations, or SODA-T maps, serve, among other things, to identify relations between transformations, their hierarchies and priorities, problem epicenters and starting points for intervention. In addition, the arsenal of graph theory can be used to cut through what would otherwise appear as interlinked chaos requiring structured operationalization. In this respect, the SODA-T map offers a high-level connective orientation which can guide the interconnections between the respective human activity systems of the transformations, resulting in the final systemic plan. Ultimately, SODA-T mapping is shown to facilitate a structured approach toward systemic planning.     

Topologies on function spaces

Function spaces play an important role in complex analysis, in the theory of differential equations, in functional analysis and in almost every other branch of modern mathematics. In this paper we give and study the notion of clopen convergence. Also, we study the notion of clopen continuity and define new topologies on function spaces. These results generalize basic results of R. Arens, J. Dugundji and A. Di Concilio (see [1], [4], [2] and [3]).     

Pulsed laser deposition of polymers doped with fluorescent molecular sensors

Pulsed laser deposition (PLD) has been used to obtain thin films of poly(methyl-methacrylate), PMMA, and polystyrene, PS, doped with fluorescent probes based in the amino aromatic compounds S6, DMA-2,4, Dans and Acrid-acryl. These compounds, both in solution and inserted in polymeric films, show solvatochromic emission band shifts upon changes of pH, polarity and viscosity in their micro-environment and, prepared in thin films, could prove advantageous for use as sensors of the presence of contaminating environmental agents. Deposits, obtained by irradiating targets consisting in films of doped PMMA and PS with a Ti:sapphire laser (800 nm, 120 fs pulse), were analyzed by optical and environmental scanning electron microscopy, fluorescence microscopy, laser-induced fluorescence, micro-Raman spectroscopy and flow injection analysis-mass spectrometry. Results show the effective transfer of the polymer and the probe to the substrate and the high dependence on film structure on the polymer used in the targets. Irradiation with a KrF laser (248 nm, 20 ns) of Dans-doped targets only produced deposits when using PMMA for target preparation. Results are discussed in terms of the participation of multiphoton processes in the fs IR irradiation, the influence of the linear absorption coefficient of the targets and of the different contributions of thermal and chemical effects in the IR femtosecond and UV nanosecond domains. PACS 81.15.Fg; 61.82.Pv     

FT-Raman spectroscopy - analytical tool for routine analysis of diazinon pesticide formulations

FT-Raman spectroscopy based on band intensity and band area measurements, was used for the quantitative determination of diazinon in pesticide formulations. Bands at 554, 604, 631, 1562 and 2971 cm(-1) were used for calibration. Spectra were acquired by averaging 100 scans at a resolution of 4 cm(-1). Calibration curves were linear (correlation coefficients, 0.992-0.9992 and 0.99-0.999 for band intensity and band area measurements, respectively) in the range of 0.2-3.5 M for 554 and 2971 cm(-1), 0.3-3.5 M for 604 cm(-1), 0.6-3.5 M for 1562 cm(-1) and 1.0-3.5 M for 631 cm(-1) bands. Normalization of calibration curves against the 802 cm(-1) cyclohexane band improved their long term stability and minimized the effect of laser beam power fluctuations. No interference was found by commonly used surfactants and the proposed method was applied to the analysis of diazinon formulations. Results obtained compare well as indicated by the t-test, with those obtained by the HPLC reference method. Precision ranged between 0.2-7.8 and 0.1-7.2% RSD, (n=4) for band intensity and band area measurements, respectively. The proposed method is rapid, simple and safe, as toxic samples are analyzed 'as received' without sample pre-treatment, permiting the routine analysis of pesticides formulations.     

On the stability of the shear flow of a viscoelastic fluid with slip along the fixed wall

In this paper we solve the time-dependent shear flow of an Oldroyd-B fluid with slip along the fixed wall. We use a non-linear slip model relating the shear stress to the velocity at the wall and exhibiting a maximum and a minimum. We assume that the material parameters in the slip equation are such that multiple steady-state solutions do not exist. The stability of the steady-state solutions is investigated by means of a one-dimensional linear stability analysis and by numerical calculations. The instability regimes are always within or coincide with the negative-slope regime of the slip equation. As expected, the numerical results show that the instability regimes are much broader than those predicted by the linear stability analysis. Under our assumptions for the slip equation, the Newtonian solutions are stable everywhere. The interval of instability grows as one moves from the Newtonian to the upper-convected Maxwell model. Perturbing an unstable steady-state solution leads to periodic solutions. The amplitude and the period of the oscillations increase with elasticity.