Open problems in some competition models

We present open problems and conjectures for some two-dimensional competition models, namely the logistic competition model and a Ricker-type competition model.     

The \bar \partial -problem on q-pseudoconvex domains with applications

For a q-pseudoconvex domain Ω in ? ⁿ , 1 ≤ q ≤ n, with Lipschitz boundary, we solve the $\bar \partial $ -problem with exact support in Ω. Moreover, we solve the $\bar \partial $ -problem with solutions smooth up to the boundary over Ω provided that it has smooth boundary. Applications are given to the solvability of the tangential Cauchy-Riemann equations on the boundary.     

Hopf bifurcation analysis on an Internet congestion control system of arbitrary dimension with communication delay

This paper carries out a Hopf bifurcation analysis on a model of Internet congestion control system for a network with arbitrary topology. The general form of the rate-based Kelly model for a multi-source multi-link network with a communication delay is considered. Assuming the communication delay as a bifurcation parameter, we find that when the delay parameter passes a critical value, a periodic solution bifurcates from the equilibrium point. The stability and direction of bifurcating periodic solutions are studied by using the center manifold theorem and the normal form theory. We simulate our model for a typical example to show the applicability of the approach.     

Molecularly imprinted polymer Based PVC-Membrane-Coated graphite electrode for the determination of metoprolol

A PVC-based membrane containing metoprolol molecularly imprinted polymer (MIP) coated directly on graphite electrode for the determination of metoprolol in real samples is reported. This potentiometric sensor was designed by dispersing the MIP particles in dioctylphthalate plasticizer as solvent mediator and then embedded in polyvinyl chloride matrix. The electrode exhibited a near-Nernstian slope of 55.4 ± 1 mV decade^-1 for metoprolol over a wide concentration range between 2.0 × 10^-7-8.0 × 10^-3 M and a detection limit of 1.3 × 10^-7 M. With a response time of about 14 s it could be used for at least 6 months without any divergence in potential. The proposed electrode can be used in the pH range of 3.5-10.5 and can reveal good selectivities for metoprolol over a wide variety of ions. Finally, the designed sensor was successfully applied as an indicator electrode to determine the concentration of metoprolol in tablets, human urine and plasma. The results were compared favorably with those obtained by HPLC method and showed satisfactory agreements with them.     

Solid-Phase Extraction of Metoprolol onto(Methacrylic acid-ethylene glycol dimethacrylate)-based Molecularly Imprinted Polymer and Its Spectrophotometric Determination

A new adsorbent for molecularly imprinted solid phase extraction (MISPE) of metoprolol was synthesized using methacrylic acid (MAA) as functional monomer and ethylene glycol dimethacrylate (EGDMA) as cross‐linking agent causing a non‐covalent, bulk, thermal radical‐polymerization. Control polymer (non‐imprinted polymer) was prepared under well defined conditions without the use of metoprolol. The synthesized polymers were characterized by IR spectroscopy, X‐ray diffraction and thermal analysis techniques. This polymer was used for the rapid extraction and preconcentration of metoprolol from real samples prior to spectrophotometric determination. Extraction efficiency and the influence of flow rates of sample and stripping solutions, pH, type of eluent for elution of metoprolol from polymer, break through volume and limit of detection were studied. The detection limit of the proposed method is 0.4 ng·mL^?1. The method was applied successfully to the recovery and determination of metoprolol in tablets, human urine and plasma samples.     

Copolycarbonates of isosorbide and various diols

Isosorbide and equimolar amounts of various diols were polycondensed with diphosgene and pyridine. Bisphenol A, 3,3′‐dimethyl bisphenol A, bisphenol C, 1,3‐bis(4‐hydroxybenzoyloxy)propane, and 1,4‐cyclohexane diol were used as comonomers. The compositions were determined by ¹H NMR spectroscopy; the random sequences were characterized by ¹³C NMR spectroscopy. For the high‐molar‐mass copolycarbonates of bisphenol A, 3,3′‐dimethyl bisphenol A, and bisphenol C, matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry proved that the chain growth was mainly limited by cyclization. Copolycarbonates with alternating sequences were obtained by the polycondensation of bisphenol A with isosorbide bischloroformiate or from isosorbide and bisphenol A bischloroformiate. In these cases, large amounts of cyclic oligo‐ and polycarbonates were also formed. The glass‐transition temperatures were determined by differential scanning calorimetry measurements. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3616–3628, 2006     

A semantical proof of the strong normalization theorem for full propositional classical natural deduction

We give in this paper a short semantical proof of the strong normalization for full propositional classical natural deduction. This proof is an adaptation of reducibility candidates introduced by J.-Y. Girard and simplified to the classical case by M. Parigot.     

Computerized data acquisition and processing for Shpol'skii high-resolution spectrofluorimetry

The program described provides simultaneously digital control of a high-resolution spectrofluorimeter, acquisition of analog signals and data storage, and contains graphics processing to visualize spectra. Automatic evaluation software, which evaluates peak heights and calculates concentrations is included. The program runs on an IBM PC-AT2 (or compatible) equipped with interface cards; it is composed of distinct modules which are obtained through a menu. The system has been applied to the determination of 13 polynuclear aromatic hydrocarbons (PAHs); it offers high selectivity, excellent detection limits, and rapidity of data acquisition. Results obtained for 9 PAHs in a standard urban dust (SRM-1649) were satisfactory.