Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

Synthesis and characterization of oligo-4-[(pyridin-3-ylimino)methyl]phenol

The oxidative polycondensation of 4-[(pyridin-3-ylimino)methyl]phenol (4-PIMP) with O₂, H₂O₂, and NaOCl was studied in an aqueous alkaline medium between 50°C and 90°C. Oligo-4-[(pyridin-3-ylimino)methyl]phenol (O-4-PIMP) prepared was characterized by ¹H-NMR, ¹³C-NMR, FT-IR, UV-VIS, size-exclusion chromatography, and elemental and thermal analyses techniques. At the optimum reaction conditions, the yield of O-4-PIMP was 18.9%, 39.4%, and 46.8% using H₂O₂, O₂, and NaOCl oxidant, respectively. According to the TG analysis, the initial degradation temperature of O-4-PIMP was 218°C, which was by 50°C higher than that of 4-PIMP. Thermal analyses of 4-PIMP and O-4-PIMP were carried out in N₂ atmosphere at 15–1000°C. The highest occupied molecular orbital, the lowest unoccupied molecular orbital, and electrochemical energy gaps of 4-PIMP and O-4-PIMP were determined from the onset potentials for n-doping and p-doping, respectively. Also, optical band gaps of 4-PIMP and O-4-PIMP were determined according to UV-VIS measurements.     

Recognition-induced transformation of microspheres into vesicles: morphology and size control

Polystyrene functionalized with diamidopyridine (DAP) recognition units self-assembles in nonpolar media to form thermally reversible micrometer-scale spherical aggregates. The size and the thermal stability of these microspheres can be controlled by the molecular weight of the polymer. The addition of thymine-functionalized polymer to these self-assembled microspheres converted them into vesicular aggregates with a controlled size. The morphology change was reversible: the addition of DAP-functionalized polymer converted the vesicles back to microspheres.     

Hydrophobic cryogels for DNA adsorption: Effect of embedding of monosize microbeads into cryogel network on their adsorptive performances

As alternative hydrophobic adsorbent for DNA adsorption, supermacroporous cryogel disks were synthesized via free radical polymerization. In this study, we have prepared two kinds of cryogel disks: (i) poly(2‐hydroxyethyl methacrylate‐N‐methacryloyl‐l ‐tryptophan) [p(HEMA‐MATrp)] cryogel containing specific hydrophobic ligand MATrp; and (ii) monosize p(HEMA‐MATrp) particles synthesized via suspension polymerization embedded into p(HEMA) cryogel structure to obtain p(HEMA‐MATrp)/p(HEMA) composite cryogel disks. These cryogel disks containing hydrophobic functional group were characterized via swelling studies, Fourier transform infrared spectroscopy, elemental analysis, surface area measurements and scanning electron microscopy. DNA adsorption onto both p(HEMA‐MATrp) cryogel and p(HEMA‐MATrp)/p(HEMA) composite cryogels was investigated. Maximum adsorption of DNA on p(HEMA‐MATrp) cryogel was found to be 15 mg/g polymer. Otherwise, p(HEMA‐MATrp)/p(HEMA) composite cryogels significantly increased the DNA adsorption capacity to 38 mg/g polymer. Composite cryogels could be used repeatedly without significant loss on adsorption capacity after 10 repetitive adsorption–desorption cycles. Copyright © 2013 John Wiley & Sons, Ltd.     

Heavy Metal Removal from Synthetic Solutions with Magnetic Beads Under Magnetic Field

The aim of this study is to prepare magnetic beads which can be used for the removal of heavy metal ions from synthetic solutions. Magnetic poly(ethylene glycol dimethacrylate‐vinyl imidazole) [m‐poly(EGDMA‐VIM)] beads were produced by suspension polymerization in the presence of magnetite Fe₃O₄ nano‐powder. The specific surface area of the m‐poly(EGDMA‐VIM) beads was found to be 63.1 m²/g with a size range of 150–200 µm in diameter and the swelling ratio was 85%. The average Fe₃O₄ content of the resulting m‐poly(EGDMA‐VIM) beads was 12.4%. The maximum binding capacities of the m‐poly(EGDMA‐VIM) beads were 32.4 mg/g for Cu²⁺, 45.8 mg/g for Zn²⁺, 84.2 mg/g for Cd²⁺and 134.5 mg/g for Pb²⁺. The affinity order on mass basis is Pb²⁺>Cd²⁺>Zn²⁺>Cu²⁺. Equilibrium data agreed well with the Langmuir model. pH significantly affected the binding capacity of the magnetic beads. Binding of heavy metal ions from synthetic wastewater was also studied. The binding capacities were 26.2 mg/g for Cu²⁺, 33.7 mg/g for Zn²⁺, 54.7 mg/g for Cd²⁺ and 108.4 mg/g for Pb²⁺. The magnetic beads could be regenerated up to about 97% by treating with 0.1 M HNO₃. These features make m‐poly(EGDMA‐VIM) beads a potential candidate for support of heavy metal removal under magnetic field.     

Determination of Paracetamol Based on 3-Amino-4H-1,2,4-triazole Coated Glassy Carbon Surface in Pharmaceutical Sample

In this present study, to determine paracetamol, an electroanalytical method is presented using differential pulse voltammetry (DPV) at 3-amino-4H-1,2,4-triazole (3AT) coated glassy carbon (GC) electrode. The electrochemical characterization and electron transfer behavior of this prepared electrode in the mixture of K₄[Fe(CN)₆]/K₃[Fe(CN)₆] contains 0.1 M KCl was confirmed by using cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) methods. Furthermore, scanning electron microscopy (SEM) was used to observe morphological structures of the bare and modified surfaces. The effect of pH was studied on the redox reaction of paracetamol in phosphate buffer in the range of pH 3.0–9.0. The limit of detection was 0.043 μM (3 s/m) for 3AT-GC electrode. The developed electrode was successfully utilized in pharmaceutical samples.     

Lower bounds for boundary roughness for droplets in Bernoulli percolation

We consider boundary roughness for the ``droplet' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l², for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l^1/3(logl)^–2/3. This complements the upper bound of order l^1/3(logl)^–2/3 proved in [Al3] for the average local roughness. The exponent 1/3 on l here is in keeping with predictions from the physics literature for interfaces in two dimensions. The research of the first author was supported by NSF grant DMS-9802368. The research of the second author was supported by NSF grants DMS-9802368 and DMS-0103790.Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B20, 82B43     

Linear and nonlinear intersubband optical absorptions in an asymmetric rectangular quantum well

The linear and nonlinear intersubband optical absorptions in Al_xlGa_1-xlAs/GaAs/Al_xr Ga_1-xrAs asymmetric rectangular quantum well are studied within the framework of the density matrix formalism. We have calculated the electron energy levels and the envelope wave functions using the effective mass approach. In addition, we have obtained an expression for saturation intensity. It is shown that the parameters such as asymmetry and width of potential well not only shift the peak positions in absorption spectrum but also considerably modify their height. These results suggest that the absorption process can be easily controlled by the structure parameters of an asymmetric rectangular quantum well. Also, the incident optical intensity has a great effect on the total absorption spectrum. We have seen that the absorption peak is reduced by half when the optical intensity is approximately 0.8 MW/cm² for well width L=90 ? and β=0.5. Moreover, it is seen that the saturation intensity is quite sensitive to the structure parameters of an asymmetric rectangular quantum well. Thus, the results presented here can be useful for electro-optical modulators and photodetectors in the infrared region.