On the Renormalization Group Approach to Perturbation Theory for PDEs

We investigate the rigorous application of the renormalization group method to (singular) perturbation theory for nonlinear partial differential equations. As a paradigm, we consider the concrete example of the nonlinear Schrödinger equation with quadratic nonlinearity in three spatial dimensions. We obtain an approximate solution using the RG method together with an estimate of the difference between the true and approximate solutions. Our analysis applies to cases where (space–time) resonances are present.     

Inverse Suspension Polymerization as a New Tool for the Synthesis of Ion‐Imprinted Polymers

Ion‐imprinted polymer beads are prepared for the first time by inverse suspension polymerization in mineral oil using nickel(II) as the template ion. As water is not used as the continuous phase, this new route of synthesis avoids the risk that the ion template leaves the suspension for the aqueous phase. The leaching of nickel from the resin beads is very good due to the large porosity of the polymer beads. The ratio between the ligand and the crosslinker has been increased leading to higher adsorption capacities. Comparing these values with those of the non‐imprinted polymers and studying the effect of some interfering ions proves that an optimum can be found for the ratio ligand/crosslinker.     

Ar plasma waveguide produced by a low-intensity femtosecond laser

Using the interaction of a low-intensity femtosecond laser pulse (30 fs, 6 × 10¹⁵ Wcm^? 2) with argon cluster jet produced from a slit nozzle, we experimentally probe the formation of a uniform plasma waveguide by the interferogram analysis. The results about evolution of plasma channel demonstrate that it is feasible to produce the plasma waveguide for an fs laser pulse of low-intensity. It takes tens of nanoseconds to form a plasma waveguide. The simulation by one-dimensional Gaussian plasma hydrodynamic expansion model indicates that the temperature of plasma channel is not high under this condition. Thus it takes tens of nanoseconds to form a plasma waveguide.     

Detailed investigation of self-imaging in multimode photonic crystal waveguides for applications in power and polarization beam splitters

Properties of the self-imaging effect based on multimode interference (MMI) in multimode photonic crystal waveguides (PCWs) are investigated and analyzed in detail. By combining photonic band gap (PBG) and total internal reflection (TIR) effects in PCWs, self-imaging phenomena are achieved for both TE and TM polarizations. To observe the images reproduced by this self-imaging phenomenon, finite-difference time-domain (FDTD) simulations are performed on a multi-mode PCW. From these numerical simulations the reproduced images are identified and their positions along the propagation axis are described. We also, present the design and simulation of novel polarization-insensitive power splitter and polarization splitter. The simulation results show that the optimized devices have excellent transmission efficiencies as well as wide operating frequency bandwidths and small structure size. So, the proposed devices are promising and may play an important role in high-density photonic integrated circuits in the future.     

Direct synthesis of nanowires with anatase and TiO2-B structures at near ambient conditions

In this study, we present a new approach toward titanium oxide nanowires. In this approach, the growth formation of the wires sets in at a temperature as low as 40 degrees C under ambient pressure. Moreover, we provide evidence that nanowires with distinctive TiO2-anatase and TiO2-B structures can be directly produced without further thermal treatment using controlled reaction conditions.     

Spectroscopic,thermal, biological activity,molecular docking and density functional theoretical investigation of novel bis Schiff base complexes

New Schiff base ligand (H₂L, 1,2‐bis[(2‐(2‐hydroxyphenylimino)‐methyl)phenoxy]ethane) came from condensation reaction of bisaldehyde and 2‐aminophenol was synthesized in a molar ratio 1:2. Metal complexes and the ligand were completely discussed with spectroscopic and theoretical mechanism. The complexes with Fe(III), Cr(III), Mn(II), Co(II), Cu(II), Ni(II), Th(IV) and Zn(II) have been discussed and characterized by elemental analyses, molar conductance, IR, mass spectroscopy, thermal, magnetic measurements, and ¹H NMR. The results proved that the Schiff base was a divalent anion with hexadentate O₄N₂ donors came from the etheric oxygens (O1, O2), azomethine nitrogens (N1, N2) and deprotonated phenolic oxygens (O3, O4). Density Functional Theory using (B3LYP/6‐31G*) level of theory were implemented to predict molecular geometry, Mulliken atomic energetic and charges of the ligand and complexes. The calculation display that complexes had weak field ligand. The binding energy ranged from 650.5 to 1499.0 kcal/mol for Mn(II) and Th(IV) complexes, respectively. The biological behavior of the Schiff base ligand and its metal complexes were displayed against bacteria and fungi organisms. Fe(III) complex gave remarkable biological activity in comparison with the parent bis Schiff base.     

In Situ Direct Measurement of Vapor Pressures and Thermodynamic Parameters of Volatile Organic Materials in the Vapor Phase: Benzoic Acid,Ferrocene, and Naphthalene

We report the direct determination of vapor pressures and optical and thermodynamic parameters of powders of low‐volatile materials in their vapor phase using a commercial UV/Vis spectrometer. This methodology is based on the linear proportionality between the density of the saturated gas of the material and the absorbance of the gas at different temperatures. The vapor pressure values determined for benzoic acid and ferrocene are in good agreement with those reported in the literature with ～2–7 % uncertainty. Thermodynamic parameters of benzoic acid, ferrocene, and naphthalene are determined in situ at temperatures below their melting points. The sublimation enthalpies of the investigated organic molecules are in excellent agreement with the ICTAC recommended values (less than 1 % difference). This method has been used to measure vapor pressures and thermodynamic parameters of organic volatile materials with vapor pressures of ～0.5–355 Pa in the 50–100 °C temperature range.     

Zn2+-Schiff’s Base Complex as an “On–Off-On” Molecular Switch and a Fluorescence Probe for Cu2+ and Ag+ Ions

The present study presents a thorough theoretical analysis of the electronic structure and conformational preference of Schiff’s base ligand N,N-bis(2-hydroxybenzilidene)-2,4,6-trimethyl benzene-1,3-diamine (H₂L) and its metal complexes with Zn²⁺, Cu²⁺ and Ag⁺ ions. This study aims to investigate the behavior of H₂L and the binuclear Zn²⁺ complex (1) as fluorescent probes for the detection of metal ions (Zn²⁺, Cu²⁺ and Ag⁺) using density functional theory (DFT) and time-dependent density functional theory (TDDFT). The six conformers of the H₂L ligand were optimized using the B3LYP/6–311?+??+?G** level of theory, while the L^?2-metal complexes were optimized by applying the B3LYP functional with the LANL2DZ/6–311?+??+?G** mixed basis set. The gas-phase and solvated Enol-cis isomer (E-cis) was found to be the most stable species. The absorption spectra of the E-cis isomer and its metal complexes were simulated using B3LYP, CAM-B3LYP, M06-2X and ωB97X functionals with a 6–311?+??+?G** basis set for C, O, N and H atoms and a LANL2DZ basis set for the metal ions (Zn²⁺, Cu²⁺ and Ag⁺). The computational results of the B3LYP functional were in excellent agreement with the experimental results. Hence, it was adopted for performing the emission calculations. The results indicated that metal complex (1) can act as a fluorescent chemosensor for the detection of Ag⁺ and Cu²⁺ ions through the mechanism of intermolecular charge transfer (ICT) and as a molecular switch “On–Off-On” via the replacement of Cu²⁺ by Ag⁺ ions, as proved experimentally.

     

CpRu-catalyzed O-H insertion and condensation reactions of α-diazocarbonyl compounds

[CpRu(CH(3)CN)(3)][PF(6)] and diimine ligands catalyze together the decomposition of α-diazocarbonyl compounds leading to O-H insertion and condensation reactions. In comparison with Rh(II) and Cu(I) complexes, the CpRu catalysts produce rapid and often more selective reactions. Promising enantioselectivities are obtained in dioxole syntheses.