Stability and asymptotic behavior of solutions for some linear partial functional differential equations in critical cases

In this work, we study the stability of the solution semigroup for some linear partial functional differential equations with infinite delay in a Banach space when the exponential stability fails. We use the so-called characteristic equation to compute the order of each pole of the resolvent operator associated with the infinitesimal generator of the solution semigroup. This result allows us to give sufficient conditions for having stability of the solution semigroup.     

Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces

In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transaction of American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions.     

A variable neighbourhood search algorithm for the open vehicle routing problem

In the open vehicle routing problem (OVRP), the objective is to minimise the number of vehicles and then minimise the total distance (or time) travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced by each vehicle must not exceed vehicle capacity. Additionally, in one variant of the problem, the travel time of each vehicle should not exceed an upper limit.     

Mechanistic implications in the Morita-Baylis-Hillman alkylation: isolation and characterization of an intermediate

An intermediate phosphonium salt has never been isolated from the Morita-Baylis-Hillman (MBH) reaction. Due to the weakly basic counterion produced in the MBH alkylation and allylation reactions, the reaction can be stopped after electrophilic attack on the zwitterionic enolate and an intermediate isolated. Upon analysis of the crystal structure, a trans geometry is observed, suggesting that there is no electrostatic interaction between phosphorus and oxygen in the zwitterionic enolate that undergoes alkylation, thus giving new mechanistic insight into the MBH reaction.     

Observation of phenyl-fused porphyrinoids during the ESI mass spectrometric analysis of meso-pentafluorophenyl-substituted porphyrin and corrole

The results of ESI(+) and ESI(-) mass spectrometry/mass spectrometry investigations of meso-tetrakisphenylporphyrin (TPP) and meso-trisphenylcorrole (TPC) in comparison with their meso-tetrakis(pentafluorophenyl)-substituted analogs T(F)PP and T(F)PC are reported. The fragmentation patterns of TPP and TPC show the expected loss of meso-aryl radicals. Analyzing the meso-pentafluorophenyl substituted analogs T(F)PP and T(F)PC, we found ESI(-) to be an excellent ionization mode. Rich and well-defined HF-elimination fragmentation patterns unique to the presence of meso-tetrafluorophenyl groups and evocative for the formation of fragments with direct covalent o-phenyl-to-beta-linkages are observed. A computation of the feasibility and relative energies of the resulting species corroborates the interpretation of the experimental findings. The computations indicate the presence of cooperative interactions between the linkages that direct the linkage formations to occur in a unidirectional fashion. MS/MS/MS experiments also provide indications for the regioselectivity of the fusions. Our observations further detail earlier reports of similar HF-eliminations and allow a generalization of the findings. The results presented may also point to strategies towards the bulk synthesis of novel porphyrinoid structures.     

Affinity monolithic capillary columns for glycomics/proteomics: 1. Polymethacrylate monoliths with immobilized lectins for glycoprotein separation by affinity capillary electrochromatography and affinity nano-liquid chromatography in either a single column or columns coupled in series

In this report, microcolumn separation schemes involving monolithic capillary columns with immobilized lectins, and relevant to nanoglycomics/nanoproteomics were introduced. Positive and neutral monoliths based on poly(glycidyl methacrylate-co-ethylene dimethacrylate) were designed for achieving lectin affinity chromatography (LAC) by nano-LC and CEC. The positive monoliths (i.e., monoliths with cationic sites) afforded relatively high permeability in nano-LC but lack predictable EOF magnitude and direction, while neutral monoliths provided a good compromise between reasonable permeability in nano-LC and predictable EOF in CEC. Lectin affinity nano-LC permitted the enrichment of classes of different glycoproteins having similar N-glycans recognized by the immobilized lectin, whereas lectin affinity CEC provided the simultaneous capturing and separation of different glycoproteins due to differences in charge-to-mass ratio. Also, this investigation demonstrated for the first time the coupling of lectin capillary columns in series (i.e., tandem columns) for enhanced separation of glycoproteins by LAC using the CEC modality. Furthermore, in the coupled columns format, glycoforms of a given glycoprotein were readily separated.     

Analytical Expressions for the Mixed-Order Kinetics Parameters of TL Glow Peaks Based on the two Heating Rates Method

The two heating rates method (originally developed for first-order glow peaks) was used for the first time to evaluate the activation energy (E) from glow peaks obeying mixed-order (MO) kinetics. The derived expression for E has an insignificant additional term (on the scale of a few meV) when compared with the first-order case. Hence, the original expression for E using the two heating rates method can be used with excellent accuracy in the case of MO glow peaks. In addition, we derived a simple analytical expression for the MO parameter. The present procedure has the advantage that the MO parameter can now be evaluated using analytical expression instead of using the graphical representation between the geometrical factor and the MO parameter as given by the existing peak shape methods. The applicability of the derived expressions for real samples was demonstrated for the glow curve of Li₂B₄O₇:Mn single crystal. The obtained parameters compare very well with those obtained by glow curve fitting and with the available published data.     

Synthesis,characterization, dielectric and rectification properties of PANI/Nd2O3:Al2O3 nanocomposites

Polyaniline–Nd₂O₃:Al₂O₃ nanocomposites were prepared by in situ oxidative polymerization method using different weight percentages of oxide powders. The prepared nanocomposites were characterized by Fourier transform infrared spectroscopy and X‐ray diffraction for molecular and crystal structures. Scanning electron microscopy and transmission electron microscopy images show the tubular structure of polyaniline nanocomposite with embedded metal oxides. The electrical conductivity of the nanocomposites increases with increase in temperature as well as with concentration of Nd₂O₃:Al₂O₃ particles in polyaniline. This is because of the hopping of charge polarons and extended chain length of the nanocomposites as evidenced by the negative thermal coefficient (NTC) characteristic. A high NTC value of 2.67 was found in nanocomposites with 15 wt% of oxide particles. These nanocomposites show low dielectric constant and dielectric loss; the electrical conductivity is higher than 0.3 S/cm as confirmed by Cole–Cole plot that indicates a decrease in both grain resistance and bulk resistance of the nanocomposites. The current–voltage and capacitance–voltage measurements were also carried out. The carrier mobility μ values of pure polyaniline and nanocomposites were found to be 4.27 × 10^?3 and 1.45 × 10^–2 H.M^?1, respectively. A significant enhancement in carrier mobility was observed in comparison with the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Charge transfer complexes of some oxazolones with iodine.

Molecular charge-transfer (CT) complexes of some oxazolone derivatives with sigma-electron acceptor iodine have been investigated spectrophotometrically in CH2Cl2 at 20 degrees C. Stability constants of the CT complexes formed were computed and discussed in terms of the donor molecular structure and solvent polarity. The thermodynamic parameters of complex formation were determined and discussed. The solid CT complexes have been synthesized and characterized. It was deduced that the complexes formed are of strong n-sigma kind.