The Morse and Maslov indices for Schrödinger operators

We study the spectrum of Schrödinger operators with matrixvalued potentials, utilizing tools from infinite-dimensional symplectic geometry. Using the spaces of abstract boundary values, we derive relations between the Morse and Maslov indices for a family of operators on a Hilbert space obtained by perturbing a given self-adjoint operator by a smooth family of bounded self-adjoint operators. The abstract results are applied to the Schrödinger operators with θ-periodic, Dirichlet, and Neumann boundary conditions. In particular, we derive an analogue of the Morse-Smale Index Theorem for multi-dimensional Schrödinger operators with periodic potentials. For quasi-convex domains in Rⁿ, we recast the results, connecting the Morse and Maslov indices using the Dirichlet and Neumann traces on the boundary of the domain.     

The Stefan problem of evaporation of a volatile component from a binary liquid mixture

The study is concerned with the Stefan problem of evaporation of a volatile component from its solution with a virtually non-volatile material. The analysis provides an analytical solution to the problem based on mass-transfer fundamentals. Results yield the evaporation rate, interfacial mole fractions, concentration profiles in the gas and liquid phases, and the location of the evaporation front. The analysis can be used to provide the binary liquid diffusion coefficient of the volatile component based on experimental data for the liquid–gas interface position as a function of time. The requirements for such a measurement are discussed in terms of the volatility of the evaporating component and its initial concentration in the liquid mixture. Fig. 1 Gas–liquid interface movement in a partially filled tube

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Hubbing and routing in postal delivery systems

We consider the combined hubbing and routing problem in postal delivery systems and develop an iterative two-stage solution procedure for the problem. In the first stage, hub locations are determined and postal offices are multiply allocated to the hubs. The second stage gives the routes in hub regions that alter the distances between points used in the hub-location problem. The procedure then iterates between two stages by updating the distances used in hubbing in order to produce a route-compatible hub configuration. Computational experience is reported for the test problems taken from the literature. For a case study Turkish postal delivery system data are utilized. As the case study is applied on a road network, a final stage, seeking improvements based on special structures in the routed network, is appended to the two-stage solution procedure.     

Development of New Atom Transfer Radical Polymerization System by Iron (III)‐Metal Salts Without Using any External Initiator and Reducing Agent

Atom transfer radical polymerization (ATRP) catalyzed by high oxidation state metal salts of FeX₃ is developed for the first time in the absence of both external initiator and reducing agent. Methyl methacrylate (MMA) and styrene are polymerized successfully using FeX₃/Phosphorous ligands with well‐controlled molecular weight distributions (=1.5). The molecular weight of the polymers increases with monomer consumption with the progress of time and the polymerization behaviors show a decent ATRP trend. Activators and initiators are suggested to generate in situ by the addition reaction of MMA and one equivalent of FeX₃. The PMMA synthesized from without‐initiator system is characterized by ¹H, ¹³C and DEPT (distortionless enhancement by polarization transfer nuclear magnetic resonance) nuclear magnetic resonance spectroscopy. Chain extension and copolymerization experiments prove the livingness of the obtained polymer.

     

Bifunctional Calix[4]arene Sensor for Pb(II) and Cr2O7 2− Ions

A readily available chromionophore 5,11,17,23-tetra-tert-butyl-25,27-bis(hydrazidecarbonylmethoxy)-26,28-dihydroxycalix[4]arene (HCC4) was employed as a chromogenic sensing probe selective for Pb(II) and Cr₂O₇ ^2? ions among a series of various ions such as Li(I), Na(I), K(I), Rb(I), Ba(II), Sr(II), Al(III), Cd(II), Co(II), Cu(II), Hg(II), Ni(II), Pb(II) and Zn(II) as well as Cr₂O₇ ^2?, CH₃CO₂ ^?, Br^?, Cl^?, F^?, I^?, ClO₄ ^? and NO₃ ^? that have been examined by UV-visible and fluorescence spectroscopic techniques. The HCC4 in DCM-MeCN system forms 2:1 (ligand-metal) complex with Pb(II). It also shows 2:1 stoichiometry with Cr₂O₇ ^2?. The complexation phenomenon has been confirmed by FTIR spectroscopy that favors the selective nature of HCC4 with Pb(II) and Cr₂O₇ ^2?. Thermal gravimetric analysis (TGA) also supports its utility in drastic conditions.     

In-plane and out-of-plane anisotropic magnetoresistances in La1 − x Pb x MnO3 thin films

The temperature and field dependences of in-plane (IP) and out-of-plane (OP) anisotropic magnetoresistances (AMRs) have been measured in La_{1 ? x} Pb _x MnO₃ (LPMO) thin films having different microstructures, namely the single-crystal (SC), nanocrystalline (NC) and polycrystalline (PC) microstructures. The OP AMR, irrespective of the microstructure, is found to be considerably larger than the IP AMR. The magnetization data show that the larger OP AMR arises because magnetization is favoured in the film plane owing to strain anisotropy. In addition, the temperature and field dependences of both IP and OP AMRs are governed by the crystallinity of the films, indicating that the AMRs are strongly influenced by the magnetization process.     

Glycerol: A Promising Benign Solvent for Catalyst‐free One‐pot Multi‐component Synthesis of 1H‐Pyrozolo[1,2‐b]phthalazine‐5,10‐diones and 2H‐Indazolo[2,1‐b]phthalazine‐triones Under Controlled Microwaves Irradiation

A simple green and efficient one‐pot multi‐component synthesis of 1H‐pyrozolo[1,2‐b]phthalazine‐5,10‐diones and 2H‐indazolo[2,1‐b]phthalazine‐triones has been developed utilizing one‐pot multi‐component reaction of aromatic aldehydes, active methylene reagents, phthalic anhydride, and hydrazine hydrate or alternatively phthalhydrazide in glycerol without catalyst under controlled microwave heating. The current synthetic protocol offers several advantages such as excellent yields, high EcoScale and atom economy, simple working up reactants and products, and the absence of hazardous catalysts or solvents.     

Naked Eye Detection of Carbonate,Hydroxide, and Cyanide Ions with 1,4′‐Diazaflavonium Bromides: A Simple Spectrophotometric Method for Cyanide Determination

Anion sensor properties of N‐alkyl‐substituted 1,4′‐diazaflavonium bromides in methanol–water were evaluated by UV–vis spectrometry. Pronounced changes were observed in the absorption spectra of all compounds for only OH^?, CO₃^2?, and CN^? among F^?, Cl^?, Br^?, I^?, OH^?, CO₃^2?, NO₃^?, PO₄^3?, CN^?, SO₄^2?, HSO₄^?, HCO₃^?, SCN^?, NO₂^?, and P₂O₇^2? ions. Two new absorption bands at 385 and 685 nm accompanying the distinct color change for OH^?, CO₃^2?, and CN^? ions were observed in case of all compounds. The color changes were from pink to blue for CO₃^2? and OH^? ions and from pink to purple for CN^? ion. Thanks to the distinct color change, the compounds can be used as selective colorimetric anion sensors. Linear changes of absorbance of N‐heptyl‐substituted compound at 385 nm as a function of the ion concentration were used to determine CN^? ion in water samples. Detection and quantification limits of the proposed method were 0.94 and 2.82 mg/L, respectively.     

Cellulose‐Derived Functional Polyacetal by Cationic Ring‐Opening Polymerization of Levoglucosenyl Methyl Ether

The unsaturated bicyclic acetal levoglucosenyl methyl ether was readily obtained from sustainable feedstock (cellulose) and polymerized by cationic ring‐opening polymerization to produce a semicrystalline thermoplastic unsaturated polyacetal with relatively high apparent molar mass (up to ca. 36 kg mol^?1) and decent dispersity (ca. 1.4). The double bonds along the chain can undergo hydrogenation and thiol–ene reactions as well as crosslinking, thus making this polyacetal potentially interesting as a reactive functional material.     

Optimization of Microwave-Assisted Extraction (MAE) for the Isolation of Antioxidants from Basil (Ocimum basilicum L.) by Response Surface Methodology (RSM)

Abstract

The recovery of antioxidants from basil (Ocimum basilicum L.) was modeled with the aid of response surface methodology (RSM) using microwave-assisted extraction (MAE). Face-centered central design (FCCD) was employed to optimize the MAE operational parameters including the extraction time (1 to 7?min), extraction temperature (30 to 120?°C), solid-to-solvent ratio (0.1 to 0.4), and solvent concentration (20 to 80% ethanol, v/v), and to obtain the best possible combinations of these parameters for a high antioxidant yield from basil. The total antioxidant capacity (TAC) was expressed in trolox (TR) equivalents per gram of dried sample (DS). Three of the operational parameters (temperature, extraction time and solvent concentration) were shown to have significant effect on the extraction efficiency of antioxidants in basil extracts (p?<?0.05). The solvent concentration was shown to be the most significant factor on antioxidant yield obtained by MAE. There was a close relationship between experimental and predicted values using the proposed method. This optimized MAE method shows an application potential for the efficient extraction of antioxidants from basil in the food and pharmaceutical industries.