Epsilon-Ritz Method for Solving a Class of Fractional Constrained Optimization Problems

In this paper, epsilon and Ritz methods are applied for solving a general class of fractional constrained optimization problems. The goal is to minimize a functional subject to a number of constraints. The functional and constraints can have multiple dependent variables, multiorder fractional derivatives, and a group of initial and boundary conditions. The fractional derivative in the problem is in the Caputo sense. The constrained optimization problems include isoperimetric fractional variational problems (IFVPs) and fractional optimal control problems (FOCPs). In the presented approach, first by implementing epsilon method, we transform the given constrained optimization problem into an unconstrained problem, then by applying Ritz method and polynomial basis functions, we reduce the optimization problem to the problem of optimizing a real value function. The choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed. The convergence of the method is analytically studied and some illustrative examples including IFVPs and FOCPs are presented to demonstrate validity and applicability of the new technique.     

Micron and Submicron-Sized Whey Protein–Pectin Aggregates Generated Via Alkali-Catalyzed Chemical Crosslinking

Citric acid was used to crosslink whey proteins and sugar beet pectin at 50°C with the aid of sodium hydroxide as catalyst. The effects of the pH of biopolymers mixed solution and the duration of the crosslinking process on various characteristics of generated particles were studied. Although the majority of the generated aggregates were of submicron size, particles as small as 59 nm were present. The crosslinking duration did not affect the size of aggregates; however, the samples crosslinked at pH 4.2 were greater than those obtained at pH 7.0. Scanning electron microscopy images revealed that aggregates were not uniformly shaped; differential scanning calorimetry indicated that conjugate whey protein–pectin aggregates had greater thermal stabilities than their parent individual biopolymers. The occurrence of crosslinkages was confirmed by the results of Fourier transform infrared spectroscopy.     

Ab initio and DFT studies on 1-(thionitrosomethylene) hydrazine: conformers, energies, and intramolecular hydrogen-bond strength

In the current study, we present an intramolecular HB, molecular structure, π-electrons delocalization and vibrational frequencies analysis of 25 possible conformers of 1-(thionitrosomethylene) hydrazine by means of DFT (B3LYP), MP2 methods in conjunction with the 6-311++G** and augmented correlation-consistent polarized-valence triple-zeta basis sets and G2MP2 theoretical level. The influence of the solvent on the stability order of conformers and the strength of intramolecular hydrogen-bonding was considered using the Tomasi’s polarized continuum model. Statistical analyses of quantitative definitions of aromaticity, nucleus independent chemical shift, harmonic oscillator model of aromaticity, aromatic fluctuation index, and the π-electron delocalization parameter (Q) as a geometrical indicator of a local aromaticity, evaluated for this conformers. Further verification of the obtained transition state structures were implemented via intrinsic reaction coordinate (IRC) analysis. Calculations of the ¹H NMR chemical shift at GIAO/B3LYP/6-311++G** levels of theory are also presented. The calculated highest occupied molecular orbital (MO) and lowest unoccupied MO energies show that charge transfer occur within the molecule. Hydrogen-bond energies for H-bonded conformers were obtained from Espinosa method and the natural bond orbital theory and the atoms in molecules theory were also applied to get a more precise insight into the nature of such H-bond interactions.     

Electrodeposition of Cobalt Oxide Nanostructure on the Glassy Carbon Electrode for Electrocatalytic Determination of para‐Nitrophenol

Cobalt oxide nanostructure (CoO_xNS) deposited on the glassy carbon (GC) electrode surface is proposed as a novel electrocatalytic system for the reduction of para‐Nitrophenol. Cyclic voltammetry, electrochemical impedance spectroscopy, atomic force microscopy and scanning electron microscopy were used for characterization of deposited CoO_xNS. CoO_xNS deposited by cycling at positive potentials (0 to +1.3 V) show less charge‐transfer resistance (Rct) and more catalytic activity for the electroreduction of p‐nitrophenol compared to those CoO_xNS obtained by scanning the applied potential throughout a negative V range. The GC/CoO_xNS electrode showed good electrocatalytic activity toward the reduction of p‐nitrophenol at different pH values.     

Molecular structure and bonding character of mono and divalent metal cations (Li+, Na+, K+, Be2+, Mg2+, and Ca2+) with substituted benzene derivatives: AIM,NBO, and NMR analyses

Cation–π complexes between several cations (Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺) and different π-systems such as para-substituted (F, Cl, OH, SH, CH₃, and NH₂) benzene derivatives have been investigated by UB3LYP method using 6-311++G** basis set in the gas phase and the water solution. The ions have shown cation–π interaction with the aromatic motifs. Vibrational frequencies and physical properties such as dipole moment, chemical potential, and chemical hardness of these compounds have been systematically explored. The natural bond orbital analysis and the Bader’s quantum theory of atoms in molecules are also used to elucidate the interaction characteristics of the investigated complexes. The aromaticity is measured using several well-established indices of aromaticity such as NICS, HOMA, PDI, FLU, and FLUπ. The MEP is given the visual representation of the chemically active sites and comparative reactivity of atoms. Furthermore, the effects of interactions on NMR data have been used to more investigation of the studied compounds.     

Adaptive synchronization of new fractional‐order chaotic systems with fractional adaption laws based on risk analysis

In this paper, a new fractional‐order chaotic system and an adaptive synchronization of fractional‐order chaotic system are proposed. Parameters adaption laws are obtained to design adaptive controllers using Lyapunov stability theory of fractional‐order system. Finally, reliability of designed controllers and risk analysis of adaptive synchronization problem are formulated and, risk of using the proposed controllers in presences of external disturbances are demonstrated. Also, risk of controllers are reduced using an optimizing method. Numerical examples are used to verify the performance of the proposed controllers.     

Synthesis of two new tripodal ligands and their cyclocondensation with 2-[2-(2-formylphenoxy)ethoxy]benzaldehyde in the presence of manganese(II) and cadmium(II) metal ions

Two new asymmetric tripodal tetraamine ligands, 2-((bis(2-aminoethyl)amino)methyl)benzenamine (L²) and 2-(((2-aminoethyl)(3-aminopropyl)amino)methyl)benzenamine (L³) were synthesized and characterized. [1+1] Macrocyclic Schiff-base complexes containing 1,2-diphenoxyethane head units and a 2-aminobenzyl pendant arm, were synthesized as [MnL⁴(MeOH)](ClO₄)₂ (1), [MnL⁵(MeOH)](ClO₄)₂ (2), [CdL⁴(H₂O)](NO₃)₂ (3) and [CdL⁵(H₂O)](NO₃)₂ (4) from the metal ion templated cyclocondensation reactions of 2-[2-(2-formylphenoxy)ethoxy]benzaldehyde with the (L²) or (L³) tripodal tetraamine ligands. The crystal structure determination of (1) and (4) showed that the complex cations that had formed consisted of pentagonal bipyramidally coordinated Mn(II) and Cd(II) ions, centrally located in a N₃O₂ macrocycle, with one 2-aminobenzyl pendant arm. Supporting ab initio HF-MO calculations have been undertaken using the standard 3-21G^∗ and 6-31G^∗ basis sets.     

Application of Multivariate Calibration Techniques to Simultaneous Spectrophotometric Determination of Copper and Iron Using 1‐(2‐Pyridylazo)‐2‐naphthol in AOT Micellar Solution

Multivariate calibration models (PCR and PLS) were developed for simultaneous determination of Fe(III) and Cu(II) with 1‐(2‐pyridylazo)‐2‐naphthol and AOT as chromogenic reagent and micellizing agent, respectively. In the presence of AOT the spectrum of Fe(III)‐PAN complex was shifted to higher wavelength and the overlapping with Cu‐PAN spectrum decreased. It seems that this anionic surfactant enters the structure of the Fe‐PAN complex to cause a shift in the absorption spectrum of it. The parameters controlling behavior of the systems were investigated and optimum conditions were selected. Sixteen ternary mixtures were selected as the calibration set. To select the number of factors in PCR and PLS algorithms, a cross validation method, leaving out one sample at a time, was employed. The calibration models were validated with 8 synthetic mixtures containing the metal ions in different proportions that were randomly designed. The best calibration model was obtained by using PLS regression. The method was successfully applied to simultaneous determination of copper and iron in biological samples.     

Synthesis of functional polyethylene graft copolymers by nitroxide‐mediated living radical polymerization

This paper describes a new method to prepare graft copolymers, such as polyethylene‐g‐polystyrene (PE‐g‐PS), with a relatively well‐controlled reaction mechanism. The chemistry involves a transformation process from the metallocene copolymerization of ethylene and m,p‐methylstyrene (m,p‐MS) to nitroxide‐mediated “living” free radical polymerization (LRFP) of styrene. The metallocene catalysis produces ethylene‐co‐m,p‐methylstyrene (EMS) random copolymers. Next, 1‐hydroxyl‐2,2,6,6‐tetramethylpiperidine (HO‐TEMPO) was synthesized by the reduction of TEMPO with sodium ascorbate. The macroinitiator (EMS‐TEMPO) was synthesized with the bromination reaction of EMS, and the following nucleofilic reaction with this functional nitroxyl compound. The resulting macroinitiator (EMS‐TEMPO) for LRFP was then heated in the presence of styrene to form graft copolymer. DSC, ¹H‐NMR, FTIR spectroscopy were employed to investigate the structure of the polymers. The results of Molau test showed that PE‐g‐PS could be a potential good compatilizer. Copyright © 2008 John Wiley & Sons, Ltd.