An Exact Reformulation Algorithm for Large Nonconvex NLPs Involving Bilinear Terms

Many nonconvex nonlinear programming (NLP) problems of practical interest involve bilinear terms and linear constraints, as well as, potentially, other convex and nonconvex terms and constraints. In such cases, it may be possible to augment the formulation with additional linear constraints (a subset of Reformulation-Linearization Technique constraints) which do not affect the feasible region of the original NLP but tighten that of its convex relaxation to the extent that some bilinear terms may be dropped from the problem formulation. We present an efficient graph-theoretical algorithm for effecting such exact reformulations of large, sparse NLPs. The global solution of the reformulated problem using spatial Branch-and Bound algorithms is usually significantly faster than that of the original NLP. We illustrate this point by applying our algorithm to a set of pooling and blending global optimization problems.     

Modeling of colloid and colloid-facilitated contaminant transport in a two-dimensional fracture with spatially variable aperture

Mathematical models are developed for two-dimensional transient transport of colloids, and cotransport of contaminant/colloids in a fracture-rock matrix system with spatially variable fracture aperture. The aperture in the fracture plane is considered as a lognormally distributed random variable with spatial fluctuations described by an exponential autocovariance function. Colloids are envisioned to irreversibly deposit onto fracture surfaces without penetrating the rock matrix; whereas, the contaminant is assumed to decay, sorb onto fracture surfaces and onto colloidal particles, as well as to diffuse into the rock matrix. The governing stochastic transport equations are solved numerically for each realization of the aperture fluctuations by a fully implicit finite difference scheme. Emphasis is given on the effects of variable aperture on colloid and colloid-facilitated contaminant transport. Simulated breakthrough curves of ensemble averages of several realizations show enhanced colloid transport and more pronounced fingering when colloids are subject to size exclusion from regions of small aperture size. Moreover, it is shown that an increase in the fracture aperture fluctuations leads to faster transport and increases dispersion. For the case of contaminant/colloids cotransport it is shown, for the conditions considered in this work, that colloids enhance contaminant mobility and increase contaminant dispersion.Nomenclature b fracture aperture, L - c contaminant concentration in the fracture, M/L³ - c _m contaminant concentration in the rock matrix, M/L³ - c _o source contaminant concentration, M/L³ - c ^* contaminant concentration adsorbed onto fracture surfaces, M/L² - c _m ^* contaminant concentration adsorbed inside the rock matrix, M/M - d _p colloidal particle diameter, L - D hydrodynamic dispersion coefficient dyadic, L²/t - D Brownian diffusion coefficient for colloids and molecular diffusion coefficient for contaminants, L²/t - D _m effective diffusion coefficient in the rock matrix, L²/t - h total head potential in the fracture, L - K _f partition coefficient for contaminant sorption onto fracture surfaces, L - K _m contaminant partition coefficient in the rock matrix, L³/M - K _n partition coefficient for contaminant sorption onto suspended colloids, L - K _n* partition coefficient for contaminant sorption onto deposited colloids, L³/M - _x fracture length in thex-direction, L - _y fracture length in they-direction, L - n colloid concentration in the liquid phase, M/L³ - n _o source colloid concentration, M/L³ - n ^* colloid concentration adsorbed onto fracture surfaces, M/L² - n _max ^* maximum deposited colloid concentration on fracture surfaces, M/L² - N ^* number of deposited colloidal particles per unit surface area of the fracture, 1/L² - N _max ^* maximum number of deposited colloidal particles per unit surface area of the fracture, 1/L² - q ^* diffusive mass flux into the rock matrix, M/L²t - R retardation factor in the fracture - R _m retardation factor in the rock matrix - s contaminant concentration adsorbed on colloids in the liquid phase, M/M - s _o source solid-phase contaminant concentration onto suspended colloids, M/M - s ^* contaminant concentration adsorbed on deposited colloids, M/M - t time, t - U interstitial velocity vector, L/t - x coordinate along the fracture length, L - y coordinate along the fracture width, L - z coordinate perpendicular to the fracture plane, L - area blocked by a deposited colloidal particle, L² - _L longitudinal dispersivity, L - _T transversal dispersivity, L - fluid specific weight, M/L²t² - fraction of the fracture surface physically covered by colloids - gz dummy integration variable - porosity of the rock matrix - colloid deposition coefficient, L - first-order decay coefficient, 1/t - fluid dynamic viscosity, M/Lt - defined in (18) - _b bulk density of the rock matrix, M/L³ - _p colloidal particle density, M/L³ - standard deviation of the lognormally distributed fluctuations of the fracture aperture     

One-pot synthesis of novel fused pentacyclic chromenopyrimidobenzimidazolones and benzimidazolyl-chromenyl-substituted thiazolidinones

The ultrasound promoted synthesis of a number of novel fused pentacyclic chromenopyrimido[1,2-α]benzimidazolones by the one-pot reaction of 3-formylchromones with 2-aminobenzimidazole is described. Moreover, the isolated pentacyclic chromone derivatives upon microwave irradiation with 2-mercaptocarboxylic acids afforded benzimidazolyl-chromenylthiazolidinones incorporating three pharmacophoric heterocycles; the same thiazolidinones were also formed through a multicomponent reaction under microwave irradiation involving 3-formylchromones, aminobenzimidazole and 2-mercaptocarboxylic acids. The structural elucidation of the products was accomplished by 1D and 2D NMR experiments and for thiazolidinones was also confirmed by X-ray crystallographic analysis. Full assignment of all ¹H and ¹³C NMR chemical shifts has been unambiguously achieved. The proposed reaction mechanism is also discussed.     

Characterization of natural resin materials using water adsorption and various advanced techniques

A physicochemical characterization of natural raw resin material was evaluated and reported. The studied material is a natural resin, a natural product from pinus halepensis trees which is collected from the forests of Chalkidiki region of North Greece. The plurality of this product combined with its special property of removing water from commercial liquid fuels commands the detailed physicochemical characterization of this material. In particular, various techniques, such as water adsorption at 22 °C, thermogravimetric analysis, differential scanning calorimetry, Fourier transform infrared spectroscopy and X-ray diffraction, were used in order to evaluate the structural and surface properties of the material. The water adsorption isotherm was also measured and fitted using the Guggenheim, Anderson and De Boer model in order to correlate the water activity characteristics. In addition, the kinetics of the adsorption was also fitted with good accuracy using the exponential Chapman model. Furthermore, as the results show, the natural resin presents good thermal characteristics. Finally, the studied material presents efficient water adsorption properties, up to 246.8 mmol/g, and it can be proposed as a promising dehydration material.     

Water‐Soluble Carbon Nanotubes by Redox Radical Polymerization

Water‐soluble single‐ and multi‐walled carbon nanotubes (CNTs) were prepared by grafting polyacrylamide chains from the graphitic surface via ceric ion‐induced redox radical polymerization. The reducing functionalities were covalently attached to the tubes by peroxide‐assisted radical reaction. The results showed that polymer chains were grafted onto CNTs by the redox process. The redox radical polymerization initiated by carbon nanotube‐bearing functionalities not only provides a powerful strategy for modifying the carbon nanostructures but also gives us the knowledge of their sidewall chemistry.

     

Synchronous fluorescence spectroscopy for quantitative determination of virgin olive oil adulteration with sunflower oil

Adulteration of extra virgin olive oil with sunflower oil is a major issue for the olive oil industry. In this paper, the potential of total synchronous fluorescence (TSyF) spectra to differentiate virgin olive oil from sunflower oil and synchronous fluorescence (SyF) spectra combined with multivariate analysis to assess the adulteration of virgin olive oil are demonstrated. TSyF spectra were acquired by varying the excitation wavelength in the region 270–720 nm and the wavelength interval (Δλ) in the region from 20 to 120 nm. TSyF contour plots for sunflower, in contrast to virgin olive oil, show a fluorescence region in the excitation wavelength range 325–385 nm. Fifteen different virgin olive oil samples were adulterated with sunflower oil at varying levels (0.5–95%) resulting in one hundred and thirty six mixtures. The partial least-squares regression model was used for quantification of the adulteration using wavelength intervals of 20 and 80 nm. This technique is useful for detection of sunflower oil in virgin olive oil at levels down to 3.4% (w/v) in just two and a half minutes using an 80-nm wavelength interval.     

Initial example of a triangular single-molecule magnet from ligand-induced structural distortion of a [MnIII3O]7+ complex

The reaction of [Mn3O(O2CR)6(py)3](ClO4) (R = Me, Et) with methyl 2-pyridyl ketone oxime (mpkoH) in a 1:3 molar ratio in MeOH/MeCN leads to [Mn3O(O2CR)3(mpko)3](ClO4) in 80-90% isolated yield. Ferromagnetic exchange interactions between the three MnIII ions in the nonplanar [MnIII3O]7+ triangular core lead to a spin ground state of S = 6; single-crystal studies reveal the temperature and sweep rate dependent hysteresis loops expected for a single-molecule magnet.     

Modeling the coordination mode of hydroxamate inhibitors in urease: preparation,X-ray crystal structure and spectroscopic characterization of the dinuclear complex [Ni2(O2CMe)(LH)2(tmen)2](O2CMe) · 0.9H2O · 0.6EtOH (LH2 = benzohydroxamic acid; tmen = N,N, N′, N′-tetramethylethylenediamine)

Transition Metal Chemistry - Reaction of [Ni2(H2O)(O2CMe)4(tmen)2], (tmen = N, N, N′, N′-tetramethylethylenediamine) with two equivalents of benzohydroxamic acid (LH2) in H2O/EtOH gives...     

A new ionic strength adjustor for nitrate analysis in waters,soils and plants using ion-selective electrode

A new ionic strength adjustor, ISA (ISA-Pb) composed of 0.02M Pb(CH₃COO)₂–0.01M PbO–0.02M CH₃COOK–0.01M NH₂SO₃H, was tested for the rapid nitrate analysis of waters, soil and plant extracts by means of ion-selective electrode (ISE). It was found that nitrate can be determined accurately and precisely within the concentration range of 5 × 10^–2 M to 2 × 10^–6 M. The proposed ISA-Pb, with a pH of 6.8, controlled the interferences of Cl^–, HCO ₃ ^– , NO ₂ ^– , and organic anions effectively, and gave results comparable to those obtained by the commonly used ISA with Ag₂SO₄ (ISA-Ag) and to well established chemical methods as well. ISA-Pb is much cheaper than ISA-Ag, and can therefore economically replace the latter when ISE is used for nitrate determination.Part of the senior author's doctorate thesis     

Automated sample preparation based on the sequential injection principle. Solid-phase extraction on a molecularly imprinted polymer coupled on-line to high-performance liquid chromatography

A molecularly imprinted polymer (MIP) prepared using caffeine, as a template, was validated as a selective sorbent for solid-phase extraction (SPE), within an automated on-line sample preparation method. The polymer produced was packed in a polypropylene cartridge, which was incorporated in a flow system prior to the HPLC analytical instrumentation. The principle of sequential injection was utilised for a rapid automated and efficient SPE procedure on the MIP. Samples, buffers, washing and elution solvents were introduced to the extraction cartridge via a peristaltic pump and a multi-position valve, both controlled by appropriate software developed in-house. The method was optimised in terms of flow rates, extraction time and volume. After extraction, the final eluent from the extraction cartridge was directed to the injection loop and was subsequently analysed on HPLC. The overall set-up facilitated unattended operation, operation and improved both mixing fluidics and method development flexibility. This system may be readily built in the laboratory and can be further used as an automated platform for on-line sample preparation.