Improved Gram–Schmidt Type Downdating Methods

The problem of deleting a row from a Q–R factorization (called downdating) using Gram–Schmidt orthogonalization is intimately connected to using classical iterative methods to solve a least squares problem with the orthogonal factor as the coefficient matrix. Past approaches to downdating have focused upon accurate computation of the residual of that least squares problem, then finding a unit vector in the direction of the residual that becomes a new column for the orthogonal factor. It is also important to compute the solution vector of the related least squares problem accurately, as that vector must be used in the downdating process to maintain good backward error in the new factorization. Using this observation, new algorithms are proposed. One of the new algorithms proposed is a modification of one due to Yoo and Park [BIT, 36:161–181, 1996]. That algorithm is shown to be a Gram–Schmidt procedure. Also presented are new results that bound the loss of orthogonality after downdating. An error analysis shows that the proposed algorithms’ behavior in floating point arithmetic is close to their behavior in exact arithmetic. Experiments show that the changes proposed in this paper can have a dramatic impact upon the accuracy of the downdated Q–R decomposition. AMS subject classification (2000) 65F20, 65F25     

Calculation of the salt separation by negatively charged gel-filled membranes

The salt separations of negatively charged gel-filled membranes composed of poly(2-acrylamido-2-methylpropanesulfonic acid) gels anchored within a polypropylene microporous substrate have been determined experimentally and modeled theoretically. The separation of these membranes were calculated by both the Teorell, Meyer and Sievers (TMS) model and the Donnan–Steric Pore (DSP) model coupled with the extended Nernst–Planck equation. For modeling, the membrane effective thickness, effective charge density, and pore radius were either directly measured or calculated from theories without the use of fitting procedures. Good agreement between the experimental measurements and the theoretical calculations of salt separation was observed. For the theoretical calculations, the TMS model is suitable for membranes with moderate gel polymer volume fractions, while the DSP model is more suitable for membranes with high gel polymer volume fractions. Moreover, with a calculated constant effective charge density, the salt separation with different salt concentrations could be accurately predicted. The separation of various other salts could also be predicted with good accuracy.     

Simplex Optimized LC Analysis of Plant Coumarins and Furanocoumarins

Sequential simplex methods are common and efficient optimization techniques applied in analytical chemistry. This study reports on the optimization of LC separation of coumarins using a variable-size simplex algorithm. The solvent systems consisted of methanol, water and tetrahydrofuran. Using an optimized method, seven standard simple coumarins and furanocoumarins derived from plants were successfully separated in one chromatographic run. The mobile phase at the point corresponding to the optimum consisted of 34% MeOH, 59% H₂O and 7% THF. Applying a solvent mixture in this proportion permitted separation of all critical pairs, such as esculetin/scopoletin, scopoletin/umbelliferone, umbelliferone/coumarin and xanthotoxin/psoralen. The retention ratio factors k for coumarins at the optimum of the simplex algorithm lay in the range 1 < k < 4. The optimal conditions assigned to the coumarin standards were then applied to the plant matter: herb of the rue (Ruta graveolens L., Rutae herba), anthodium of the camomile (Chamomilla recutita L., Chamomillae anthodium), herb of the southernwood (Artemisia abrotanum L., Abrotani herba), and radix of the lovage (Levisticum officinale K., Levistici radix). The validity of the method was confirmed with respect to these samples.     

Physicochemical and Adsorption Characteristics of Divinylbenzene-co-Triethoxyvinylsilane Microspheres as Materials for the Removal of Organic Compounds

In this work, organic-inorganic materials with spherical shape consisting of divinylbenzene (DVB) and triethoxyvinylsilane (TEVS) were synthesized and investigated by different complementary techniques. The obtained microspheres may be applied as sorbent systems for the purification of organic compounds from water. The hybrid microspheres combine the properties of the constituents depending on the morphologies and interfacial bonding. In this work, the influence of the molar ratio composition of crosslinked monomer (DVB) and silane coupling agent (TEVS) (DVB:TEVS molar ratios: 1:2, 1:1 and 2:1) on the morphology and quality of organic-inorganic materials have been examined. The materials were analysed using small angle X-ray scattering (SAXS) analysis, low-temperature nitrogen sorption, scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) to provide information on their structural and surface properties. Moreover, thermal analysis was performed to characterize the thermal stability of the studied materials and the adsorbent-adsorbate interactions, while adsorption kinetic studies proved the utility of the synthesized adsorbents for water and wastewater treatment.     

Enantiomeric Enrichments via the Self‐Disproportionation of Enantiomers (SDE) by Achiral,Gravity‐Driven Column Chromatography: a Case Study Using N‐(1‐Phenylethyl)acetamide for Optimizing the Enantiomerically Pure Yield and Magnitude of the SDE

This work explores the self‐disproportionation of enantiomers (SDE) via achiral, gravity‐driven column chromatography as typically used in laboratory settings for the purpose of enantiomeric enrichment using N‐(1‐phenylethyl)acetamide (PEA) as a case study. The major finding of this work is the very large magnitude of the SDE for PEA across a variety of conditions and broad range of starting ee values, thereby facilitating a simple, reliable, and predictable means of obtaining enantiomerically pure samples. For example, starting with a sample of PEA of ee as low as 28%, a single column run yielded an enantiomerically pure sample (>99.9% ee) from the first fractions and a significantly enantiomerically depleted sample (<17% ee) from the final fractions. An assessment of SDE via achiral, gravity‐driven column chromatography was also rendered with regard to the differing objectives that workers might target – a large magnitude of the SDE, obtaining an optimum sample of desired ee, or preparative‐scale separation of the excess enantiomer. Overall, it can be considered that the SDE phenomenon via achiral, gravity‐driven column chromatography – readily applicable in the usual laboratory settings – is a simple and convenient method for enantiomeric enrichment with a high degree of proficiency. Advantages of SDE via achiral, gravity‐driven column chromatography over conventional fractional recrystallization for the enantiomeric enrichment of amides/amines, and applicable also to many other classes of compounds as well, are discussed.     

Mechanistic studies on the reactions of cyanide with a water-soluble Fe(III) porphyrin and their effect on the binding of NO

The reaction of the water-soluble Fe(III)(TMPS) porphyrin with CN(-) in basic solution leads to the stepwise formation of Fe(III)(TMPS)(CN)(H(2)O) and Fe(III)(TMPS)(CN)(2). The kinetics of the reaction of CN(-) with Fe(III)(TMPS)(CN)(H(2)O) was studied as a function of temperature and pressure. The positive value of the activation volume for the formation of Fe(III)(TMPS)(CN)(2) is consistent with the operation of a dissociatively activated mechanism and confirms the six-coordinate nature of the monocyano complex. A good agreement between the rate constants at pH 8 and 9 for the formation of the dicyano complex implies the presence of water in the axial position trans to coordinated cyanide in the monocyano complex and eliminates the existence of Fe(III)(TMPS)(CN)(OH) under the selected reaction conditions. Both Fe(III)(TMPS)(CN)(H(2)O) and Fe(III)(TMPS)(CN)(2) bind nitric oxide (NO) to form the same nitrosyl complex, namely, Fe(II)(TMPS)(CN)(NO(+)). Kinetic studies indicate that nitrosylation of Fe(III)(TMPS)(CN)(2) follows a limiting dissociative mechanism that is supported by the independence of the observed rate constant on [NO] at an appropriately high excess of NO, and the positive values of both the activation parameters ΔS(?) and ΔV(?) found for the reaction under such conditions. The relatively small first-order rate constant for NO binding, namely, (1.54 ± 0.01) × 10(-2) s(-1), correlates with the rate constant for CN(-) release from the Fe(III)(TMPS)(CN)(2) complex, namely, (1.3 ± 0.2) × 10(-2) s(-1) at 20 °C, and supports the proposed nitrosylation mechanism.     

Mass spectrometric study of amino acid–triethylborane chelates

Abstract  Synthesis of chelates from selected l-amino acids and triethylborane, and the mass spectra of the chelates, are described. Conditions for forming dimers between the chelates and the sodium ion are discussed, and structures are proposed for the dimers. Graphical abstract