A Weighted Simplex Procedure for the Solution of Simultaneous Non-Linear Equations

The Weighted Simplex procedure, a version of the secant algorithm,provides an alternative to the Newton-Raphson procedure in thesolution of a set of non-linear equations. The results of trialsshow that, given a sufficiently good initial approximation toa solution, the two procedures converge with comparable efficiencies.Unlike the Newton-Raphson procedure the Weighted Simplex proceduredoes not involve the computation of partial derivatives.     

Rapid freeze-quench 57Fe Mössbauer spectroscopy: monitoring changes of an iron-containing active site during a biochemical reaction

Nuclear gamma resonance spectroscopy, also known as M?ssbauer spectroscopy, is a technique that probes transitions between the nuclear ground state and a low-lying nuclear excited state. The nucleus most amenable to M?ssbauer spectroscopy is 57Fe, and 57Fe M?ssbauer spectroscopy provides detailed information about the chemical environment and electronic structure of iron. Iron is by far the most structurally and functionally diverse metal ion in biology, and 57Fe M?ssbauer spectroscopy has played an important role in the elucidation of its biochemistry. In this article, we give a brief introduction to the technique and then focus on two recent exciting developments pertaining to the application of 57Fe M?ssbauer spectroscopy in biochemistry. The first is the use of the rapid freeze-quench method in conjunction with M?ssbauer spectroscopy to monitor changes at the Fe site during a biochemical reaction. This method has allowed for trapping and subsequent detailed spectroscopic characterization of reactive intermediates and thus has provided unique insight into the reaction mechanisms of Fe-containing enzymes. We outline the methodology using two examples: (1) oxygen activation by the non-heme diiron enzymes and (2) oxygen activation by taurine:alpha-ketoglutarate dioxygenase (TauD). The second development concerns the calculation of M?ssbauer parameters using density functional theory (DFT) methods. By using the example of TauD, we show that comparison of experimental M?ssbauer parameters with those obtained from calculations on model systems can be used to provide insight into the structure of a reaction intermediate.     

Crystal chemistry of VAPOL

Ligands employed in enantioselective catalysis are capable of displaying rich phase behavior that can significantly impact their properties, both structural and physical. To illuminate these issues in a model system, the solid-state structure and properties of the vaulted biaryl ligand VAPOL were investigated. Racemic VAPOL and solvates with toluene and ethyl acetate were structurally characterized. In addition, two polymorphs of (S)-VAPOL were found, and the crystal packing in these and a very stable CH(2)Cl(2) solvate was elucidated. In contrast to BINOL, the unsolvated forms of the ligand lack classical hydrogen-bonding motifs. Remarkably, the melting point of racemic VAPOL is 86 degrees C higher than that of (S)-VAPOL form I, and there is a 2.0 kcal/mol difference in stability at room temperature, favoring the racemate. These values are at the upper end of those observed in the literature for differences between a racemic/chiral pair.     

Green chemical functionalization of single-walled carbon nanotubes in ionic liquids

Single walled carbon nanotubes (SWNTs) are exfoliated and functionalized predominantly as individuals by grinding them for minutes at room temperature with aryldiazonium salts in the presence of ionic liquids (ILs) and K(2)CO(3). This constitutes an extremely rapid and mild green chemical functionalization process for obtaining the individualized nanotube structures. A number of ILs and various reaction conditions were surveyed. Raman, XPS, UV/vis/NIR spectroscopies, thermogravimetric analysis, and atomic force and transmission electron microscopies were used to characterize the products.     

Crystalline polymorph selection and discovery with polymer heteronuclei

The discovery and selective production of crystalline polymorphs, an outstanding problem in solid-state chemistry, is of great importance industrially in, for example, the manufacture of pharmaceuticals and pigments. Despite considerable efforts, no reliable method exists to produce all of the stable polymorphs of a given compound. Herein, we report methodology to control the phenomenon of crystal polymorphism through the use of diverse libraries of polymer heteronuclei including both commercially available polymers and combinatorially synthesized cross-linked polymers. This new approach for exploring polymorph space offers the advantage of high throughput crystallization to discover multiple polymorphs combined with the ability to selectively produce a given form from a single solvent and temperature condition by simply varying the nature of the polymer substrate. This technique is successfully demonstrated on the pharmaceuticals acetaminophen, sulfamethoxazole, and carbamazepine and on the pharmaceutical intermediate 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (ROY). High throughput screening, accomplished by optical microscopy and Raman spectroscopy, identified the selective production of the two stable polymorphs of acetaminophen and all six stable forms of ROY. Furthermore, one new form of carbamazepine and two new forms of sulfamethoxazole were discovered; in these cases, single crystals were obtained enabling the structural characterization of two new tetramorphic systems.     

Relative hazard of weapons impulses

Arguments in favor of a theoretically based damage-risk criterion (DRC) for intense noise [G.R. Price, J. Acoust. Soc. Am. 69, 171-177 (1981); 66, 456-465 (1979); J. Acoust. Soc. Am. Suppl. 1 62, S95 (1977)] are further developed here to make a crucial prediction. Based on measured spectral differences, it was predicted that rifle impulses would cause permanent threshold shifts at approximately 9 dB lower peak pressures than cannon impulses. In contrast, DRCs in use in the world predict that the cannon would be more hazardous than the rifle by 7 to 10 dB. Electrophysiological measures of sensitivity were used in 38 cats (76 ears) which were exposed to 60 impulses, approximately 3 s apart, at various peak pressures, from either a rifle or a 105-mm Howitzer. Hearing changes were followed until recovery was complete (2 months). Permanent threshold shifts began at about 140 dB for rifle impulses and 150-155 dB for cannon impulses, confirming the prediction and supporting the contention that there is a spectrally dependent critical level for the ear at high intensities. Implications for present DRCs and future risk assessment schemes are discussed.     

Solving Goal-Programming Manpower Models Using Advanced Network Codes

This paper shows that a certain class of manpower systems that are often modelled using goal programming can also be modelled as capacitated transshipment problems. The goal programming structure can be preserved in most cases through careful definition of the flow-cost function and through the use of multiple arcs in the network. This latter feature is made practical through the use of advanced network codes, such as GNET, that are now available. Solution times and costs are significantly lower than those obtained with the original goal programming formulation through the use of generalized linear programming codes.