Understanding and improving direct UV detection of monosaccharides and disaccharides in free solution capillary electrophoresis

Direct UV detection of carbohydrates in free solution capillary electrophoresis at 270 nm is made possible by a photo-oxidation reaction. Glucose, rhamnose and xylose were shown to have unique UV absorption spectra hypothesizing different UV absorbing intermediates for their respective photo-oxidation. NMR spectroscopy of the photo-oxidation end products proved they consisted of carboxylates and not malondialdehyde as previously theorized and that oxygen thus plays a key role in the photo-oxidation pathway. Adding the photo-initiator Irgacure^® 2959 in the background electrolyte increased sensitivity by 40% at an optimum concentration of 1 × 10⁻⁴ mM and 1 × 10⁻⁸ mM for conventional 50 μm i.d. capillaries and for the corresponding extended light path capillaries, respectively.     

Finite-difference solution of Poisson's equation in rectangles of arbitrary proportions

The recently devised sixth order method for solving difference analogues of Poisson's equation affords much economy of computing effort if squares can be used for the grid elements. However, some developments result in rectangles with one side an irrational multiple of the other, for which the grid elements cannot be squares. A method is presented for handling this situation.

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Zusammenfassung Die vor kurzem hergeleitete Methode sechster Ordnung für die Lösung der Poissonschen Differentialgleichung analogen Differenzengleichungen führt zu grosser Ökonomie im Rechenaufwand, falls man Quadrate für die Netzelemente benutzen kann. In gewissen Situationen hat man es jedoch mit Rechtecken zu tun, deren eine Seite ein irrationales Vielfaches der anderen Seite ist, für die die Netzelemente also keine Quadrate sein können. Eine Methode zur Handhabung solcher Situationen wird angegeben.

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The author wishes to acknowledge the sponsorship of the United States Army under Contract No. DAAG29-75-C-0024 and of the Science Research Council under grant B/RG 4121 at Brunel University.     

Effect of discontinuous boundary conditions on finite-difference solutions

If one is solving a Laplace differential equation by the standard 5-point or 9-point difference approximation, a discontinuity of the boundary values will cause the approximate solution to be in error in the interior. The amount and nature of these errors is discussed, and it is shown that a properly chosen 9-point approximation yields greater accuracy than a 5-point approximation for certain problems of this type.

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Zusammenfassung Wenn man die Laplace'sche Differentialgleichung mit den üblichen Differenzenverfahren mit 5 oder 9 Stützstellen löst, dann erzeugt eine Unstetigkeit in den Randwerten einen gewissen Fehler der Näherungsfunktion im Innern. Die Grösse und das Verhalten dieser Fehler werden untersucht und es wird gezeigt, dass bei gewissen Problemen dieser Art eine zweckmässig gewählte Approximation mit 9 Stützstellen höhere Genauigkeit gibt als eine Approximation mit 5 Stützstellen.

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Sponsored by the United States Army under Contract No. DAAG29-75-C-0024.     

Reliable determination of amidicity in acyclic amides and lactams

Two independent computational methods have been used for determination of amide resonance stabilization and amidicities relative to N,N-dimethylacetamide for a wide range of acyclic and cyclic amides. The first method utilizes carbonyl substitution nitrogen atom replacement (COSNAR). The second, new approach involves determination of the difference in amide resonance between N,N-dimethylacetamide and the target amide using an isodesmic trans-amidation process and is calibrated relative to 1-aza-2-adamantanone with zero amidicity and N,N-dimethylacetamide with 100% amidicity. Results indicate excellent coherence between the methods, which must be regarded as more reliable than a recently reported approach to amidicities based upon enthalpies of hydrogenation. Data for acyclic planar and twisted amides are predictable on the basis of the degrees of pyramidalization at nitrogen and twisting about the C-N bonds. Monocyclic lactams are predicted to have amidicities at least as high as N,N-dimethylacetamide, and the β-lactam system is planar with greater amide resonance than that of N,N-dimethylacetamide. Bicyclic penam/em and cepham/em scaffolds lose some amidicity in line with the degree of strain-induced pyramidalization at the bridgehead nitrogen and twist about the amide bond, but the most puckered penem system still retains substantial amidicity equivalent to 73% that of N,N-dimethylacetamide.     

Debating the role of econophysics

Research in econophysics has been going on for more than a decade with considerable publicity in some of the leading general science journals. Strong claims have been made by some advocates regarding its reputed superiority to economics, with arguments that in fact the teaching of microeconomics and macroeconomics as they are currently constituted should cease and be replaced by appropriate courses in mathematics, physics, and some other harder sciences. The lack of invariance principles in economics and the failure of economists to deal properly with certain empirical regularities are held against it in this line of argument. Responding arguments address four points: (a) that many econophysicists lack awareness of what has been done in economics and thus sometimes claim a greater degree of originality and innovativeness in their work than is deserved, (b) that econophysicists do not use as sufficiently rigorous or sophisticated statistical methodology as econometricians, (c) that econophysicists search for universal empirical regularities in economics that probably do not exist, and (d) that the theoretical models they adduce to explain empirical phenomena have many difficulties and limits. This article examines the arguments and concludes that nonlinear dynamics and entropy concepts may provide a productive way forward.     

Endogenous chaotic dynamics in transitional economies

This paper examines a model of labor market dynamics in an economy undergoing transition from command socialism to market capitalism. State sector layoffs are modeled as a function of forecasts made by state planners of private sector wages where the laidoff workers are to be re-employed. The state switches between using a high information cost perfect forecast and a free naive forecast in a system that resembles a cobweb supply-demand model. Under certain specifications and parameter values chaotic dynamics are shown to endogenously emerge along with several other varieties of complex dynamics including strange attractors, coexistence of infinitely many stable cycles, cascades of infinitely many period doubling bifurcations and fractal basin boundaries between coexisting non-chaotic attractors.     

SOFT X-RAY SCANNING MICROSCOPY: ITS PRACTICAL USE FOR ELEMENTAL MAPPING AT THE NSLS U15 BEAMLINE

Scanning soft X-ray microscopy offers several advantages over other forms of X-ray microscopy. It subjects the specimen to the lower doses of radiation and by digitally recording the image, gives direct quantitative information on the absorption of the specimen as a function of position. Elemental maps can be produced easily by comparing images taken at different wavelengths, chosen to exploit X-ray absorption edges or resonances. This technique was used to explore the distribution of calcium in 0.2 μm-thick bone specimens, detecting concentrations of 5% by weight, with a spatial resolution of 0.2 μm. Progress in X-ray sources in the form of undulators and in X-ray optics indicates that soon the range of elements that can be mapped will be extended and the spatial resolution and elemental sensitivity will be improved by an order of magnitude.     

Speculations on Nonlinear Speculative Bubbles

This paper reviews a variety of issues related to speculative bubbles, especially those involving nonlinear dynamics. Models of irrational bubbles, rational bubbles, and bubbles arising from heterogeneous agents with varying degrees of knowledge or rationality are examined. The latter are shown to be prone to nonlinear dynamics with catastrophic discontinuities, chaos, and other forms of complex phenomena. Empirical evidence regarding the existence of bubbles in various markets is reviewed, eventually examining strong evidence in closed-end country mutual funds markets.