Two-dimensional1H and13C NMR spectroscopy and the structural aspects of amylose and amylopectin

Summary A complete assignment of the¹³C and¹H NMR signals of amylose dissolved in dimethylsulfoxide was achieved using two-dimensional H-H and C-H correlated spectroscopy and deuterium exchange. The same methods together with an INEPT experiment provided the assignments of the¹H and¹³C NMR signals of the amylose type glucan units, the branch end glucan fragments, and a few assignments of nuclei within the branching glucan units of amylopectin dissolved in dimethylsulfoxide. From these assignments and from the integration of pertinent proton signals the branching degrees of amylose and amylopectin were derived to amount to 3.9 and 8–9%.

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Zweidimensionale¹H und¹³C-NMR-Spektroskopie und die strukturellen Aspekte von Amylose und Amylopektin

Zusammenfassung Die vollständige Zuordnung der¹³C- und¹H-NMR-Signale von in Dimethylsulfoxid gelöster Amylose konnte mit Hilfe zweidimensionaler H-H- und C-H-Korrelationsspektroskopie und Deuteriumaustausch erzielt werden. Die gleichen Methoden sowie ein INEPT-Experiment ermöglichten auch die Zuordnung der¹³C- und¹H-NMR-Signale der amylosischen Glucaneinheiten, der Verzweigungsendfragmente und einzelner Kerne im Bereich der Verzweigungsstellen von in Dimethylsulfoxid gelöstem Amylopektin. Aus diesen Zuordnungen und der Integration entsprechender Protonensignale konnte ein Verzweigungsgrad von Amylose und Amylopektin von 3.9 und 8–9% abgeleitet werden.

     

The Surgical Separation of Sets

Given a pair of finite disjoint setsA andB inR ⁿ, a fundamental problem with many important applications isto efficiently determine a hyperplaneH(w,) which separates these sets when they are separable, or nearly separates themwhen they are not. We seek a hyperplane which minimizes a natural errormeasure in the latter case, and so will surgically separate the sets. Whenthe sets are separable in a strong sense, we show that the problem is aconvex program with a unique solution, which has been investigated byothers. Using the KKT conditions, we improve on an existing algorithm. Whenthe sets are not separable, the problem is nonconvex, generally with properlocal solutions, and we solve an equivalent problem by Branch and Bound.Numerical results are presented.     

On Mad and Comedians

A popular robust measure of dispersion of a random variable (rv) X is the median absolute deviation from the median med(|X - med(X)|), MAD for short, which is based on the median med(X) of X. By choosing Y = X, the MAD turns out to be a special case of the comedian med((X - med(X))(Y - med(Y))), which is a robust measure of covariance between rvs X and Y. We investigate the comedian in detail, in particular in the normal case, and establish strong consistency and asymptotic normality of empirical counterparts. This leads to a robust competitor of the coefficient of correlation as an asymptotic level--statistic for testing independence of X and Y. An example shows the weird fact that knowledge of the population med(X) does not necessarily pay (in the sense of asymptotic relative efficiency) when estimating the MAD.     

Bounds on a trauma outcome function via optimization

One measure of the effectiveness of institutional trauma and burn management based on collected patient data involves the computation of a standard normal Z statistic. A potential weakness of the measure arises from incomplete patient data. In this paper, we apply methods of fractional programming and global optimization to efficiently calculate bounds on the computed effectiveness of an institution. The measure of effectiveness (i.e., the trauma outcome function) is briefly described, the optimization problems associated with its upper and lower bounds are defined and characterized, and appropriate solution procedures are developed. We solve an example problem to illustrate the method.