Trigonometric polynomial approximation in theL 1-norm

Ohne Zusammenfassung     

Beiträge zur Chemie der Pyrrolpigmente, 13. Mitt. Die thermische Stabilität der geometrischen Isomeren von Arylmethylidenpyrrolinonen

From kinetic studies and the investigation of several model compounds it has been deduced that the interconversion of (E)- and (Z)-arylmethylidenepyrrolinones proceeds via a thermal accessible dipolar (singlet) state thus being analogous to the many known thermal (Z)—(E)-isomerizations. There is a pronounced dependence of this reaction on the solvent and the substitution of the aryl part of the molecule; the equilibrium position between (Z)- and (E)-isomers is determined by the substituent in position 4 of the pyrrolinone ring.

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12. Mitt.:H. Falk undJ. M. Ribó, Mh. Chem.107, 307 (1976).     

Zur simultanen Diophantischen Approximation. I

An important problem in the field of Diophantine Approximation was solved in 1891 byHurwitz. He could show that any irrational number can be approximated by infinitely many rationals in such a way that the modulus of the difference multiplied with the square of the denominator is less than 5^–1/2, and there 5^–1/2 is best possible.-The generalization of this problem in the direction of simultaneous Diophantine Approximation is still unsolved.Furtwängler in 1925 gave lower bounds for the maximum difference, conjecturing that these were best possible.-Here it is shown that in the two dimensional caseFurtwängler's bounds are indeed best possible for certain irrationals lying in cubic number fields which are not totally real. Yet by considering totally real cubic fields we are led to replaceFurtwängler's conjecture by a new one.     

An accurate model for power DMOSFETs including interelectrodecapacitances

A SPICE-compatible circuit model for power MOSFETs is presented. It is based on device physics and uses a subcircuit representation. The interelectrode capacitances are modeled accurately as nonlinear functions of the applied biases. Various second-order effects relating to the gate capacitance model are discussed, and strategies are presented to include them in the model. The model parameters can be obtained from device measurements. The model is verified by comparing measured and simulated waveforms from a gate charge test circuit     

A necessary and sufficient condition for the aggregation of linear diophantine equations

Summary The set of the integer values a linear form can take may be called its spectrum. Aggregating two equations means establishing a linear combination of the two left hand side spectra, the coefficients of which are the aggregation weights. If and only if this linear combination does not contain any spectral correlation point other than the right hand side vector, the equation found by aggregation is equivalent to the two given ones.Methods for calculating the spectrum and the spectral correlation set are given.

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Zusammenfassung Der Wertevorrat einer Diophantischen Linearform möge als deren Spektrum bezeichnet werden. Die Zusammenfassung zweier Diophantischer Gleichungen läuft auf die Bildung einer Linearkombination der Spektren hinaus, die zu den beiden auf der linken Seite stehenden Linearformen gehören. Die Koffizienten der Linearkombination sind gleich den für die Zusammenfassung verwendeten Gewichten. Wenn und nur wenn die erwähnte Linearkombination ausser dem Punkt, dessen Koordinaten die auf der rechten Seite des Gleichungssystems stehenden Zahlen sind, keine anderen Spektral-Korrelationspunkte enthält, ist die durch Zusammenfassung gebildete Gleichung äquivalent dem System der beiden Ausgangsgleichungen.Methoden für die Berechnung von einfachen und korrelierten Spektren werden gegeben.

     

A generalization of the arithmetic-geometric mean inequality and an application to finite sequences of zeros and ones

We generalize the arithmetic-geometric mean inequality to a new class of polynomials and give a combinatorial application. The work for this research was supported by the Max Kade Foundation.