Bier Spheres and Posets

In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n – 2)-spheres on 2n vertices, as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that “cut across an ideal.” Thus we arrive at a substantial generalization of Bier’s construction: the Bier posets Bier(P, I) of an arbitrary bounded poset P of finite length. In the case of face posets of PL spheres this yields cellular “generalized Bier spheres.” In the case of Eulerian or Cohen–Macaulay posets P we show that the Bier posets Bier(P, I) inherit these properties. In the boolean case originally considered by Bier, we show that all the spheres produced by his construction are shellable, which yields “many shellable spheres,” most of which lack convex realization. Finally, we present simple explicit formulas for the g-vectors of these simplicial spheres and verify that they satisfy a strong form of the g-conjecture for spheres.     

Solving certain singly constrained convex optimization problems in production planning

This paper considers the problem of minimizing a special convex function subject to one linear constraint. Based upon a theorem for lower and upper bounds on the Lagrange multiplier a fully polynomial time approximation scheme is proposed. The efficiency of the algorithm is demonstrated by a computational experiment.     

RPA for the linewidth of the van der Pol Oscillator

The linewidth of then component van der Pol Oxcillator is calculated in random phase approximation. Forn=2 this model describes a single mode laser. This approximation is asymptotically correct for weak and strong pumping and also in the largen limit for all pumping. The result is in good agreement with numerical results forn=2 in the whole range including the threshold. The corresponding vertex renormalized approximation on the other hand yields poor agreement and the wrong asymptotic value in the limit of strong pumping. The reason for this failure is discussed.     

Optimization of the ion-pair high-performance liquid chromatographic separation of purine derivatives in erythrocytes, thymocytes and liver mitochondria

Various methods are described for the analysis of purine derivatives in biological samples by ion-pair high-performance liquid chromatography (HPLC) with both gradient and isocratic systems. A new approach is proposed that is suitable for the separation of nuclei acid constituents in different cells with a specific enzymatic activity pattern. The ion-pair HPLC methods were developed for the analysis of erythrocytes, lymphocytes and mitochondria acid-soluble fractions in clinical and experimental studies of normal and altered nucleotide metabolism. The results of studies of purine metabolite redistribution in mouse liver mitochondria during a 30-min incubation at 37 degrees C and data on purine metabolic alterations in mouse thymocytes during hepatoma growth are discussed.     

Plastizität ohne Thermodynamik?

The theory of the plastic potential may be based on the principle of maximum rate of dissipation work represented by inequality (1.2). The second fundamental theorem of Thermodynamics yields another inequality, (1.1). Since a consistent theory must include both inequalities, the origin of stress space cannot lie outside the yield locus.     

Über einen Versuch zur Berechnung der Fragmentation von β-Lactamen mittels der EHT-Methode

Zusammenfassung Die Fragmentation von -Lactamen ergibt massenspektroskopisch sowie thermisch entweder die Ausgangsverbindungen Keten und Azomethin oder bevorzugt Äthylene und Isocyanate. Dabei brechen jeweils zwei gegenüberliegende Bindungen. Eine Berechnung der Überlappungsenergien im Ring mittels der EHT-Methode zeigt, daß der induktive Einfluß der Substituenten die Richtung des Zerfalls bestimmt. Es kann auch bei anderen Vierring-Ketonen eine bevorzugte Fragmentation des Ketenbestandteiles nachgewiesen werden.

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An attempt to calculate the fragmentation of -lactams by the EHT method

Both mass spectroscopic and thermal fragmentation of -lactams yield either the reactants (ketenes and azomethines), or preferentially ethylenes and isocyanates. In each case two opposite bonds are broken. Calculation of the overlap energies in the ring by the EHT method shows that the direction of fragmentation is determined by the inductive influence of the substituents. Preferential fragmentation of the ketene constituent can also be demonstrated in other four-membered ring ketones.

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Mit 4 Abbildungen

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Herrn Prof. Dr. techn. Dr. h. c.O. Kratky, Vorstand des Institutes für Physikalische Chemie der Universität Graz, zum 70. Geburtstag gewidmet.