New Non-Linear Inequalities for Flag-Vectors of 4-Polytopes

In this paper we prove four new (infinite) lists of quadratic inequalities, and four cubic inequalities, for the flag f-vectors of 4-polytopes. These extend and supplement the only four currently known non-linear inequalities, which were proved by Bayer in 1987. The new lists of inequalities for flag f-vectors yield new lists of inequalities for f-vectors of 4-polytopes. Using the latter, we managed to improve an estimate discovered by Hoppner and Ziegler concerning upper bounds of f₁ in terms of f₀ and f₃.     

Mikrochemie. Technische Anwendungen

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Erstarrung des Fluorwasserstoffs und des Phosphorwasserstoffs,Verflüssigung und Erstarrung des Antimonwasserstoffs

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Zur Theorie der algebraischen Functionen einer Veränderlichen und der Abel'schen Integrale

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A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.     

Kreiszylindrische Behälter auf nachgiebiger Unterlage

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