Eine Verallgemeinerung der Neumannschen Polynome

Ohne Zusammenfassung     

Non-Trivial t-Intersection in the Function Lattice

The function lattice, or generalized Boolean algebra, is the set of ℓ-tuples with the ith coordinate an integer between 0 and a bound n_i. Two ℓ-tuples t-intersect if they have at least t common nonzero coordinates. We prove a Hilton–Milner type theorem for systems of t-intersecting ℓ-tuples.Received September 29, 2004     

Multiplicities of interpoint distances in finite planar sets

What is the maximum number of unit distances between the vertices of a convex n-gon in the plane? We review known partial results for this and other open questions on multiple occurrences of the same interpoint distance in finite planar subsets. Some new results are proved for small n. Challenging conjectures, both old and new, are highlighted.     

Variations on the theme of repeated distances

We give an asymptotically sharp estimate for the error term of the maximum number of unit distances determined byn points in ^{d, d}4. We also give asymptotically tight upper bounds on the total number of occurrences of the favourite distances fromn points in ^{d, d}4. Related results are proved for distances determined byn disjoint compact convex sets in ².At the time this paper was written, both authors were visiting the Technion — Israel Institute of Technology.     

Problems and results on additive properties of general sequences,V

A very special case of one of the theorems of the authors states as follows: Let 1a ₁a ₂... be an infinite sequence of integers for which all the sumsa _i +a _j , 1ij, are distinct. Then there are infinitely many integersk for which 2k can be represented in the forma _i +a _j but 2k+1 cannot be represented in this form. Several unsolved problems are stated.Dedicated to our friend Professor E. Hlawka on the occasion of his seventieth birthday     

Die Bildungswärmen von MnSi1,73, MnSi,Mn5Si3 und Mn3Si

By means of vapor pressure measurements using theTorker method (Torsion-Knudsen Effusion Recoil) as well as theKnudsen tanspiration technique in connection with a mass spectrometer, the heats of formation of the following compounds were found to be –6.5±0.7 kcal/g atom (Mn_0.366Si_0.634), –7.8±0.6 kcal/g atom (Mn_0.50Si_0.50), –7.3±0.6 kcal/g atom (Mn_0.625Si_0.375), and –6.6±0.6 kcal/g atom (Mn_0.75Si_0.25).

---

---

Mit 7 Abbildungen     

Convex nonagons with five intervertex distances

The vertices of a convex planar nonagon determine exactly five distances if and only if they are nine vertices of a regular 10-gon or a regular 11-gon. This result has important ties to related concerns, including the maximum number of points in the plane that determine exactly five distances and, for each n7, the samllest t for which there exists a convex n-gon whose vertices determine t distances and are not all on one circle.     

All-Solid-State PVC Membrane Ag+-Selective Electrodes Based on Diaza-18-Crown-6 Compounds

Two diaza-crown ether compounds were synthesized and evaluated as Ag⁺-selective carriers in polyvinylchloride (PVC) membrane electrodes of solid-state type. The all-solid-state PVC membrane electrode based on N,N-Dibenzyl-dibenzo-diaza-18-crown-6 exhibited a super-Nernstian response (75±10mV per decade) over the concentration range of 1×10^–1 to 7×10^–6M of Ag⁺ ion and a detection limit of 3×10^–6M, at a wide range of pH (pH 4–7). The response time of the electrode was fast (less than 10s), and it can be used for three months without any significant deviation in potential. The proposed all-solid-state PVC membrane electrodes revealed high selectivity toward Ag⁺ ion with respect to alkali, alkaline earth, heavy and transition metal ions. A flow-through cell of all-solid-state PVC membrane Ag⁺-selective electrode based on N,N-Dibenzyl-dibenzo-diaza-18-crown-6 has also been prepared and applied for flow-injection analysis of Ag⁺ ion in solution.     

Remez-, Nikolskii-, and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros

Sharp Remez-, Nikolskii-, and Markov-type inequalities are proved for functions of the form