Duality

Starting from the study of the physical world, we develop the concept of a dual pair, Comparing dual pairs is known as duality. We show that duality is a basic mechanism for our intellectual curiosity.     

Zur Vollständigkeit des Biorthogonalsystems von Eigenfunktionen irregulärer Eigenwertprobleme

Ohne Zusammenfassung     

Synthese disubstituierter Pyridine über Radikalreaktionen, 2. Mitt.

The synthesis of benzyl and phenethyl substituted 3-pyridine carbonitriles and 3-pyridine carboxylic acid methylesters resp. by homolytic alkylation is reported.     

Bewegflächen einer Ellipse als Quadriken

Ohne ZusammenfassungHerrn Martin Barner zum 60. Geburtstag gewidmet     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).