Directed triangles in directed graphs

We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3.     

Harze und Harzs?uren

Ohne Zusammenfassung     

Untersuchung von Textilien und Textilrohstoffen

Ohne Zusammenfassung     

Die Einwirkung-dunkler elektrischer Entladungen auf ein Gemisch von Wasserstoff und Titantetrachloriddampf

Ohne ZusammenfassungDie vorliegende Untersuchung wurde im Laboratorium für allgemeine Experimentalchemie und in jenem für analytische Chemie an der technischen Hochschule in Wien durchgeführt. Es ist uns eine angenehme Pflicht, den Vorständen dieser Institute, den Herren Professoren Dr. M. Bamberger und Dr. G. Vortmann für ihr stetes Entgegenkommen unseren wärmsten Dank zu sagen.     

Collisional Relaxation of Luminescence Anisotropy in Rarefied Gases in the Condensed Phase

The orientational relaxation of optically induced anisotropy in rarefied gases and at a damped rotation has been investigated. It has been found that the anisotropy relaxation in rarefied gases is described by a reduced kinetic equation depending only on free rotation integrals. The behavior of the integral anisotropy of luminescence for free symmetric and asymmetric top molecules has been elucidated. The law of luminescence depolarization has been obtained for asymmetric top molecules in the Gordon J-diffusion model. It represents the sum of two Stern–Volmer-type dependences, whose relative contribution is determined by the orientation of the dipole moments of transitions with absorption and emission of light in the molecular coordinate system and by the principal moments of inertia of the molecular top. It has been established that in the limit of a strongly damped rotation, kinetic equations of the general form reduce to equations of rotational diffusion. A number of modified diffusion equations correctly describing the contribution of inertial effects to the orientational relaxation of anisotropy have been obtained.