Ein Beitrag zum Einfluß des Stoffüberganges auf eine erzwungene Konvektion an einer fluiden Phasengrenze

The interfacial-dynamic behaviour of a fluid two-phase-system with mass transfer was investigated under influence of forced convection in the manner of flat jets directed to the interface. The tangential velocities were measured at a characteristic point near to the interface air/water or in the interface itself using a Laser-Doppler-Velocimeter in dependence on the velocities of jets into two phases in both cases with and without transfer of acetone. The variations of velocities due to the interfacial effects are only detectable at small velocities of the jets. They are discussed by model conceptions and compared with the results of a theoretical research of heat transfer in a fluid two-phase-system (Interfacial-dynamic surface renewal model).     

Convergence of Stirling's method in Banach spaces

Aequationes mathematicae -     

Domination game and minimal edge cuts

In this paper a relationship is established between the domination game and minimal edge cuts. It is proved that the game domination number of a connected graph can be bounded above in terms of the size of minimal edge cuts. In particular, if $C$ a minimum edge cut of a connected graph $G$, then ${\gamma }_g\left(G\right)\le {\gamma }_g(G?C)+2{\kappa }^{\prime }\left(G\right)$. Double-Staller graphs are introduced in order to show that this upper bound can be attained for graphs with a bridge. The obtained results are used to extend the family of known traceable graphs whose game domination numbers are at most one-half their order. Along the way two technical lemmas, which seem to be generally applicable for the study of the domination game, are proved.     

Packing chromatic number versus chromatic and clique number

The packing chromatic number \(\chi _{\rho }(G)\) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into sets \(V_i\), \(i\in [k]\), where each \(V_i\) is an i-packing. In this paper, we investigate for a given triple (a, b, c) of positive integers whether there exists a graph G such that \(\omega (G) = a\), \(\chi (G) = b\), and \(\chi _{\rho }(G) = c\). If so, we say that (a, b, c) is realizable. It is proved that \(b=c\ge 3\) implies \(a=b\), and that triples \((2,k,k+1)\) and \((2,k,k+2)\) are not realizable as soon as \(k\ge 4\). Some of the obtained results are deduced from the bounds proved on the packing chromatic number of the Mycielskian. Moreover, a formula for the independence number of the Mycielskian is given. A lower bound on \(\chi _{\rho }(G)\) in terms of \(\Delta (G)\) and \(\alpha (G)\) is also proved.     

The solution of characteristic value-vector problems by Newton's method

LetT(λ) be a bounded linear operator in a Banach spaceX for eachλ in the scalar fieldS. The characteristic value-vector problemT(λ)x = 0 with a normalization conditionφ x = 1, whereφ ε X ^*, is formulated as a nonlinear problem inX xS:P(y) ≡ (T(λ)x, φ x - 1) = 0,y= (X, A). Newton's method and the Kantorovič theorem are applied. For this purpose, representations and criteria for existence ofP′(y)⁻¹ are obtained. The continuous dependence onT of characteristic values and vectors is investigated. A numerical example withT(λ) =A +λB +λ ² C is presented. Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.