On Karnaugh maps and magic squares

In 1953, Karnaugh maps were developed at the Harvard Computation Laboratory for the minimization of Boolean algebraic expressions (as an approach to logic circuit synthesis) [5].     

Approximating minimum cocolorings

A cocoloring of a graph G is a partition of the vertex set of G such that each set of the partition is either a clique or an independent set in G. Some special cases of the minimum cocoloring problem are of particular interest.We provide polynomial-time algorithms to approximate a minimum cocoloring on graphs, partially ordered sets and sequences. In particular, we obtain an efficient algorithm to approximate within a factor of 1.71 a minimum partition of a partially ordered set into chains and antichains, and a minimum partition of a sequence into increasing and decreasing subsequences.     

Managing Structural Information by Higher-Order Colored Unification

Coloring terms (rippling) is a technique developed for inductive theorem proving that uses syntactic differences of terms to guide the proof search. Annotations (colors) to symbol occurrences in terms are used to maintain this information. This technique has several advantages; for example, it is highly goal oriented and involves little search. In this paper we give a general formalization of coloring terms in a higher-order setting. We introduce a simply typed calculus with color annotations and present appropriate algorithms for the general, pre-, and pattern unification problems. Our work is a formal basis to the implementation of rippling in a higher-order setting, which is required, for example, in the case of middle-out reasoning. Another application is in the construction of natural the language semantics, where the color annotations rule out linguistically invalid readings that are possible using standard higher-order unification.     

Analysis of the temperature dependence of the fracture stress of sharp notched bending specimens of a structural steel with respect to intermediate transitions

The flow and fracture stresses, σ_y^g and σ_f^g (δ = crack tip displacement), of sharply notched bending specimens of a structural steel U St 37-1 are measured in the temperature range from full scale to small scale yielding. The best adaption of the experimental results for σ_f^g is obtained by a curve which exhibits an intermediate transition, i.e. which follows in a temperature range between an upper, T_tM¹ and a lower, T_tl¹, transition temperature to the curve σ_y^g(T) for the flow stress with a constant δ = δ₁. This transition corresponds to that of the slip to the twin nucleated fracture. Two analyses [3,5] according to the local fracture stress, σ_f^*, concept show that the amount and the temperature dependence of σ_f^* are somewhat different for both methods, but that both exhibit an increase of σ_f^* in the transition range. It is concluded that each transition in the nucleation mode of the fracture is connected with such a transition in the fracture stress. It may, however, become indistinct or even be covered by the scatter of the experimental points.     

Diffusion von Silizium,Phosphor, Schwefel und Mangan in flüssigem Eisen

Zusammenhang zwischen Diffusion und Aktivität. Messung der Diffusionskoeffizienten von Silizium, Phosphor, Schwefel und Mangan in flüssigem Eisen sowie in kohlenstoffgesättigtem, flüssigem Eisen. Angabe der Konzentrationsabhängigkeit und der Temperaturabhängigkeit der ermittelten Diffusionskoeffizienten.