On shortest cocycle covers of graphs

A cocycle (resp. cycle) cover of a graph G is a family C of cocycles (resp. cycles) of G such that each edge of G belongs to at least one member of C. The length of C is the sum of the cardinalities of its members. While it is known (see [5, 6]) that every bridgeless graph G = (V, E) has a cycle cover of length not greater than $\text{5}\text{3}\text{|E|}$, it is shown that there exists no α < 2 such that every loopless graph G = (V, E) has a cocycle cover with length not greater than α |E|. To do this, cocycle covers of minimal length are determined for the complete graphs, thus solving a problem stated at the end of [6].     

Some logical aspects of information processing

This paper is concerned with dynamic aspects of knowledge representation. A model for information processing is introduced which is based on acyclic directed graphs with starting points. This approach is combined with ideas from non-monotonic reasoning.     

On the edge-coloring problem for a class of 4-regular maps

A (plane) 4-regular map G is called C-simple if it arises as a superposition of simple closed curves (tangencies are not allowed); in this case σ (G) is the smallest integer k such that the curves of G can be colored with k colors in such a way that no two curves of the same color intersect. We prove that if σ (G) ≤ 4, G is edge colorable with 4 colors. Moreover we show that a similar result for maps G with σ(G) ≤ 5 would imply the Four-Color Theorem.     

Hydrogen on W (100): Electron stimulated desorption and a structural model

Prompted by the peculiar shape of the curve of election-induced H⁺ current versus coverage for hydrogen on W(100) which has been observed before, we have restudied this system by correlated ESD, thermal desorption, and LEED measurements. The maxima in ESD signal and intensity of the half-order LEED spots, and the appearance of a second desorption peak are roughly correlated at $\text{1}\text{4}$ coverage. Using this observation and the exact shape of the ESD curve, a structural model is derived in which two different, but uniform states (i and f) exist, the first, i, being exclusively occupied up to $\text{1}\text{4}$ monolayer, and the second, f, at saturation. A gradual conversion from i to f takes place at $\text{1}\text{4}\text{< θ < 1}$ which is caused by the interaction between adsorbed H atoms. From this model a differential equation for the occupation numbers of i and f states, respectively, is derived and solved numerically; it yields good agreement with the experimental ESD curve. Discussing the possible physical realization of the two states, it can be made probable that they must exist on two different sites and have fourfold (i) and twofold (f) symmetry, so that the conversion is accompanied by a shift of the binding site of the adatom.     

Reactions in microemulsion media. Nucleophilic displacement reaction of benzyl chloride with bromide ion

A kinetic and synthetic study of the reaction of benzyl chloride with bromide ion has been performed in microemulsions composed of cetyltrimethylammonium bromide, 1-butanol, water, potassium bromide, and hexane; rates and yields of benzyl bromide formation decreased with increasing hexane content.     

Determination of bile acids and lysolecithin in artificial and natural gastric juice by HPLC for characterization of antacida

Work-up procedures and HPLC separation systems for determination of taurocholic, glycocholic, chenodeoxycholic, and cholic acids and lysolecithin in artificial and natural gastric juice are described. These compounds are used for testing the binding capacity of antacida to the individual analytes. Work-up is simple, no extraction or filtration being required. The optimized combinations of stationary and mobile phases allow selective and sensitive determination of the respective bile acids in gastric juice. For optimization, the capacity factors of two related bile acids were evaluated for numerous commercial stationary phases. The mechanism of retention is different for free and conjugated bile acids. Special aspects of routine analysis are discussed.