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.     

Hybrid continuum–coarse-grained modeling of erythrocytes

The red blood cell (RBC) membrane is a composite structure, consisting of a phospholipid bilayer and an underlying membrane-associated cytoskeleton. Both continuum and particle-based coarse-grained RBC models make use of a set of vertices connected by edges to represent the RBC membrane, which can be seen as a triangular surface mesh for the former and a spring network for the latter. Here, we present a modeling approach combining an existing continuum vesicle model with a coarse-grained model for the cytoskeleton. Compared to other two-component approaches, our method relies on only one mesh, representing the cytoskeleton, whose velocity in the tangential direction of the membrane may be different from that of the lipid bilayer. The finitely extensible nonlinear elastic (FENE) spring force law in combination with a repulsive force defined as a power function (POW), called FENE–POW, is used to describe the elastic properties of the RBC membrane. The mechanical interaction between the lipid bilayer and the cytoskeleton is explicitly computed and incorporated into the vesicle model. Our model includes the fundamental mechanical properties of the RBC membrane, namely fluidity and bending rigidity of the lipid bilayer, and shear elasticity of the cytoskeleton while maintaining surface-area and volume conservation constraint. We present three simulation examples to demonstrate the effectiveness of this hybrid continuum–coarse-grained model for the study of RBCs in fluid flows.     

Der Einfluß von Grenzflächenerscheinungen auf den Stoffübergang und die Prozeßführung in Gegenstromkolonnen mit überkritischem CO2

Zusammenfassung Mittels des Einsatzes einer Hochdrucksichtzelle wurden Eigenschaften der Kontaktbereiche in Trennverfahren mit unterschiedlichen wäßrigen Lösungen und CO₂ unter hohen Drücken untersucht. Die Methode des hängenden Tropfens wurde zur Messung der Grenzflächenspannung bis zu Drücken von 280 bar angewandt. Der mit dem Druck abnehmende Verlauf weist nach der Gibbs'schen Theorie auf die Anreicherung von CO₂ in der Phasengrenze. Weiterhin wurde die für Packungskolonnen bedeutsame Feststoffbenetzung in Abhängigkeit von Druck und Oberflächenbeschaffenheit des Feststoffes untersucht. Der die Feststoffbenetzung charakterisierende Kontaktwinkel wurde mittels der Methode der gekippten Platte vermessen und ergab eine schlechtere Benetzung bei höheren Drücken und glatten Stahloberflächen.

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The effect of interfacial phenomena on mass transport and performance of separations in countercurrent columns with supercritical CO₂

Interfacial phenomena affecting countercurrent separation processes have been studied in systems containing aqueous solutions and CO₂ at elevated pressures by means of a high pressure optical cell. The pendant drop method was applied in order to measure the interfacial tension up to 280 bar. The decreasing course as a function of the pressure is due to the adsorption of CO₂ at the interface according to Gibbs' law. Further, wetting characteristics have been investigated as they are of considerable importance to packed columns. Therefore, the contact angle was determined by the method of the tilting plate and came out to increase with pressure and smoothness of the solid surface, indicating the loss of wettability.

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On Spin Models, Modular Invariance, and Duality

A spin model is a triple (X, W ⁺, W ^–), where W ⁺ and W ^– are complex matrices with rows and columns indexed by X which satisfy certain equations (these equations allow the construction of a link invariant from(X, W ⁺, W ^–) ). We show that these equations imply the existence of a certain isomorphism between two algebras and associated with (X, W ⁺, W ^–) . When is the Bose-Mesner algebra of some association scheme, and is a duality of . These results had already been obtained in [15] when W ⁺, W ^– are symmetric, and in [5] in the general case, but the present proof is simpler and directly leads to a clear reformulation of the modular invariance property for self-dual association schemes. This reformulation establishes a correspondence between the modular invariance property and the existence of spin models at the algebraic level. Moreover, for Abelian group schemes, spin models at the algebraic level and actual spin models coincide. We solve explicitly the modular invariance equations in this case, obtaining generalizations of the spin models of Bannai and Bannai [3]. We show that these spin models can be identified with those constructed by Kac and Wakimoto [20] using even rational lattices. Finally we give some examples of spin models at the algebraic level which are not actual spin models.