Gap Continuity of Multimaps

We introduce a notion of continuity for multimaps (or set-valued maps) which is mild. It encompasses both lower semicontinuity and upper semicontinuity. We give characterizations and we consider some permanence properties. This notion can be used for various purposes. In particular, it is used for continuity properties of subdifferentials and of value functions in parametrized optimization problems. We also prove an approximate selection theorem.      

4-chromatic edge critical Grötzsch-Sachs graphs

Let G be a 4-regular plane graph and suppose that G has a cycle decomposition S (i.e., each edge of G is in exactly one cycle of the decomposition) with every pair of adjacent edges on a face always in different cycles of S. Such a graph G arises as a superposition of simple closed curves in the plane with tangencies disallowed. Two 4-chromatic edge critical graphs of order 48 generated by four curves are presented.     

Numerical analysis of fatigue striations

A computational model was developed to numerically analyse fatigue striations. The inclined strip yield model with continuous distributions of infinitesimal dislocations was utilized to express the crack tip plasticity in this model. The fatigue crack tip blunting process was approximated by sequential activation of two slip lines under loading, and crack closure during unloading was taken into account. The plastic zone at a growing fatigue crack tip at the maximum load was independent of the crack growth up to ten cycles while the reversed plastic zone decreased in a size to one twentieth of that at the maximum load as the crack grew. The ratio of these plastic zone sizes and also the crack tip opening displacement were quite different from the simple prediction by J.R. Rice for a stationary crack. The computed striation spacings were compared with the observed ones and moderate agreement between them obtained.     

Complexes of zinc,cadmium and mercury(II) with the zwitter-ionic form of NN′-ethylenebis (salicylideneimine)

The Schiff base NN′-ethylenebis(salicylideneimine), H₂ salen reacts with hydrous and anhydrous Zinc, Cadmium and Mercury(II) salts to give complexes M(H₂ salen)X₂·nH₂O (M = Zn, Cd, Hg; XCl, Br, I, NO₃; MZn, X₂SO₄; n = 0?2). Spectroscopic and other evidence indicated that; (i) halide and sulphate are coordinated to the metal ion, whereas the nitrate group is ionic in mercury nitrate compound and covalently bonded in zinc and cadmium nitrato complexes, (ii) the Schiff base is coordinated through the negatively charged phenolic oxygen atoms and not the nitrogen atoms, which carry the protons transferred from phenolic groups on coordination, (iii) therefore the coordination numbers suggested are 4-, in mercury and 4- or 6- in zinc and cadmium Schiff base complexes.     

The general harmonic force field of fluoroform

Anharmonicity constants and harmonic frequencies of HC¹²F₃ and DC¹²F₃ are obtained for the first time. These data are combined with ζ^z, ζ^x,y and centrifugal distortion constants and carbon-13 frequency shifts to obtain, using the display method, the general harmonic force field (GHFF) of fluoroform. All 12 force constants in the GHFF, including off-diagonal elements in the A₁ block, are determined with significance. The carbon-13 frequency shifts proved to be most important for precise determination of A₁ off-diagonal elements. The GHFF is compared with the predictions of the Hybrid Orbital Force Field (HOFF).     

Evaluation of Automated ECG Monitoring: Theoretical Model Based upon Point Process Techniques

The development of practical methods of ECG monitoring using dedicated computers has presented problems in the evaluation and comparison of the relative effectiveness of various ECG monitoring systems. A theoretical model based on the application of point process techniques is discussed in this paper.     

Study of a lacunary solid phase I—Thermodynamic and crystallographic characteristics of its formation

The dehydration of the barium acid oxalate H₂C₂O₄·BaC₂O₄·2H₂O, depending on the conditions in which it is performed, can lead to two different anhydrous salts. That designated αH₂C₂O₄·BaC₂O₄ has all the features of a stable lacunary phase. Its crystalline structure has been determined and the atomic movements during this structure's formation are described. The other variety βH₂C₂O₄·BaC₂O₄ can be prepared either directly from the dihydrate or by transformation of the α form at higher temperature. An infinite number of nonstoichiometric hydrates (designated as H₂C₂O₄·BaC₂O₄·?H₂O with 0 < ? < 2) can be prepared in particular conditions, which identifies the “hydrate-vapor” system studied as divariant. A structural interpretation of this phenomenon is proposed; it takes into account the particular role of water molecules in the coordination polyhedron of the Ba²⁺ cations.     

Ferromagnetism in γ-iron

F.c.c. γ-Fe(111)-films, prepared by epitaxial growth in UHV on Cu(111), are ferromagnetic. The spontaneous magnetization was determined as 0.58 ± 0.13 μ_B/atom. This is independent of film thickness (up to 80 Å) and applies both for island-films and for layer-grown films. The Curie-temperature for bulk material was estimated to T_c(∞) = 900 ± 300 K. The apparent contradiction to antiferromagnetism in γ-Fe-precipitates is explained by different lattice parameters.