Upper semicontinuous fuzzy sets and applications

Let (X, τ) be a generalized topological space of type $\text{V}$_α (see A. Appert and K. Fan, “Espaces topologiques intermédiares,” Herman, Paris, 1951) and (L, ?) be a complete Brouwerian lattice such that the dual lattice of (L, ?) is also Brouwerian. We prove that every upper semicontinuous L-fuzzy subset of X can be represented by a τ-closed random set. As an important application we obtain a fuzzification of measurable spaces as well as of topological spaces. In particular a concept of measurable (open) L-fuzzy sets is developed.     

Mechanical Properties of Organic-Inorganic Hybrid Materials Determined by Indentation Techniques

The mechanical properties of hybrid materials consisting of polystyrene (PS), which was cross-linked with different proportions of the multifunctional cluster Zr₆O₄(OH)₄(methacrylate)₁₂ (Zr6) were investigated. With the help of (micro)indentation and scratch testing, the influence of the Zr6 clusters on mechanical properties, such as hardness, stiffness, creep, craze initiation, and scratch resistance was shown. There was only a slight increase in hardness and in indentation modulus with higher cluster loadings. While this observation was in agreement with the compression behaviour of the materials, the tensile properties showed a much stronger dependence on the Zr6 content. With increasing cluster loading, an increase of craze initiation stress, as determined by ball indentation experiments, was found. Performing scratch testing with constant load, a reduction of pile-up and a stronger recovery were observed for the hybrid materials compared to the neat PS. Scratch tests with a constant increase of load showed an increase of the critical load for crack opening during scratching.     

Critical evaluation of additivity schemes for estimating heats of atomization

Additivity schemes for estimating heats of formation and heats of atomization of alkanes and halo- alkanes are scrutinized. A least squares analysis of the heats of atomization of alkanes leads to a revision of the values of the parameters. The improvement in the estimated heats of atomization over the values obtained with parameters previously suggested amounts to at least 100%. The reasons for the deviations from the experimental values are discussed. These parameters can be transfered to haloalkanes. Additional parameters necessary for estimating heats of atomization of haloalkanes are also obtained through least squares analyses.     

A Theoretical Study of Amine Bonding in Titanium Alkoxide Adducts

Summary. DFT calculations were carried out on Ti₂(OCH₃)₈ (NH₂CH₃)₂ and Ti₂(OCH₃)₈(NH₃)₂, which are model compounds for the previously isolated amine adducts Ti₂(OR)₈(NH₂ R′)₂. The calculations show that the Ti–N bond strength is weak; however, coordination of the amine to the metal center is supported by a N–H···O hydrogen bond of the amine with the neighboring alkoxo ligand. The Ti–N interaction is purely σ in nature, while the Ti–O interactions include both σ and π contributions. The lowest unoccupied molecular orbitals are mainly localized on Ti t_2g-like orbitals.     

The Diammoniates of dipotassiumtetraethinylozincate and -cadmate: K2M(C2H)4.2NH3 (M = Zn, Cd)

By reaction of KC(2)H and K(2)Zn(CN)(4) in liquid ammonia, the diammoniate K(2)Zn(C(2)H)(4).2NH(3) was obtained. K(2)Cd(C(2)H)(4).2NH(3) was synthesized by reacting KC(2)H, Cd(NH(2))(2), and acetylene in liquid ammonia. The crystal structures of the air and temperature sensitive compounds were determined by X-ray single crystal diffraction at low temperatures (T = 170 K). Both compounds crystallize in the monoclinic space group I2/a (No. 15) with Z = 4. K(2)Zn(C(2)H)(4).2NH(3): a = 7.289(1) A, b = 12.765(2) A, c = 14.066(2) A, beta = 98.11(2) degrees. K(2)Cd(C(2)H)(4).2NH(3): a = 7.444(1) A, b = 12.619(3) A, c = 14.304(2) A, beta = 98.94(1) degrees. Characteristic structural motifs are tetrahedral [M(C(2)H)(4)](2-) fragments (M = Zn, Cd) and zigzag chains of edge sharing distorted (C(2)H)(6) octahedra centered by potassium ions. These zigzag chains are connected by a second type of crystallographically distinct potassium ions that also bind to two ammonia molecules.     

Beiträge zur Chemie der Silicium—Stickstoff-Verbindungen, 16. Mitt.: N-Silyl-carbonamide und N-Silyl-carbamidsäureester

Zusammenfassung Die durch direkte Silylierung von Carbonamidgruppen mit Halogensilanen nicht zugänglichen Verbindungen der Gruppierung R-CONHSiR₃ konnten durch Umsetzung von Säureamiden oder Säurechloriden mit Hexamethyldisilazan gewonnen werden. So wurden Derivate mit R=CH₃, C₂H₅, C₆H₅, CONHSiR₃ , OCH₃, OC₂H₅, OCH(CH₃)₂; R=CH₃ (vgl. Tab. 1) dargestellt und in ihren physikalischen und chemischen Eigenschaften näher studiert.Herrn Prof. Dr.A. Zinke zum 70. Geburtstag gewidmet.15. Mitt.:U. Wannagat undH. Kuckertz, Angew. Chem.74, 117 (1962).Auszug aus der DissertationJ. Pump, Techn. Hochsch. Aachen 1962.     

Ersatz der Podbielniak-Destillation durch eine Kombination von Graschromatographie und Gravimetrie

Zusammenfassung An Stelle der Podbielniak-Analyse für Gasproben, die neben Inertgasen und leichten Kohlenwasserstoffen auch C₅- und höhere Kohlenwasserstoffe enthalten, wird ein neues Verfahren vorgeschlagen. Die Inertgase und leichten Kohlenwasserstoffe werden wie üblich gaschromatographisch bestimmt. Zusätzlich trennt man aus einer zweiten Probe gaschromatographisch die leichten Anteile ab, spült durch Umkehr der Trägergasrichtung die Summe der schweren Kohlenwasserstoffe wieder aus der Säule und bestimmt ihre Menge durch Wägung.     

Self-assembly of amphiphilic hexapyridinium cations at the air/water interface and on HOPG surfaces.

Mono- and multilayers of a novel amphiphilic hexapyridinium cation with six eicosyl chains (3) are spread at the air/water interface as well as on highly ordered pyrolytic graphite (HOPG). On water, the monolayer of 3 is investigated by recording surface pressure/area and surface potential/area isotherms, and by Brewster angle microscopy (BAM). Self-organized tubular micelles with an internal edge-on orientation of molecules form at the air/water interface at low surface pressure whereas multilayers are present at high surface pressure, after a phase transition. Packing motifs suggesting a tubular arrangement of the constituting molecules were gleaned from atomic force microscopy (AFM) investigations of Langmuir-Blodgett (LB) monolayers being transferred on HOPG at different surface pressures. These LB film structures are compared to the self-assembled monolayer (SAM) of 3 formed via adsorption from a supersaturated solution, which is studied by scanning tunnelling microscopy (STM). On HOPG the SAM of 3 consists of nanorods with a highly ordered edge-on packing of the aromatic rings and an arrangement of alkyl chains which resembles the packing of molecules at the air/water interface at low surface pressure. Additional details of the molecular packing were gleaned from single-crystal X-ray structure analysis of the hexapyridinium model compound 2b, which possesses methyl instead of eicosyl residues.