A Krasnosel’skii-type result for planar sets starshaped via orthogonally convex paths

A Krasnosel’skii-type theorem for compact sets that are starshaped via staircase paths may be extended to compact sets that are starshaped via orthogonally convex paths: Let S be a nonempty compact planar set having connected complement. If every two points of S are visible via orthogonally convex paths from a common point of S, then S is starshaped via orthogonally convex paths. Moreover, the associated kernel Ker S has the expected property that every two of its points are joined in Ker S by an orthogonally convex path. If S is an arbitrary nonempty planar set that is starshaped via orthogonally convex paths, then for each component C of Ker S, every two of points of C are joined in C by an orthogonally convex path. Communicated by Imre Bárány     

Simply connected orthogonal polygons as unions of two orthogonally starshaped sets

Let S be a simply connected orthogonal polygon in the plane. The set S is a union of two sets which are starshaped via staircase paths (i.e., orthogonally starshaped) if and only if for every three points of S, at least two of these points see (via staircase paths) a common point of S. Moreover, the simple connectedness condition cannot be deleted.     

A maximal chain of principal ideals in the semigroup of binary relations on a finite set

A maximal chain of F_n+3−1 principal ideals in the semigroup of the binary relations on an n-element set X is constructed by representing a binary relation as a Boolean matrix. Here F_n stands for the n-th Fibonacci number.     

57Fe Conversion Electron Mössbauer Spectroscopy of Factors Influencing Fe–Sn Intermetallic Phase Formation in Tinplated Steel

Hyperfine Interactions - The formation of intermetallic phases influences the properties of commercial alloys. CEMS can be used to reveal the presence of Fe-Sn intermetallics at the interface on...     

A Helly-type theorem for simple polygons

Let be a family of simple polygons in the plane. If every three (not necessarily distinct) members of have a simply connected union and every two members of have a nonempty intersection, then {P:P in } . Applying the result to a finite family of orthogonally convex polygons, the set {C:C in } will be another orthogonally convex polygon, and, in certain circumstances, the dimension of this intersection can be determined.Supported in part by NSF grant DMS-9207019.     

Selective electroless metal deposition using microcontact printing of phosphine-phosphonic acid inks

We report a low-cost approach to selectively deposit films of nickel and copper on glass substrates. Our approach uses microcontact printing of organic inks containing phosphonic acid groups to bind the ink to a glass substrate and phosphine groups to bind a colloidal catalyst that initiates electroless metallization. We demonstrate this procedure by fabricating patterned nickel and copper films with areas as large as 15 cm2 and minimum feature sizes of approximately 2 microm. We present studies on the use of two ink types, an oligomer and a bifunctional molecule, and demonstrate that pattern quality and adhesion of the metallized films depends on the molecular weight of the ink and the ratio of phosphine and phosphonic acid groups.     

Overlap partitioning as a tool for predicting molecular rearrangements

A partitioned total diatomic overlap is suggested as a tool for predicting the course of rearrangements in carbonium ions and other reactive intermediates by use of CNDO molecular orbital calculations.

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Zusammenfassung Ein Aufteilungsmodus für die zweiatomige Gesamt-Überlappung wird vorgeschlagen. Damit läßt sich der Verlauf von Carbonium-Umlagerungen, bzw. anderer reaktiver Zwischenstufen, mittels CNDO-Rechnungen voraussagen.

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Résumé Proposition d'un procédé de partition du recouvrement diatomique total pour la prédiction du cours des réarrangements dans les ions carbonium et autres intermédiaires réactifs par l'emploi de calculs d'orbitales moléculaires CNDO.

     

A variable-temperature diffuse reflectance infrared fourier transform spectroscopy study of the binding of water and pyridine to the surface of acid-activated metakaolin

Four metakaolins were prepared by heating a Spanish kaolin at 600, 700, 800, and 900 degrees C for 10 h. Following preliminary optimization, these metakaolins were acid activated in 6 M hydrochloric acid at 90 degrees C for 6 h; the samples calcined at 600, 700, and 800 degrees C produced the highest surface area solids and were selected for further study. Variable-temperature diffuse reflectance infrared Fourier transform spectroscopy analysis of the resulting acid-activated metakaolins (AAMKs) identified a wide range of hydrogen bond strengths in adsorbed water at room temperature. Above 300 degrees C it was possible to fit the broad hydroxyl stretching band to seven contributing components at 3730, 3700, 3655, 3615, 3583, 3424, and 3325 cm(-1). As the sample temperature was increased, the 3730 cm(-1) band increased in intensity as the water hydrogen bonded to AlOHAl was thermally desorbed. The other six bands decreased in intensity. The spectra of adsorbed pyridine indicated the presence of both Br?nsted and Lewis acid sites on the surface of the air-dried AAMKs. Preheating the AAMK at 200 degrees C prior to pyridine sorption reduced the number of Br?nsted acid sites and increased the number of thermally stable Lewis acid sites. A reduction in the amount of adsorbed pyridine after pretreating the AAMK at 400 degrees C was tentatively attributed to a reduction in surface area. This was reflected in fewer thermally stable Lewis acid sites in the AAMK pretreated at 400 degrees C compared to the number present in the sample pretreated at 200 degrees C.