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.     

Polarized photoluminescence from poly(p-phenylene-ethynylene) via a block copolymer nanotemplate

A new approach based on a conjugated polymer/block copolymer guest/host system for the generation of polarized photoluminescence is reported. Synthetic modification of a poly(p-phenylene-ethynylene) (PPE) conjugated polymer is used for domain-specific incorporation into a cylindrical morphology block copolymer host matrix. Subsequent ordering of the host nanostructure via roll cast processing templates uniaxial alignment of the guest PPE. The ordered films are optically anisotropic displaying both polarized absorption with a dichroic ratio of 3.0 at 440 nm and polarized emission with a polarization ratio of 7.3 at 472 nm.     

ℒ2 sets which are almost starshaped

Let S be a subset of R ^d . The set S is said to be an set if and only if for every two points x and y of S, there exists some z S such that [x, z] [z, y] S. Clearly every starshaped set is an set, yet the converse is false and introduces an interesting question: Under what conditions will an set S be almost starshaped; that is, when will there exist a convex subset C of S such that every point of S sees some point of C via SThis paper provides one answer to the question above, and we have the following result: Let S be a closed planar set, S simply connected, and assume that the set Q of points of local nonconvexity of S is finite. If some point p of S see each member of Q via S, then there is a convex subset C of S such that every point of S sees some point of C via S.     

A Krasnosel'skii theorem for nonclosed sets in Rd

This work will be concerned with a Krasnosel'skii theorem for nonclosed bounded sets in R^d, and the following theorem will be obtained: For each d 2, define f(d) = d² – 2d+3 if d 3 and f(d)=2d+1 if d = 3. Let S be a nonempty bounded set in R^d, d 2, and assume that cl S S is a finite union of convex components, each having closure a polytope. If every f(d) points of S see via S a common point, then there is a point p in cl S such that B_p s:s in S and (p,s] S is nowhere dense in S.