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.     

An m-convexity property for complementary pairs in the plane

Let A and B be closed nonempty sets in the plane with A B=R², A B=bdry A=bdry B=C. Assume that for every m 2 points in C, at least one of the corresponding segments is in A, at least one in B. Then each of A and B is locally expressible as a union of m–1 or fewer convex sets.     

Structural investigation of the promotional effect of hydrogen during the selective catalytic reduction of NOx with hydrocarbons over Ag/Al2O3 catalysts

In situ EXAFS has been used to examine the hydrogen effect on the selective catalytic reduction of NOx over silver/alumina catalysts. For all SCR conditions used, with or without co-reductant (H2 or CO), the catalyst structure remained the same. Significant changes in the catalyst were only found under reducing conditions. The enhanced activity found in the presence of hydrogen is thought to be due to a chemical effect and not the result of a change in the structure of the active site.     

A Krasnosel’skii-type theorem for paths of bounded length

Let S be a nonempty closed, simply connected set in the plane, and let α τ; 0. If every three points of 5 see a common point of S via paths of length at most α, then for some point s0 of S, s0 sees each point of S via such a path. That is, S is starshaped via paths of length at most α. Supported in part by NSF grant DMS-9207019     

Finitely starlike sets whose F-stars have positive measure

Let and assume that there is a countable collection of lines {L _i : 1 i} such that (int cl S) and ((int cl S) S) L _i has one-dimensional Lebesgue measure zero, 1 i. Then every 4 point subset ofS sees viaS a set of positive two-dimensional Lebesgue measure if and only if every finite subset ofS sees viaS such a set. Furthermore, a parallel result holds with two-dimensional replaced by one-dimensional. Finally, setS is finitely starlike if and only if every 5 points ofS see viaS a common point. In each case, the number 4 or 5 is best possible.Supported in part by NSF grant DMS-8705336.     

Characterizing compact unions of two starshaped sets inR d

SetS inR ^d has propertyK ₂ if and only ifS is a finite union ofd-polytopes and for every finite setF in bdryS there exist points c₁,c₂ (depending onF) such that each point ofF is clearly visible viaS from at least one c_i,i = 1,2. The following characterization theorem is established: Let , d2. SetS is a compact union of two starshaped sets if and only if there is a sequence {S _j } converging toS (relative to the Hausdorff metric) such that each setS _j satisfies propertyK ₂. For , the sufficiency of the condition above still holds, although the necessity fails.