The smooth structure set of <Emphasis Type="Italic">S</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> × <Emphasis Type="Italic">S</Emphasis><Superscript><Emphasis Type="Italic">q</Emphasis></Superscript>

We calculate \({\mathcal{S}^{{\it Diff}}(S^p \times S^q)}\), the smooth structure set of S ^p × S ^q , for p, q ≥ 2 and p + q ≥ 5. As a consequence we show that in general \({\mathcal{S}^{Diff}(S^{4j-1}\times S^{4k})}\) cannot admit a group structure such that the smooth surgery exact sequence is a long exact sequence of groups. We also show that the image of the forgetful map \({\mathcal{S}^{Diff}(S^{4j}\times S^{4k}) \rightarrow \mathcal{S}^{Top}(S^{4j}\times S^{4k})}\) is not in general a subgroup of the topological structure set.     

A Reduced-Symmetry Heterobimetallic [PdPtL4]4+ Cage: Assembly,Guest Binding,and Stimulus-Induced Switching

A strategy is presented that enables the quantitative assembly of a heterobimetallic [PdPtL₄]⁴⁺ cage. The presence of two different metal ions (Pd^II and Pt^II) with differing labilities enables the cage to be opened and closed selectively at one end upon treatment with suitable stimuli. Combining an inert Pt^II tetrapyridylaldehyde complex with a suitably substituted pyridylamine and Pd^II ions led to the assembly of the cage. ¹H and DOSY NMR spectroscopy and ESI mass spectrometry data were consistent with the quantitative formation of the cage, and the heterobimetallic structure was confirmed using single-crystal X-ray crystallography. The structure of the host–guest adduct with a 2,6-diaminoanthraquinone guest molecule was determined. Addition of N,N′-dimethylaminopyridine (DMAP) resulted in the formation of the open-cage [PtL₄]²⁺ compound and [Pd(DMAP)₄]²⁺ complex. This process could then be reversed, with the reformation of the cage, upon addition of p-toluenesulfonic acid (TsOH).     

Centrifugal waves on a flexible chain

A chain is attached at one end to a rigid rotating hub. Centrifugal force induces a nonuniform tension in the chain, which therefore supports transverse vibrations. Solution of the appropriate wave equation shows that the natural frequencies depend only on the rotational speed and the length of the chain relative to the hub diameter. Experiments demonstrating the existence of these vibrations show that an initial impulsive disturbance reoccurs as an “echo” in which all the eigenmodes reinforce each other. This echo occurs even though the eigenfrequencies are not harmonically related. The explanation of the echo is found in the (almost) linear relation between eigenfrequency and mode number.     

Principal Bundles and the Dixmier Douady Class

A systematic consideration of the problem of the reduction and “lifting” of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady class in various contexts including string structures, bundles and other examples motivated by considerations from quantum field theory. Received: 26 February 1997 / Accepted: 5 August 1997     

Geochemical profile of Chautauqua Lake sediments

Neutron activation analysis techniques were used to study sediments from Chautauqua Lake. The concentrations of Eu, Na, Mn, K, Br, As, Ga, La, Hf, Cs, Tb, Sc, Fe, Ta, Sb were determined and compared with similar data for the bedrock and soils surrounding the lake. The lake sediments are found to be enriched in Na, Mn, Br, As, Hf, Tb, Ta, and Sb relative to the surrounding source beds. High pairwise linear correlation coefficients (R～0.9) were found between the concentrations of antimony, cesium, and scandium. For many elements a relationship was indicated between their concentrations and the clay fraction of the sediment, possibly due to the higher cation exchange potential of the clay minerals.     

Azo compounds for free radical crosslinking of polysiloxane stationary phases

There has been much effort spent in recent years developing the technology for free radical crosslinking of polysiloxane polymers to prepare capillary columns coated with thermally stable and nonextractable stationary phases. Organic peroxides have been used extensively as the free radical initiators for the in situ polymerization of the stationary phases. However, these peroxides adversely affect the phase polarity and column activity. Seven azo compounds were studied for crosslinking efficiency. Azo compounds can be used as free radical initiators to prepare nonextractable stationary phases without the adverse effects caused by peroxides.     

Pressure‐Dependent Polymorphism and Band‐Gap Tuning of Methylammonium Lead Iodide Perovskite

We report the pressure‐induced crystallographic transitions and optical behavior of MAPbI₃ (MA=methylammonium) using in situ synchrotron X‐ray diffraction and laser‐excited photoluminescence spectroscopy, supported by density functional theory (DFT) calculations using the hybrid functional B3PW91 with spin‐orbit coupling. The tetragonal polymorph determined at ambient pressure transforms to a ReO₃‐type cubic phase at 0.3 GPa. Upon continuous compression to 2.7 GPa this cubic polymorph converts into a putative orthorhombic structure. Beyond 4.7 GPa it separates into crystalline and amorphous fractions. During decompression, this phase‐mixed material undergoes distinct restoration pathways depending on the peak pressure. In situ pressure photoluminescence investigation suggests a reduction in band gap with increasing pressure up to ≈0.3 GPa and then an increase in band gap up to a pressure of 2.7 GPa, in excellent agreement with our DFT calculation prediction.     

Electron spectroscopy with excited atoms and photons.: X. Halogen-substituted methanes and methyl amines

Electron binding energy spectra have been measured for CH₃Cl, CH₃Br, CH₃I, CFCl₃, CF₂Cl₂, CF₃Cl, CF₄, CH₃NH₂, (CH₃)₂ NH and (CH₃)₃N. Measurements have been made using 584 Å (21.22 eV) photons as well as with 2³S(19.82 eV) and 2¹S(20.62 eV) metastable helium atoms. Relative spectral intensities are compared for photoionization and Penning ionization.