Topological charge quantization via path integration: An application of the Kustaanheimo-Stiefel transformation

Editorial note: The complete text of this paper, dedicated to Professor Asim O. Barut, will appear in the August 1993 issue ofFoundations of Physics.     

Variable-priority queue and doughnut routing

This paper proposes a new data structure called a variable-priority queue. The queue supports, in addition to the ordinary queue operations, an operation MIN to find an item of minimum key and three operations to change keys of items. Any sequence of these m operations can be processed in O(m) time. Furthermore, as its application, this paper presents two efficient algorithms for network problems. The first finds multicommodity flows in cycles in linear time. The second, using the first, finds edge-disjoint paths connecting terminal pairs in a doughnut-shaped grid. The grid is bounded by two nested rectangles, and terminals are specified on the two rectangular boundaries outside the four corners. If there are k terminal pairs and all the terminals are ordered in clockwise order around rectangles, then the algorithm decides in O(k) time whether there are edge-disjoint paths connecting terminals in the grid, and actually finds edge-disjoint paths in O(k log k) time.     

Randomly displaced phase distribution design for computer-generated binary hologram with narrow recording spots

A random phase mask is often used for Fourier transform holography to improve its recording and reconstruction characteristics. However, a conventional random phase pattern has the disadvantage of expanding the recording spot, which is caused by the high-resolution phase modulation. Previously, we proposed a random phase pattern that makes the recording spot narrower than the conventional one with maintaining a moderate reconstruction quality. In the present study, we apply the proposed random phase pattern to computer-generated binary holograms and evaluate both the hologram distribution and reconstruction quality in terms of practical holographic memory systems. The results confirm the effectiveness of the random phase in the reconstruction for an elementary data pattern.     

Unipotent Algebraic Affine Supergroups and Nilpotent Lie Superalgebras

We characterize hereditary (as coalgebras) Hopf algebras by the property of ‘equivariant smoothness’, and apply the result to generalize to the super-context, the category equivalence, due to Hochschild, between the unipotent algebraic affine groups and the finite-dimensional nilpotent Lie algebras, in characteristic zero. The global dimension of commutative Hopf algebras, regarded as coalgebras, is also discussed. Presented by S. Montgomery Mathematics Subject Classification (2000) 16W30.     

Size-selected copper oxide nanoparticles synthesized by laser ablation

Size-tuned copper oxide nanoparticles with sizes of 9, 12, and 15 nm were fabricated by laser ablation and on-line size selection using a differential mobility analyzer at a gas pressure of 666 Pa. The dependence of the particle properties on the in situ annealing temperatures and selection sizes was investigated. The crystalline phases of the nanoparticles fabricated at temperatures below 973 K were assigned to monoclinic cupric oxide (CuO) which converted into cubic cuprous oxide (Cu₂O) when the annealing temperature was above 1,173 K. This indicates that the crystalline phases can be easily controlled by changing the annealing temperature. TEM images confirmed that well-crystallized and well-dispersed CuO and Cu₂O nanoparticles with narrow size distributions were obtained using this method. This fabrication process is useful and promising for the future investigation of the intrinsic size-dependent properties of CuO and Cu₂O.     

On a conjecture of ōshima

The set of homotopy classes of self maps of a compact, connected Lie group G is a group by the pointwise multiplication which we denote by H(G), and it is known to be nilpotent. ōshima [H. ōshima, Self homotopy group of the exceptional Lie group G₂, J. Math. Kyoto Univ. 40 (1) (2000) 177-184] conjectured: if G is simple, then H(G) is nilpotent of class ?rankG. We show this is true for PU(p) which is the first high rank example.     

Solvation dynamics of coumarin 153 in alcohols confined in silica nanochannels

Solvation dynamics in alcohols confined in silica nanochannels was examined by time-resolved fluorescence spectroscopy using coumarin 153 (C153) as a fluorescent probe. Surfactant-templated mesoporous silica was fabricated inside the pores of an anodic alumina membrane. The surfactant was removed by calcination to give mesoporous silica (Cal-NAM) containing one-dimensional (1D) silica nanochannels (diameter, 3.1 nm) whose inner surface was covered with silanol groups. By treating Cal-NAM with trimethylchlorosilane, trimethylsilyl (TMS) groups were formed on the inner surface of the silica nanochannels (TMS-NAM). Fluorescence dynamic Stokes shifts of C153 were measured in alcohols (ethanol, butanol, hexanol, and decanol) confined in the silica nanochannels of Cal- and TMS-NAMs, and the time-dependent fluorescence decay profiles could be best fitted by a biexponential function. The estimated solvent relaxation times were much larger than those observed in bulk alcohols for both Cal- and TMS-NAMs when ethanol or butanol was used as a solvent, indicating that the mobility of these alcohol molecules was restricted within the silica nanochannels. However, hexanol or decanol in Cal- and TMS-NAMs did not cause a remarkable increase in the solvent relaxation time in contrast to ethanol or butanol. Therefore, it was concluded that a relatively rigid assembly of alcohols (an alcohol chain) was formed within the silica nanochannels by hydrogen bonding interaction and van der Waals force between the surface functional groups of the silica nanochannels and alcohol molecules and by the successive interaction between alcohol molecules when alcohol with a short alkyl chain (ethanol or butanol) was used as a solvent.     

Synthesis of novel pentafluorosulfanylfurans. Two retro-Diels-Alder approaches

The first examples of furan substituted with an SF5 group are reported. 3-pentafluorosulfanylfurans were prepared from their respective 2-pentafluorosulfanyl-5-cyano-7-oxabicyclo[2.2.1]hept-2-ene precursors via retro-Diels-Alder reactions. Also, a tandem cycloaddition/retrocycloaddition reaction between 4-phenyloxazole and 1-pentafluorosulfanylhex-1-yne was used to prepare 3-pentafluorosulfanyl-4-butylfuran. [reaction: see text].