The generation and classification of tile-k-transitive tilings of the Euclidean plane,the sphere and the hyperbolic plane

Algorithms based on the theory of Delaney-Dress symbols are discussed that can be used to recursively produce all possible equivariant types of tile-k-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane, for any (reasonable)k. A number of results can be obtained using computer implementations of the algorithms.     

Encapsulation of Mithramycin in Liposomes in Response to a Transmembrane Gradient of Calcium Ions

The recent discovery that mithramycin(MTR) in aqueous solution forms a high affinity[Ca(MTR)4]2- complex led us to the idea thatCa2+-loaded liposomes might be able to accumulateMTR in their aqueous internal compartment. Wetherefore investigated the uptake of MTR into largeunilamellar vesicles (LUV) containing NaCl orCaCl2. Our data show that MTR was efficientlyaccumulated within LUV made fromdipalmitoylphosphatidylcholine and cholesterol, onlywhen the liposomes contained Ca2+ and wereresuspended in a Ca2+-free medium. A drugencapsulation efficiency as high as 60% was achieved,at a drug to lipid molar ratio of 1/18. The circulardichroism and fluorescence excitation spectra ofliposome-encapsulated MTR (LMTR) displayed strongsimilarities with those of the [Ca(MTR)4]2-complex. LMTR was found to be stable, when submittedto conditions that destabilized the[Ca(MTR)4]2- complex. Upon dilution andincubation for 24 h at 37 °C, MTR-containingliposomes did not release a significant amount of MTR.These properties were attributed to the formation ofa high affinity complex between MTR and Ca2+inthe aqueous compartment of liposomes.     

Two finiteness theorems for periodic tilings of d-dimensional euclidean space

Consider the d -dimensional euclidean space E ^d . Two main results are presented: First, for any N∈ N, the number of types of periodic equivariant tilings that have precisely N orbits of (2,4,6, . . . ) -flags with respect to the symmetry group Γ , is finite. Second, for any N∈ N, the number of types of convex, periodic equivariant tilings that have precisely N orbits of tiles with respect to the symmetry group Γ , is finite. The former result (and some generalizations) is proved combinatorially, using Delaney symbols, whereas the proof of the latter result is based on both geometric arguments and Delaney symbols. <lsiheader> <onlinepub>7 August, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>20n2p143.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>no <sectionname> </lsiheader> Received September 5, 1996, and in revised form January 6, 1997.     

Periodic Delone Tilings

Given a periodic point set in 3-dimensional Euclidean space, an algorithm is described for computing the corresponding Delone tiling (and its Delaney symbol). Examples of applications in tiling theory and crystallography are discussed.     

Pion and nucleon dissociation in π−p→π−π+π−p at 205 GeV/c

In a 48 000-picture exposure of the Fermilab 30-inch hydrogen bubble chamber to a 205 GeV/cπ^?beam, we have measured 169 events of the reaction, π^?p→π^?π⁺π^?p, with a cross section of 635 ± 61 μb. This reaction proceeds almost entirely via low mass π^? → 3π and p → pππ dissociation. Factorization is satisfied for p → pππ dissociation in πp and pp interactions.     

Atomic force microscopy analysis of wool fibre surfaces in air and under water

Wool fibre surfaces have been treated by solvent cleaning which leaves the native covalently bound surface lipid layer intact, and by alcoholic alkali which removes the lipid layer. The resultant surfaces have been analysed by atomic force microscopy (AFM), with particular emphasis on force–distance (F–d) methods. Methodologies were developed for investigation in situ in water of both the surface topography and the characteristics of the lipid layer. Longitudinal surface texturing was resolved in images of wool fibre surfaces in air; the texturing remained prominent after exposure to water. High resolution F–d curves revealed features associated with the lipid layer. A simple formalism was used to show that the layer had a thickness of a few nm, and an effective stiffness of some 0.12±0.01 N/m. Strong adhesive interactions, equivalent to a pressure of 0.1 MPa, acted on the tip at the tip-to-substrate interface. The methodology and formalism are likely to be relevant in the broad field of thin-film analysis and for fibre technology.