Topological equivalence of discontinuous norms

We show that for everyp>0 there is an autohomeomorphismh of the countable infinite product of linesR ^Nsuch that for everyr>0,h maps the Hilbert cube [−r, r] ^N precisely onto the “elliptic cube” . This means that the supremum norm and, for instance, the Hilbert norm (p=2) are topologically indistinguishable as functions onR ^N.The result is obtained by means of the Bing Shrinking Criterion. Research supported in part by a grant from NSF-EPSCoR Alabama.     

Measurement of mass and lifetime of hadronically produced charmed F mesons

We have observed three unique decays of F mesons into KKπ and five unique decays of D mesons into KKπ using the NA11 spectrometer together with a telescope of high-resolution silicon microstrip detectors. The mass value obtained for the F meson is (1975 ± 4) MeV, the lifetime (3.2±_1.3^3..0)×10^?13 s.     

Information theory applied to qualitative analysis

Summary Fundamental aspects of information theory and its usefulness for qualitative analysis are discussed in view of the applications described so far in the literature. General expressions for the uncertainty, information, equivocation and information content are described and related to the more commonly used expressions of the information parameters.It is shown that the information content (or equivocation) can serve — with certain restrictions — as an important criterion for the evaluation, selection or optimization of analytical procedures.The information theoretical concepts are easy to apply to one-channel identification or classification procedures. However, when multi-channel procedures (combinations of one-channel procedures) are involved, a straightforward use of information theory is to a large extent restricted by the excessive computations. Therefore, the further development of simple methods for the calculation of reliable estimates of information contents and of optimization strategies enabling the calculation of only small numbers of information contents, is of great importance for the future use of information theory in qualitative analysis.

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Anwendung der Informationstheorie in der qualitativen Analyse

Zusammenfassung Grundlegende Aspekte der Informationstheorie und ihre Anwendbarkeit für die qualitative Analyse werden unter Berücksichtigung der bisher in der Literatur beschriebenen Anwendungen besprochen. Allgemeine Ausdrücke für Unsicherheit, Information, Äquivokation und Informationsgehalt werden beschrieben und ihre Beziehung zu den gebräuchlicheren Ausdrücken für die Informationsparameter wird angegeben.Es wird gezeigt, daß der Informationsgehalt (oder die Äquivokation) — unter bestimmten Bedingungen — als ein wichtiges Kriterium für die Auswertung, Selektion oder Optimierung von analytischen Verfahren dienen kann.Die Grundlagen der Informationstheorie können auf einfache Weise für einkanalige Identifizierungsoder Klassifizierungsverfahren angewendet werden. Wenn es sich jedoch um mehrkanalige Verfahren (Kombinationen von Einkanal-Verfahren) handelt, wird die Anwendung der Informationstheorie in hohem Maße durch übermäßige Berechnungen begrenzt.Die weitere Entwicklung von einfachen Verfahren für die Berechnung zuverlässiger Schätzungen von Informationsgehalten und von Optimierungsstrategien, die die Berechnung einer beschränkten Anzahl von Informationsgehalten erfordern, ist deshalb von großer Wichtigkeit für die künftige Anwendung der Informationstheorie in der qualitativen Analyse.

     

Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field

Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field.     

Capillary freezing or complete wetting of hard spheres in a planar hard slit?

Extensive simulations of a hard sphere fluid confined between two planar hard walls show the onset of crystalline layers at the walls at about 98.3% of bulk crystallization density rho(f) independent of the wall separations L(z), and is, hence, a single wall phenomenon. As the bulk density far from the wall rho(b) increases, the thickness of the crystalline film appears to increase logarithmically, with (rho(f)-rho(b)) indicating complete wetting by the hard sphere crystal of the wall-fluid interface. Increasing rho(b) further, we observe a jump in the adsorption which depends on L(z) and corresponds to capillary freezing. The formation of crystalline layers below bulk crystallization, the logarithmic growth of the crystalline film, its independence of L(z), and its clear distinction from capillary freezing lend strong evidence for complete wetting by the hard sphere crystal at the wall-fluid interface.     

Nitrogen stable isotope composition of leaves and roots of plants growing in a forest and a meadow

In controlled N-nutrition experiments, differences in delta15N composition of leaves and roots are regularly found. In this paper we report results from a survey of nitrogen stable isotope signatures of leaves and roots of 16 plant species growing under natural conditions in a meadow and a forest understorey, which differed in nitrate and ammonium availability. Significant differences between leaf and root were observed. The range of delta15N [leaf-root] values was -0.97 to +0.86 per thousand, small compared to published values from controlled N-nutrition experiment, but almost as large as the range of leaf delta15N values (-1.04 to +1.08 per thousand). Forbs showed the largest differences between leaves and roots and showed a significant difference with respect to habitat. Grasses and legumes did not show significant differences in delta15N [leaf-root] between the two habitats. Care must be taken when using leaf delta15N values as representative for whole-plant 15N composition in these two habitats.     

Low temperature scanning force microscopy of the Si(111)-(7x7) surface

A low temperature scanning force microscope (SFM) operating in a dynamic mode in ultrahigh vacuum was used to study the Si(111)- (7x7) surface at 7.2 K. Not only the twelve adatoms but also the six rest atoms of the unit cell are clearly resolved for the first time with SFM. In addition, the first measurements of the short range chemical bonding forces above specific atomic sites are presented. The data are in good agreement with first principles computations and indicate that the nearest atoms in the tip and sample relax significantly when the tip is within a few A of the surface.     

Poly(ethylene glycol)–poly(L‐lactide) star block copolymer hydrogels crosslinked by metal–ligand coordination

The aqueous solution behavior and thermoreversible gelation properties of pyridine‐end‐functionalized poly(ethylene glycol)–poly(L ‐lactide) (PEG–(PLLA)₈–py) star block copolymers in the presence of coordinating transition metal ions were studied. In aqueous solutions, the macromonomers self‐assembled into micelles and micellar aggregates at low concentrations and formed physically crosslinked, thermoreversible hydrogels above a critical gel concentration (CGC) of 8% w/v. In the presence of transition metal ions like Cu(II), Co(II), or Mn(II), the aggregate dimensions increased. Above the CGC, the gel–sol transition shifted to higher temperatures due to the formation of additional crosslinks from intermolecular coordination complexes between metal ions and pyridine ligands. Furthermore, as an example, PEG–(PLLA)₈–py hydrogels stabilized by Mn(II)–pyridine coordination complexes were more resistant against degradation/dissolution when placed in phosphate buffered saline at 37 °C when compared with hydrogels prepared in water. Importantly, the stabilizing effect of metal–ligand coordination was noticeable at very low Cu(II) concentrations, which have been reported to be noncytotoxic for fibroblasts in vitro. These novel PEG–(PLLA)₈–py metallo‐hydrogels, which are the first systems to combine metal–ligand coordination with the advantageous properties of PEG–PLLA copolymer hydrogels, are appealing materials that may find use in biomedical as well as environmental applications like the removal of heavy metal ions from waste streams. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

On the structure ofn-point sets

Letn be an integer greater than one. Our main result, called the “Structure Theorem” is that a set that containsn−1 disjoint continua that are cut by a single line cannot be ann-point set, that is, a set that meets every line in preciselyn points. This theorem unifies and significantly improves upon a number of known theorems. The second part of the paper is devoted to several theorems that address the question when a set that meets every line in at mostn points can be extended to ann-point set. These theorems also highlight the sharpness of the Structure Theorem.     

Crystal nucleation of colloidal hard dumbbells

Using computer simulations, we investigate the homogeneous crystal nucleation in suspensions of colloidal hard dumbbells. The free energy barriers are determined by Monte Carlo simulations using the umbrella sampling technique. We calculate the nucleation rates for the plastic crystal and the aperiodic crystal phase using the kinetic prefactor as determined from event driven molecular dynamics simulations. We find good agreement with the nucleation rates determined from spontaneous nucleation events observed in event driven molecular dynamics simulations within error bars of one order of magnitude. We study the effect of aspect ratio of the dumbbells on the nucleation of plastic and aperiodic crystal phases, and we also determine the structure of the critical nuclei. Moreover, we find that the nucleation of the aligned close-packed crystal structure is strongly suppressed by a high free energy barrier at low supersaturations and slow dynamics at high supersaturations.