Extensible Embeddings of Black-Hole Geometries

Removing a black hole conic singularity by means of Kruskal representation is equivalent to imposing extensibility on the Kasner–Fronsdal local isometric embedding of the corresponding black hole geometry. Allowing for globally non-trivial embeddings, living in Kaluza–Klein-like M ₅ × S ₁ (rather than in standard Minkowski M ₆ ) and parametrized by some wave number k, extensibility can be achieved for apparently forbidden frequencies in the range ₁ (k) ₂ (k). As k 0, _{1, 2} (0) _H (e.g., _H = 1/4M in the Schwarzschild case) such that the Hawking–Gibbons limit is fully recovered. The various Kruskal sheets are then viewed as slices of the Kaluza–Klein background. Euclidean k discreteness, dictated by imaginary time periodicity, is correlated with flux quantization of the underlying embedding gauge field.     

The two-neutron transfer reactions (O, O) with O, C and Mg targets

Excitation functions, angular distributions and differential ranges were measured for the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction at ¹⁸O beam energies of 20–45 MeV. Excitation functions only were measured for the reactions ¹⁴C(¹⁸O, ¹⁹O)¹³C, ¹⁴C(¹⁸O, ¹⁶O)¹⁶C, ¹⁴C(¹⁸O, ²⁰O)¹²C, ¹⁴C(¹⁸O, ¹⁵N)¹⁷N and ¹⁸O(¹⁸O, ¹⁹O)¹⁷O, ¹⁸O(¹⁸O, ¹⁶O)²⁰O, ¹⁸O(¹⁸O, ¹⁵N)²¹F at ¹⁸O beam energies of 13–41 MeV. We have identified these as direct reactions in which a single neutron, a two-neutron cluster, a deuteron and a triton are transferred between projectile and target.

The cross sections for two-neutron transfer reactions were found to be relatively high and those for the ¹⁸O+¹⁸O and the ¹⁴C+¹⁸O reactions were higher than the ones of single-neutron transfers over most of the energy range.

Attempts were made to apply the theory of Buttle and Goldfarb for single-neutron transfer to the case of two-neutron transfer in the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction below the Coulomb barrier. It is shown that for those reactions for which the assumptions, implicit in the model, are valid, good agreement is obtained with experiment. We also tried to apply the diffraction model of Dar and Kozlovsky to the calculation of the angular distribution of these reactions. A good fit to the experimental results could be obtained if quite different sets of parameters were used in the calculations for the two bombarding energies.     

Extremal functions for functionals on some classes of analytic functions

It is shown that the theorem of Carathéodory and Toeplitz on the characterization of the Taylor coefficients of analytic functions with positive real part can be applied to extremal problems in several classes of analytic functions.     

Declining valuations in sequential auctions

We analyze an independent private values model where a number of objects are sold in sequential first- and second-price auctions. Bidders have unit demand and their valuation for an object is decreasing in the rank number of the auction in which it is sold. We derive efficient equilibria if prices are announced after each auction or if no information is given to bidders. We show that the sequence of prices constitutes a supermartingale. Even if we correct for the decrease in valuations for objects sold in later auctions we find that average prices are declining.Received June 2004We are grateful to Christian Groh, Wolfgang Köhler and Benny Moldovanu for helpful suggestions. Financial support from the German Science Foundation through SFB 504 and SFB/TR 15 at the University of Mannheim and the University of Bonn is gratefully acknowledged.     

Long term behavior of lithographically prepared in vitro neuronal networks

We measured the long term spontaneous electrical activity of neuronal networks with different sizes, grown on lithographically prepared substrates and recorded with multi-electrode-array technology. The time sequences of synchronized bursting events were used to characterize network dynamics. All networks exhibit scale-invariant Lévy distributions and long-range correlations. These observations suggest that different-size networks self-organize to adjust their activities over many time scales. As predictions of current models differ from our observations, this calls for revised models.     

Hasse invariants for Hilbert modular varieties

Given a totally real fieldL of degreeg, we constructg Hasse invariants on Hilbert modular varieties in characteristicp and characterize their divisors. We show that these divisors give the type stratification defined by the action of on theα _p -elementary subgroup. Under certain conditions, involving special values of zeta functions, the product of these Hasse invariants is the reduction of an Eisenstein series of weightp−1     

Short range order in anomalous liquid metals

Liquid metals with anomalous physical properties such as increasing sound velocity with temperature or density anomalies, exhibit a complex structure in their one dimensional experimental diffraction patterns. Typically, their radial distribution functions are characterized by an asymmetric first peak and a subsidiary peak or shoulder on the right hand side of the first main peak. It has been hypothesized that the complex structure is associated with short range ordering the liquid. Specifically in the liquid pnictides, it has been proposed that such order may be associated with the underlying solid A7 structure. We present an analysis of the short range order in liquids using a modified quasi-crystalline model of liquid structure. This model is shown to fit the experimental radial distribution function very well and to reproduce the experimentally observed structure factor. Using this model we find that the short range order in the liquid pnictides is dominated by an A7-like structure with two types of bonds, in close agreement with the underlying solid phase. The existence of two bond lengths is necessary within this model to explain the asymmetry in the first peak as well as the change in coordination number along the pnictide series. The quasi-crystalline model is discussed and shown to correlate with the Lindemann melting criterion.     

Electrospun fibers of functional nanocomposites composed of single‐walled carbon nanotubes,fullerene derivatives,and poly(3‐hexylthiophene)

Electrospinning of fibers composed of poly(3‐hexylthiophene) (P3HT), fullerene derivative, phenyl‐C₆₁‐butyric acid methyl ester (PCBM), and single‐walled carbon nanotubes (SWNT) is reported. While of great promise for photovoltaic applications, morphological control of functional structures is a great challenge for most processing methods. It is demonstrated that the use of a tailor‐made block‐copolymer for dispersion of individual SWNT enables the preparation of stable dispersions of individual tubes that may be further cospun from chloroform solutions with PCBM and P3HT into submicron fibers. The block copolymer used to mediate the colloidal and interfacial interactions in the combined system enables the spinning of centimeters long and uniform fibers. Structural characterization indicates a high degree of ordering and alignment within the fibers and absorption and quenching of the photoluminescence indicate significant interactions among the components. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1263–1268, 2011