Almost simple groups of Suzuki type acting on polytopes

Let , with an odd power of two. For each almost simple group such that , we prove that is not a C-group and therefore is not the automorphism group of an abstract regular polytope. For , we show that there is always at least one abstract regular polytope such that . Moreover, if is an abstract regular polytope such that , then is a polyhedron.

     

High-throughput screening and optimization of photoembossed relief structures

A methodology for the rapid design, screening, and optimization of coating systems with surface relief structures, using a combination of statistical experimental design, high-throughput experimentation, data mining, and graphical and mathematical optimization routines was developed. The methodology was applied to photopolymers used in photoembossing applications. A library of 72 films was prepared by dispensing a given amount of sample onto a chemically patterned substrate consisting of hydrophilic areas separated by fluorinated hydrophobic barriers. Film composition and film processing conditions were determined using statistical experimental design. The surface topology of the films was characterized by automated AFM. Subsequently, models explaining the dependence of surface topologies on sample composition and processing parameters were developed and used for screening a virtual 4000-membered in silico library of photopolymer lacquers. Simple graphical optimization or Pareto algorithms were subsequently used to find an ensemble of formulations, which were optimal with respect to a predefined set of properties, such as aspect ratio and shape of the relief structures.     

Generalizing minimal supergravity

In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the generic gauge coupling relations at the GUT scale, and the general gaugino mass relations which are valid from the GUT scale to the electroweak scale at one loop. We define the index k   for these relations, which can be calculated in GUTs and can be determined at the Large Hadron Collider and the future International Linear Collider. Thus, we give a concrete definition of the GUT scale in these theories, and suggest a new way to test general GUTs at future experiments. We also discuss five special scenarios with interesting possibilities. With our generic formulae, we present all the GUT-scale gauge coupling relations and all the gaugino mass relations in the SU(5)$\mathit{SU}(5)$ and SO(10)$\mathit{SO}(10)$ models, and calculate the corresponding indices k. Especially, the index k   is 5/3 in the traditional SU(5)$\mathit{SU}(5)$ and SO(10)$\mathit{SO}(10)$ models that have been studied extensively so far. Furthermore, we discuss the field theory realization of the U(1)$U(1)$ flux effects on the SM gauge kinetic functions in F-theory GUTs, and calculate their indices k as well.     

Comments on ultra-high-energy photons and D-foam models

We revisit the constraints that the non-observation of ultra-high-energy photons due to the GZK cutoff can impose on models of Lorentz violation in photon propagation, following recent work by Maccione, Liberati and Sigl (2010) [arXiv:1003.5468] that carries further an earlier analysis by the present authors [J. Ellis et al., Phys. Rev. D 63 (2001) 12402, hep-th/0012216]. We argue that the GZK cutoff constraint is naturally evaded in the D-brane model of space–time foam presented recently by the present authors [J. Ellis et al., Phys. Lett. B 665 (2008) 412, arXiv:0804.3566], in which Lorentz-violating effects on photon propagation are independent of possible effects during interactions. We also note a novel absorption mechanism that could provide a GZK-like cutoff for photons in low-scale string models.     

Highly efficient synthesis and solid-state characterization of 1,2,4,5-tetrakis(alkyl- and arylamino)benzenes and cyclization to their respective benzobis(imidazolium) salts

[reaction: see text] New synthetic methodology to a variety of 1,2,4,5-tetraaminobenzenes and their corresponding benzobis(imidazolium) salts has been accomplished. Palladium-catalyzed coupling of various 1,2,4,5-tetrabromo- or 1,2,4,5-tetrachlorobenzenes with aryl- or tert-alkylamines afforded the respective tetrakis(N-substituted)aminobenzenes in excellent yields. This enabled comparative solid-state structural analyses of this elusive class of electron-rich arenes with their oxidized derivatives. The tetraamines were found to undergo formylative cyclization to the corresponding benzobis(imidazolium) salts in good to excellent yields.     

Uhlenbeck–Donaldson compactification for framed sheaves on projective surfaces

We construct a compactification $M^{\mu ss}$ of the Uhlenbeck–Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma :M^{ss} \rightarrow M^{\mu ss}$ , where $M^{ss}$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin–Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.     

A fluorescence toolbox: A review of investigation of electrophoretic separations,process, and interfaces

This review focuses on fluorescence spectroscopy techniques for the investigation of electrophoretic separations. Fluorescence has been used as a sensitive detector for capillary, gel, and microchip electrophoresis for decades. However, advanced fluorescence methods can be used to study transport, interfacial phenomena, intermolecular and affinity interactions, and other processes that occur during separation. This so‐called spectroscopic toolkit can be implemented to understand fundamental behavior in electrophoresis and electrokinetic chromatography. Techniques such as fluorescence recovery after photobleaching, fluorescence correlation spectroscopy, and fluorescence anisotropy are discussed in relation to electrophoretic separations. Newer methods such as super‐resolution microscope are also introduced.     

Ab initio and Monte Carlo studies of phase transitions and magnetic properties of YCrO3: Heisenberg model

By using the density functional theory (DFT) and Monte Carlo simulations (MCS) with the Heisenberg model, we have studied magnetic properties of the bulk perovskite YCrO₃. The exchange couplings of the Heisenberg model and the magnetic anisotropy are investigated. The 110 direction in the crystalline structure of the compound has shown the minimum energy, it is the easy magnetic direction. Using Monte Carlo simulations, the magnetizations behavior, the effects of system parameters and the critical exponents of the compound YCrO₃ are implemented. It is shown that the bulk perovskite YCrO₃ belongs to the 3D Heisenberg universality class.     

A Mössbauer spectral study of the Jilin meteorite

The iron57 Mössbauer spectra of three different samples of the Jilin meteorite have been measured at 78 and 295 K. Five iron containing major components are identified, two magnetic components, kamacite and troilite, and three nonmagnetic components, olivine, pyroxene, and an iron(III) component. The relative absorption areas of these five components show that sample A contains a larger fraction of magnetic components, ca. 50 percent, than samples B and C, which contain ca. 30 percent. This difference indicates a significant compositional inhomogeneity in the Jilin meteorite. The fit of the troilite component sextet is extensively discussed in the paper and requires the adjustment of not only the isomer shift and hyperfine field, but also of the quadrupole interaction, the asymmetry parameter of the electric field gradient tensor, and the orientation of the hyperfine field in the principal axes of the electric field gradient tensor. The smaller isomer shift and hyperfine field of the kamacite mineral in sample B indicate that this sample contains less nickel than the kamacite in samples A and C, in which the amount of nickel is estimated to be ca. 9 percent. On the basis of its hyperfine parameters, the iron(III) component is assigned to iron(III) substituted on the M1 site of pyroxene.