Glicci simplicial complexes

This note is a case study for the potential of liaison-theoretic methods to applications in Combinatorics. One of the main open questions in liaison theory is whether every homogeneous Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the G-liaison class of a complete intersection. We give an affirmative answer to this question for Stanley-Reisner ideals defined by simplicial complexes that are weakly vertex-decomposable. This class of complexes includes matroid, shifted and Gorenstein complexes respectively. Moreover, we construct a simplicial complex which shows that the property of being glicci depends on the characteristic of the base field. As an application of our methods we establish new evidence for two conjectures of Stanley on partitionable complexes and Stanley decompositions.     

The price of anarchy in an exponential multi-server

We consider two criteria for routing selection in a multi-server service station: the equilibrium and social optimization. The ratio between the average mean waiting times in these two routings is called the price of anarchy (PoA). We show that the worst-case PoA is precisely the number of servers.     

Hyperbolic Fibrations and q-Clans

We show there is a bijection between regular hyperbolic fibrations with constant back half and normalized q-clans. Thus there is also a bijection with flocks of a quadratic cone, once a conic of the flock has been specified. This yields a plethora of two-dimensional translation planes of even and odd order which arise from spreads admitting a regular elliptic cover.     

Untersuchung von Kakao, Schokolade, Kaffee und Tee

Ohne Zusammenfassung     

Magnus’ expansion for time-periodic systems: Parameter-dependent approximations

Magnus’ expansion solves the nonlinear Hausdorff equation associated with a linear time-varying system of ordinary differential equations by forming the matrix exponential of a series of integrated commutators of the matrix-valued coefficient. Instead of expanding the fundamental solution itself, that is, the logarithm is expanded. Within some finite interval in the time variable, such an expansion converges faster than direct methods like Picard iteration and it preserves symmetries of the ODE system, if present. For time-periodic systems, Magnus expansion, in some cases, allows one to symbolically approximate the logarithm of the Floquet transition matrix (monodromy matrix) in terms of parameters. Although it has been successfully used as a numerical tool, this use of the Magnus expansion is new. Here we use a version of Magnus’ expansion due to Iserles [Iserles A. Expansions that grow on trees. Not Am Math Soc 2002;49:430–40], who reordered the terms of Magnus’ expansion for more efficient computation. Though much about the convergence of the Magnus expansion is not known, we explore the convergence of the expansion and apply known convergence estimates. We discuss the possible benefits to using it for time-periodic systems, and we demonstrate the expansion on several examples of periodic systems through the use of a computer algebra system, showing how the convergence depends on parameters.     

Ueber Milchzucker und Galaktose

Ohne Zusammenfassung     

Labeling of macrophages using bacterial magnetosomes and their characterization by magnetic resonance imaging

This work investigated macrophages labeled with magnetosomes for the possible detection of inflammations by MR molecular imaging. Pure magnetosomes and macrophages containing magnetosomes were analyzed using a clinical 1.5 T MR-scanner. Relaxivities of magnetosomes and relaxation rates of cells containing magnetosomes were determined. Peritonitis was induced in two mice. T₁, T₂ and T₂* weighted images were acquired following injection of the probes. Pure magnetosomes and labeled cells showed slight effects on T₁, but strong effects on T₂ and T₂* images. Labeled macrophages were located with magnetic resonance imaging (MRI) in the colon area, thus demonstrating the feasibility of the proposed approach.     

Emission spectroscopy of flame fronts in aluminum suspensions

Spatially resolved emission spectra from Bunsen-type flames stabilized in aluminum suspensions in air and oxygen–argon/helium mixtures were obtained using a mechanical-optical scanning system. A low resolution (1.5 nm) spectrometer was used to acquire the broad spectra over the 350–1000 nm range, and a high-resolution (0.04 nm) instrument was used for observation of AlO molecular bands and non-ionized atomic aluminum. The temperature of condensed phase emitters in the flame was derived using polychromatic fitting of the continuum spectra to Planck’s law. AlO temperature was found by fitting of the theoretically calculated shape of the band to experimental data. Peak temperatures of the condensed emitters were found to be approximately 3250 K in aluminum-air flames and approximately 3350 K for oxygen–argon/helium flames. Temperatures derived from AlO spectra coincide with the temperature of the condensed emitters with measurement accuracy and are only 100–200 °C lower than the computed equilibrium flame temperatures. The radial distribution of the temperature profile of the continuous emitters was found via Abel deconvolution and recovered the double-front structure of the Bunsen flame cone, with the outer flame being attributed to a diffusion flame of the fuel-rich products with ambient air. The observation of atomic aluminum lines seen in emission from the outer flame edge and partial self-absorption from the inner flame confirms the structure associated with the double-front structure. The implications of these results for the regime of particle combustion in a dust flame are discussed.