On periodic homeomorphisms of spheres

The purpose of this paper is to study how small orbits of periodic homemorphisms of spheres can be.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-22.abs.htm

Regular Incidence Complexes, Polytopes, and C-Groups

Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of abstract regular polytopes has been well-studied. The paper describes the combinatorial structure of a regular incidence complex in terms of a system of distinguished generating subgroups of its automorphism group or a flag-transitive subgroup. Then the groups admitting a flag-transitive action on an incidence complex are characterized as generalized string C-groups. Further, extensions of regular incidence complexes are studied, and certain incidence complexes particularly close to abstract polytopes, called abstract polytope complexes, are investigated.Comment: 24 pages; to appear in "Discrete Geometry and Symmetry", M. Conder, A. Deza, and A. Ivic Weiss (eds), Springe

Finite density phase transition of QCD with Nf=4N_f=4 and Nf=2N_f=2 using canonical ensemble method

In a progress toward searching for the QCD critical point, we study the finite density phase transition of $N_f = 4$ and 2 lattice QCD at finite temperature with the canonical ensemble approach. We develop a winding number expansion method to accurately project out the particle number from the fermion determinant which greatly extends the applicable range of baryon number sectors to make the study feasible. Our lattice simulation was carried out with the clover fermions and improved gauge action. For a given temperature, we calculate the baryon chemical potential from the canonical approach to look for the mixed phase as a signal for the first order phase transition. In the case of $N_f=4$, we observe an "S-shape" structure in the chemical potential-density plane due to the surface tension of the mixed phase in a finite volume which is a signal for the first order phase transition. We use the Maxwell construction to determine the phase boundaries for three temperatures below $T_c$. The intersecting point of the two extrapolated boundaries turns out to be at the expected first order transition point at $T_c$ with $\mu = 0$. This serves as a check for our method of identifying the critical point. We also studied the $N_f =2$ case, but do not see a signal of the mixed phase for temperature as low as 0.83 $T_c$.Comment: 28 pages, 11 figures,references added, final versio

The local atomic quasicrystal structure of the icosahedral Mg25Y11Zn64 alloy

A local and medium range atomic structure model for the face centred icosahedral (fci) Mg25Y11Zn64 alloy has been established in a sphere of r = 27 A. The model was refined by least squares techniques using the atomic pair distribution (PDF) function obtained from synchrotron powder diffraction. Three hierarchies of the atomic arrangement can be found: (i) five types of local coordination polyhedra for the single atoms, four of which are of Frank-Kasper type. In turn, they (ii) form a three-shell (Bergman) cluster containing 104 atoms, which is condensed sharing its outer shell with its neighbouring clusters and (iii) a cluster connecting scheme corresponding to a three-dimensional tiling leaving space for few glue atoms. Inside adjacent clusters, Y8-cubes are tilted with respect to each other and thus allow for overall icosahedral symmetry. It is shown that the title compound is essentially isomorphic to its holmium analogue. Therefore fci-Mg-Y-Zn can be seen as the representative structure type for the other rare earth analogues fci-Mg-Zn-RE (RE = Dy, Er, Ho, Tb) reported in the literature.Comment: 12 pages, 8 figures, 2 table

Adjoint quarks and fermionic boundary conditions

We study quenched SU(2) lattice gauge theory with adjoint fermions in a wide range of temperatures. We focus on spectral quantities of the Dirac operator and use the temporal fermionic boundary conditions as a tool to probe the system. We determine the deconfinement temperature through the Polyakov loop, and the chiral symmetry restoration temperature for adjoint fermions through the gap in the Dirac spectrum. This chiral transition temperature is about four times larger than the deconfinement temperature. In between the two transitions we find that the system is characterized by a non-vanishing chiral condensate which differs for periodic and anti-periodic fermion boundary conditions. Only for the latter (physical) boundary conditions, the condensate vanishes at the chiral transition. The behavior between the two transitions suggests that deconfinement manifests itself as the onset of a dependence of spectral quantities of the Dirac operator on boundary conditions. This picture is supported further by our results for the dual chiral condensate.Comment: Minor changes; final version to appear in JHE

The Fermat-Torricelli problem in normed planes and spaces

We investigate the Fermat-Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat-Torricelli locus in a geometric way. We present many new results, as well as give an exposition of known results that are scattered in various sources, with proofs for some of them. Together, these results can be considered to be a minitheory of the Fermat-Torricelli problem in Minkowski spaces and especially in Minkowski planes. This demonstrates that substantial results about locational problems valid for all norms can be found using a geometric approach

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang-Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson-Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.Comment: 15 pages, 9 figures. For clarification one paragraph and two references added in the introduction and two sentences at the end of the first and last paragraph of the summary. Appeared in EPJ

Multimodal imaging of pancreatic beta cells in vivo by targeting transmembrane protein 27 (TMEM27)

Aims/hypothesis: Non-invasive diagnostic tools specific for pancreatic beta cells will have a profound impact on our understanding of the pathophysiology of metabolic diseases such as diabetes. The objective of this study was to use molecular imaging probes specifically targeting beta cells on human samples and animal models using state-of-the-art imaging modalities (fluorescence and PET) with preclinical and clinical perspective. Methods: We generated a monoclonal antibody, 8/9-mAb, targeting transmembrane protein 27 (TMEM27; a surface N-glycoprotein that is highly expressed on beta cells), compared its expression in human and mouse pancreas, and demonstrated beta cell-specific binding in both. In vivo imaging was performed in mice with subcutaneous insulinomas overexpressing the human TMEM27 gene, or transgenic mice with beta cell-specific hTMEM27 expression under the control of rat insulin promoter (RIP-hTMEM27-tg), using fluorescence and radioactively labelled antibody, followed by tissue ex vivo analysis and fluorescence microscopy. Results: Fluorescently labelled 8/9-mAb showed beta cell-specific staining on human and mouse pancreatic sections. Real-time PCR on islet cDNA indicated about tenfold higher expression of hTMEM27 in RIP-hTMEM27-tg mice than in humans. In vivo fluorescence and PET imaging in nude mice with insulinoma xenografts expressing hTMEM27 showed high 8/9-mAb uptake in tumours after 72h. Antibody homing was also observed in beta cells of RIP-hTMEM27-tg mice by in vivo fluorescence imaging. Ex vivo analysis of intact pancreas and fluorescence microscopy in beta cells confirmed these findings. Conclusions/interpretation: hTMEM27 constitutes an attractive target for in vivo visualisation of pancreatic beta cells. Studies in mouse insulinoma models and mice expressing hTMEM27 demonstrate the feasibility of beta cell-targeted in vivo imaging, which is attractive for preclinical investigations and holds potential in clinical diagnostic

Synthesis, structural characterization, antimicrobial and cytotoxic effects of aziridine, 2-aminoethylaziridine and azirine complexes of copper(II) and palladium(II).

The synthesis, spectroscopic and X-ray structural characterization of copper(II) and palladium(II) complexes with aziridine ligands as 2-dimethylaziridine HNCH2CMe2 (a), the bidentate N-(2-aminoethyl)aziridines C2H4NC2H4NH2 (b) or CH2CMe2NCH2CMe2NH2 (c) as well as the unsaturated azirine NCH2CPh (d) are reported. Cleavage of the cyclometallated Pd(II) dimer [μ-Cl(C6H4CHMeNMe2-C,N)Pd]2 with ligand a yielded compound [Cl(NHCH2CMe2)(C6H4CHMe2NMe2-C,N)Pd] (1a). The reaction of the aziridine complex trans-[Cl2Pd(HNC2H4)2] with an excess of aziridine in the presence of AgOTf gave the ionic chelate complex trans-[(C2H4NC2H4NH2-N,N′)2Pd](OTf)2 (2b) which contains the new ligand b formed by an unexpected insertion and ring opening reaction of two aziridines (“aziridine dimerization”). CuCl2 reacted in pure HNC2H4 or HNCH2CMe2 (b) again by “dimerization” to give the tris-chelated ionic complex [Cu(C2H4NC2H4NH2-N,N′)3]Cl2 (3b) or the bis-chelated complex [CuCl(C2H2Me2NC2H2Me2NH2-N,N′)2]Cl (4c). By addition of 2H-3-phenylazirine (d) to PdCl2, trans-[Cl2Pd(NCH2CPh)2] (5d) was formed. All new compounds were characterized by NMR, IR and mass spectra and also by X-ray structure analyses (except 3b). Additionally the cytotoxic effects of these complexes were examined on HL-60 and NALM-6 human leukemia cells and melanoma WM-115 cells. The antimicrobial activity was also determined. The growth of Gram-positive bacterial strains (S. aureus, S. epidermidis, E. faecalis) was inhibited by almost all tested complexes at the concentrations of 37.5–300.0 μg mL−1. However, MIC values of complexes obtained for Gram-negative E. coli and P. aeruginosa, as well as for C. albicans yeast, mostly exceeded 300 μg mL−1. The highest antibacterial activity was achieved by complexes 1a and 2b. Complex 2b also inhibited the growth of Gram-negative bacteria. Graphical abstract: Synthesis, structural characterization, antimicrobial and cytotoxic effects of aziridine, 2-aminoethylaziridine and azirine complexes of copper(ii) and palladium(ii