The Number of Group Homomorphisms from DmD_m into DnD_n

Counting homomorphisms between cyclic groups is a common exercise in a first course in abstract algebra. A similar problem, accessible at the same level, is to count the number of group homomorphisms from a dihedral group of order $2m$ into a dihedral group of order $2n$. While the solution requires only elementary group theory, the result does not appear in the literature or in the usual texts. As the solution may be of interest, particularly to those teaching undergraduate abstract algebra, it is provided in this note

Draft Genome Sequence of Proteus mirabilis Strain UMB0038, Isolated from the Female Bladder

Proteus mirabilis is a Gram-negative motile and rod-shaped bacterium that is a common pathogen of the urinary tract. Here, we report the draft genome sequence of P. mirabilis UMB0038, which was isolated from a woman without lower urinary tract symptoms

Blood group typing in five Afghan populations in the North Hindu-Kush region: implications for blood transfusion practice.

International audienceBACKGROUND AND OBJECTIVES: Blood incompatibility arises from individual and ethnic differences in red blood cell (RBC) antigen profiles. This underlines the importance of documenting RBC antigen variability in various ethnic groups. Central Asia is an area with a long and complex migratory history. The purpose of this article is to describe key antigen frequencies of Afghan ethnic groups in the Hindu-Kush region of Afghanistan as a basis for improving blood transfusion practices in that area. MATERIALS AND METHODS: The key ABO, Rh and Kell antigens were investigated in five Afghan populations. In order to depict accurately the blood group gene diversity in the area, DNA from eight additional Pakistani populations were included, and the entire sample set screened using two multiplex polymerase chain reactions sensitive for 17 alleles in 10 blood group genetic systems (MNS, Kell, Duffy, Kidd, Cartwright, Dombrock, Indian, Colton, Diego and Landsteiner-Wiener). RESULTS: Phenotype and allele frequencies fell within the ranges observed in Western European and East Asian populations. Occurrence of DI*01, IN*01, LW*07 and FY*02N.01 and prevalence of ABO*B were consistent with migratory history as well as with putative environmental adaptation in the subtropical environment Hindu-Kush region. CONCLUSION: These findings expand the current knowledge about key antigen frequencies. Regarding occurrence of viral markers, further blood transfusion in the region requires rigorous typing

USDA-ARS sugar beet germplasm developed in Salinas, CA, evaluated for rhizomania resistance in Idaho

Thirty-one sugar beet germplasm breeding lines and releases produced by the USDA-ARS sugarbeet program at Salinas, CA, and one line from the USDA-ARS sugarbeet program at East Lansing, MI, were evaluated for resistance to rhizomania under south-central Idaho conditions at Twin Falls, ID. The field had been identified as having Beet necrotic yellow vein virus (BNYVV), which overcomes resistance conditioned by the Rzl gene. Single-row plots 10 ft long with 22-in. spacing were planted on 23 May 05. Plants were thinned to 4 to 6-in. spacing in mid-Jun. The materials were predominantly multigerm; they were hand thinned to single plants during the first week of Jul. The trial layout was a randomized complete block with eight replicates, however, the blocks were divided into 16 sub-blocks of six rows in which single-row plots of two entries and four control lines were randomized. The control lines were Beta443OR (Rzl gene), GO17R (Rz2 gene), Angelina (Rzl+Rz2 genes) and Beta6600 (no resistance to rhizomania). This allowed each entry plot to have its own control (Local Control). This was necessary given the uneven distribution in the field of resistance breaking strains of BNYVV. Naturally occurring Curly top virus infection was found throughout the field early in the season. Many plants of the rhizomania susceptible control were killed apparently by curly top and therefore this should be considered when evaluating the results. Plants were scored 19 Sep for curly top using a 0-9 scale with 0 showing no symptoms and 9 being dead. Plants were topped, roots lifted then scored on 12-13 Oct. Four teams evaluated the trial for rhizomania with each team rating two replicates. Each root was scored based on the traditional 0 to 6 scale which was converted to a 0 to 9 scale. The categories were 0, 1, 3, 5, 6, 7 and 9 with 0-3 being resistant, 5-7 susceptible and 9 was dead. The average disease severity was determined to create a disease index (DI) for each entry and control. A second index (DI2) was calculated for each entry-plot to evaluate the entry relative to the mean of the Rz2 and Rzl+Rz2 Local Controls (DI of entry/mean DI of the Rz2 and Rzl+Rz2 Local Controls). The percent healthy roots (categories 0-3 combined) and the percent of healthy roots relative to Rz2 and Rzl+Rz2 Local Controls were calculated (PR and PR2, respectively). The DI and DI2 were transformed with the inverse square root and analyzed using PROC MIXED - SAS with Dunnett's test (P = 0.05) option and PROC GLM – SAS with Fisher's protected LSD test (P = 0.05) option, respectively. PR and PR2 were analyzed with PROC GLM –SAS using Dunnett's test (P = 0.05) and Fisher's protected LSD (P = 0.05) test, respectively. The analysis of variance of DI2 showed that block effects were significant, therefore Spearman's partial correlation (PROC CORR Spearman partial - SAS) was used to analyze the relationship of D1, PR, DI2, PR2, and curly top. PROC CORR Spearman -SAS was used to analyze the relationship between DI and DI2

Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lens-chain structures for a general $N$-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure

Vertex labeling and routing in expanded Apollonian networks

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their vertices that allows to determine a shortest path routing between any two vertices of the network based only on the labels.Comment: 16 pages, 2 figure

Effective spin physics in two-dimensional cavity QED arrays

We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis–Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya's enumeration theorem