Spectral analysis of the free orthogonal matrix

We compute the spectral measure of the standard generators $u_{ij}$ of the Wang algebra $A_o(n)$. We show in particular that this measure has support $[-2/\sqrt{n+2},2/\sqrt{n+2}]$, and that it has no atoms. The computation is done by using various techniques, involving the general Wang algebra $A_o(F)$, a representation of $SU^q_2$ due to Woronowicz, and several calculations with orthogonal polynomials.Comment: 22 pages, 4 figure

Some morphological and histological effects of the poison of Lophopodella Carteri (Hyatt) on young Ambystoma Opacum (Gravenhorst) and Carassius Auratus (Linnaeus)

Larvae of the marbled salamander, Ambystoma onscum, and the goldfish, Carassius auratus, were subjected to poi­ soning by homogenates of Lonhopodella carteri. Stock homogenates were prepared by grinding specimens of frozen L. carteri in a rotary blender and adding distilled water to give a 20 percent concentration (wt./vol.); the stock was used to prepare working solutions. Homogenates from bryozoans collected in 1964 were approximately twice as poisonous as those from the 1963 col­ lection. It ls possible that chemical changes during stor­ age and bacterial action prior to freezing caused deterioration of the poisonous principle in the material from 1963. Stock homogenates were prepared immediately before testing as their toxicity declined over a period of several hours. The stock homogenate from 1964 was used at the rate of 2.0 ml per 50 ml of spring water; that from the 1963 collection at the rate of 4.0 ml per 50 ml of spring water. Salamanders were capable of surviving for longer periods of time in concentrations that ere lethal to fish in 60 minutes, and the stock homogenate fro 1964 was used at the rate of 5.0 ml per 50 ml of water. Test fishes showed an increase in respiratory movements accompanied by ganing opercles, a gradual loss of balance, and emission of mucus and blood from the gill regions prior to death. Size of the fish was not related to the rate of poisoning. With the salamanders, there was a progressive increase in blistering of the gill filaments, sloughing of the epithelium, and exudation of blood and mucus from the gill region. Histological preparations of the poisoned fiahes and salamanders showed a hypertrophy of the epithelial lining of the gills, destruction of the lamella and fimbriae respectively, a breakdown of the canillary walls, and an increase in the number of goblet cells in the pharynx

On polynomial integrals over the orthogonal group

We consider integrals of type $\int_{O_n}u_{11}^{a_1}... u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} du$, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such integrals, by using combinatorial methods. We present as well a general formula for such integrals, as a sum of products of factorials.Comment: 20 page

Extending the Globular Cluster System-Halo Mass Relation to the Lowest Galaxy Masses

High mass galaxies, with halo masses $M_{200} \ge 10^{10} M_{\odot}$, reveal a remarkable near-linear relation between their globular cluster (GC) system mass and their host galaxy halo mass. Extending this relation to the mass range of dwarf galaxies has been problematic due to the difficulty in measuring independent halo masses. Here we derive new halo masses based on stellar and HI gas kinematics for a sample of nearby dwarf galaxies with GC systems. We find that the GC system mass--halo mass relation for galaxies populated by GCs holds from halo masses of $M_{200} \sim 10^{14} M_{\odot}$ down to below $M_{200}$ $\sim 10^9 M_{\odot}$, although there is a substantial increase in scatter towards low masses. In particular, three well-studied ultra diffuse galaxies, with dwarf-like stellar masses, reveal a wide range in their GC-to-halo mass ratios. We compare our GC system--halo mass relation to the recent model of El Badry et al., finding that their fiducial model does not reproduce our data in the low mass regime. This may suggest that GC formation needs to be more efficient than assumed in their model, or it may be due to the onset of stochastic GC occupation in low mass halos. Finally, we briefly discuss the stellar mass-halo mass relation for our low mass galaxies with GCs, and we suggest some nearby dwarf galaxies for which searches for GCs may be fruitful.Comment: 16 pages, 5 figures, accepted for publication in MNRA

Chemical functionalisation of silicon and germanium nanowires

The reduced dimensionality of nanowires implies that surface effects significantly influence their properties, which has important implications for the fabrication of nanodevices such as field effect transistors and sensors. This review will explore the strategies available for wet chemical functionalisation of silicon (Si) and germanium (Ge) nanowires. The stability and electrical properties of surface modified Si and Ge nanowires is explored. While this review will focus primarily on nanowire surfaces, much has been learned from work on planar substrates and differences between 2D and nanowire surfaces will be high-lighted. The possibility of band gap engineering and controlling electronic characteristics through surface modification provides new opportunities for future nanowire based applications. Nano-sensing is emerging as a major application of modified Si nanowires and the progress of these devices to date is discussed

Engineering metallic nanoparticles for enhancing and probing catalytic reactions

Recent developments in tailoring the structural and chemical properties of colloidal metal nanoparticles (NPs) have led to significant enhancements in catalyst performance. Controllable colloidal synthesis has also allowed tailor-made NPs to serve as mechanistic probes for catalytic processes. The innovative use of colloidal NPs to gain fundamental insights into catalytic function will be highlighted across a variety of catalytic and electrocatalytic applications. The engineering of future heterogenous catalysts is also moving beyond size, shape and composition considerations. Advancements in understanding structure-property relationships have enabled incorporation of complex features such as tuning surface strain to influence the behavior of catalytic NPs. Exploiting plasmonic properties and altering colloidal surface chemistry through functionalization are also emerging as important areas for rational design of catalytic NPs. This news article will highlight the key developments and challenges to the future design of catalytic NPs

Observational constraints on stellar feedback in dwarf galaxies

Feedback to the interstellar medium (ISM) from ionising radiation, stellar winds and supernovae is central to regulating star formation in galaxies. Due to their low mass ($M_{*} < 10^{9}$\,M$_\odot$), dwarf galaxies are particularly susceptible to such processes, making them ideal sites to study the detailed physics of feedback. In this perspective, we summarise the latest observational evidences for feedback from star forming regions and how this drives the formation of 'superbubbles' and galaxy-wide winds. We discuss the important role of external ionising radiation -- 'reionisation' -- for the smallest galaxies. And, we discuss the observational evidences that this feedback directly impacts galaxy properties such as their star formation histories, metal content, colours, sizes, morphologies and even their inner dark matter densities. We conclude with a look to the future, summarising the key questions that remain unanswered and listing some of the outstanding challenges for galaxy formation theories.Comment: Invited Perspective article, accepted for publication in Nature Astronom