Remarks on the structure constants of the Verlinde algebra associated to sl3sl_3

The structure constants $N_{\lambda, \mu}^{\mu+\nu}$ of the $sl_2$ Verlinde algebra as functions of $\mu$ either vanish or can be expressed after a change of variable as the weight function of an irreducible representation of $sl_2$. We give a similar formula in the $sl_3$ case.Comment: 5 pages, AmsTeX, 1 figure available on reques

08/09/1948 Letter from New Auburn Legion Post 153

Letter from Commander Alphonse Gardner by Maurice A. Begin to Louis-Philippe Gagné.https://digitalcommons.usm.maine.edu/fac-lpg-letters-1948-07-12/1015/thumbnail.jp

A 3D insight on the catalytic nanostructuration of few-layer graphene

The catalytic cutting of few-layer graphene is nowadays a hot topic in materials research due to its potential applications in the catalysis field and the graphene nanoribbons fabrication. We show here a 3D analysis of the nanostructuration of few-layer graphene by iron-based nanoparticles under hydrogen flow. The nanoparticles located at the edges or attached to the steps on the FLG sheets create trenches and tunnels with orientations, lengths and morphologies defined by the crystallography and the topography of the carbon substrate. The cross-sectional analysis of the 3D volumes highlights the role of the active nanoparticle identity on the trench size and shape, with emphasis on the topographical stability of the basal planes within the resulting trenches and channels, no matter the obstacle encountered. The actual study gives a deep insight on the impact of nanoparticles morphology and support topography on the 3D character of nanostructures built up by catalytic cutting

Polyol synthesis, functionalisation, and biocompatibility studies of superparamagnetic iron oxide nanoparticles as potential MRI contrast agents

Iron oxide nanoparticles (IONPs) of low polydispersity were obtained through a simple polyol synthesis in high pressure and high temperature conditions. The control of the size and morphology of the nanoparticles was studied by varying the solvent used, the amount of iron precursor and the reaction time. Compared with conventional synthesis methods such as thermal decomposition or co-precipitation, this process yields nanoparticles with a narrow particle size distribution in a simple, reproducible and cost effective manner without the need for an inert atmosphere. For example, IONPs with a diameter of ca. 8 nm could be made in a reproducible manner and with good crystallinity as evidenced by X-ray diffraction analysis and high saturation magnetization value (84.5 emu g(-1)). The surface of the IONPs could be tailored post synthesis with two different ligands which provided functionality and stability in water and phosphate buffer saline (PBS). Their potential as a magnetic resonance imaging (MRI) contrast agent was confirmed as they exhibited high r1 and r2 relaxivities of 7.95 mM(-1) s(-1) and 185.58 mM(-1) s(-1) respectively at 1.4 T. Biocompatibility and viability of IONPs in primary human mesenchymal stem cells (hMSCs) was studied and confirmed

Berenstein-Zelevinsky triangles, elementary couplings and fusion rules

We present a general scheme for describing su(N)_k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way a complete solution of su(4)_k fusion rules is obtained.Comment: 14 page

Small iron oxide nanoparticles as MRI T1 contrast agent: scalable inexpensive water-based synthesis using a flow reactor

Small iron oxide nanoparticles (IONPs) were synthesised in water via co-precipitation by quenching particle growth after the desired magnetic iron oxide phase formed. This was achieved in a millifluidic multistage flow reactor by precisely timed addition of an acidic solution. IONPs (≤5 nm), a suitable size for positive T1 magnetic resonance imaging (MRI) contrast agents, were obtained and stabilised continuously. This novel flow chemistry approach facilitates a reproducible and scalable production, which is a crucial paradigm shift to utilise IONPs as contrast agents and replace currently used Gd complexes. Acid addition had to be timed carefully, as the inverse spinel structure formed within seconds after initiating the co-precipitation. Late quenching allowed IONPs to grow larger than 5 nm, whereas premature acid addition yielded undesired oxide phases. Use of a flow reactor was not only essential for scalability, but also to synthesise monodisperse and non-agglomerated small IONPs as (i) co-precipitation and acid addition occurred at homogenous environment due to accurate temperature control and rapid mixing and (ii) quenching of particle growth was possible at the optimum time, i.e., a few seconds after initiating co-precipitation. In addition to the timing of growth quenching, the effect of temperature and dextran present during co-precipitation on the final particle size was investigated. This approach differs from small IONP syntheses in batch utilising either growth inhibitors (which likely leads to impurities) or high temperature methods in organic solvents. Furthermore, this continuous synthesis enables the low-cost (<£10 per g) and large-scale production of highly stable small IONPs without the use of toxic reagents. The flow-synthesised small IONPs showed high T1 contrast enhancement, with transversal relaxivity (r2) reduced to 20.5 mM−1 s−1 and longitudinal relaxivity (r1) higher than 10 mM−1 s−1, which is among the highest values reported for water-based IONP synthesis