In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed. At the end of the paper, we discuss the recent counter-examples, in all dimensions greater than two, to the Markus-Yamabe conjecture (Global asymptotic Jacobian conjecture). RésuméDans ce papier nous présentons un rapport actualisé sur les résultats les plus importants concernant la conjecture Jacobienne : plusieurs formulations équivalentes et diverses conjectures connexes sont considérées. A la fin du papier, nous donnons les contre-exemples récents, en toute dimension plus grande que deux, à la conjecture de Markus-Yamabe.

VENUS is a third generation electron cyclotron resonance (ECR) ion source, which incorporates a high field superconducting NbTi magnet structure, a 28 GHz gryotron microwave source and a state of the art closed cycle cryosystem. During the decade from initial concept to regular operation, it has demonstrated both the feasibility and the performance levels of this new generation of ECR ion sources and required innovation on magnet construction, plasma chamber design, and beam transport. In this paper, the development, performance, and major innovations are described as well as a look to the potential to construct a fourth generation ECR ion source.

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The magnet system of the VENUS ECR Ion Source at LBNL has two 1.5-watt cryocoolers suspended in the cryostat vacuum. Helium vapor from the liquid reservoir is admitted to a finned condenser bolted to the cryocooler 2 nd stage and returns as liquid via gravity. Small-diameter flexible tubes allow the cryocoolers to be located remotely from the reservoir. With 3.1 watts load, the helium reservoir is maintained at 4.35 K, 0.05K above the cryocooler temperature. Design, analysis, and performance are presented. VENUS MAGNET SYSTEMVENUS (Versatile ECR ion source for NUclear Science) is a next generation superconducting ECR ion source, designed to produce high current, high charge state ions for the 88-Inch Cyclotron at the Lawrence Berkeley National Laboratory. VENUS also serves as the prototype ion source for the RIA (Rare Isotope Accelerator) front end. The magnetic confinement configuration consists of three superconducting axial coils and six superconducting radial coils in a sextupole configuration. The nominal design fields of the axial magnets are 4T at injection and 3T at extraction; the nominal radial design field strength at the plasma chamber wall is 2T, making VENUS the world's most powerful ECR plasma confinement structure. The magnetic field strength has been designed for optimum operation at 28 GHz. The magnet system has been described elsewhere [i,ii]. FIGURE 1 is a mechanical cross section of VENUS showing the magnets, cryostat, iron shielding, and service tower. FIGURE 2 is a schematic illustration of the superconducting coils.

The aim of this research was to investigate the use of shear wave elastography as a novel tool to quantify and visualize scar stiffness after a burn. Increased scar stiffness is indicative of pathologic scarring which is associated with persistent pain, chronic itch and restricted range of movement. Fifty-five participants with a total of 96 scars and 69 contralateral normal skin sites were evaluated. A unique protocol was developed to enable imaging of the raised and uneven burn scars. Intra-rater and inter-rater reliability was excellent (intra-class correlation coefficient >0.97), and testÀretest reliability was good (intra-class correlation coefficient >0.85). Shear wave elastography was able to differentiate between normal skin, pathologic scars and non-pathologic scars, with preliminary cutoff values identified. Significant correlations were found between shear wave velocity and subjective clinical scar assessment (r = 0.66). Shear wave elastography was able to provide unique information associated with pathologic scarring and shows promise as a clinical assessment and research tool.