97 research outputs found

    Doubly connected minimal surfaces and extremal harmonic mappings

    Get PDF
    The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

    Scalable In Situ Hybridization on Tissue Arrays for Validation of Novel Cancer and Tissue-Specific Biomarkers

    Get PDF
    Tissue localization of gene expression is increasingly important for accurate interpretation of large scale datasets from expression and mutational analyses. To this end, we have (1) developed a robust and scalable procedure for generation of mRNA hybridization probes, providing >95% first-pass success rate in probe generation to any human target gene and (2) adopted an automated staining procedure for analyses of formalin-fixed paraffin-embedded tissues and tissue microarrays. The in situ mRNA and protein expression patterns for genes with known as well as unknown tissue expression patterns were analyzed in normal and malignant tissues to assess procedure specificity and whether in situ hybridization can be used for validating novel antibodies. We demonstrate concordance between in situ transcript and protein expression patterns of the well-known pathology biomarkers KRT17, CHGA, MKI67, PECAM1 and VIL1, and provide independent validation for novel antibodies to the biomarkers BRD1, EZH2, JUP and SATB2. The present study provides a foundation for comprehensive in situ gene set or transcriptome analyses of human normal and tumor tissues

    On the application of the Perrin process for ferro‐alloy production

    No full text
    This paper supplements a previous review of the Perrin process for steelmaking with the same focus on its principles, technology and economics. Metallurgically, Perrin's idea of emulsification as a means of achieving rapid reaction also applies to the production of ferro-alloys. However, the larger proportion of the amount of slag in relation to that of metal makes it necessary to use other procedures for the intimate mixing of the two phases than was the case of steelmaking. Together with the prevailing high reaction temperatures this requirement means that considerable know-how is needed for acquiring regular production. The major application of the Perrin process to ferro-alloys has been for low-carbon ferrochromium, for which it has retained a niche market. To a minor extent it has also been used for ferromanganese and ferronickel. The history and success of the Perrin process for such purposes can be understood in terms of the concept of the so-called development blocks. This resembles the case of steelmaking inasmuch as its inventor has played a decisive role. The complexity and difficulties of the procedures called for an important contribution by his engineering associates

    Some effects of resistance to organophosphorus insecticides in Myzus persicae

    No full text
    corecore