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We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.
Small-subunit (SSU) rRNA genes (rDNA) were amplified by PCR from a hot pool environmental DNA sample using Bacteria- or Archaea-specific rDNA primers. Unique rDNA types were identified by restriction fragment length polymorphism (RFLP) analysis and representative sequences were determined. Family 10 glycoside hydrolase consensus PCR primers were used to explore the occurrence and diversity of xylanase genes in the hot pool environmental DNA sample. Partial sequences for three different xylanases were obtained and genomic walking PCR (GWPCR), in combination with nested primer pairs, was used to obtained a unique 1,741-bp nucleotide sequence. Analysis of this sequence identified a putative XynA protein encoded by the xynA open reading frame. The single module novel xylanase shared sequence similarity to the family 10 glycoside hydrolases. The purified recombinant enzyme, XynA expressed in E. coli exhibited optimum activity at 100 degrees C and pH 6.0, and was extremely thermostable at 90 degrees C. The enzyme showed high specificity toward different xylans and xylooligosaccharides.
After reviewing the research on Saxon regionalized intonation and giving an overview of our research project on regionalized intonation in German, a particular salient regionalized intonation contour from the Dresden vernacular is described in detail. In addition to a more widespread contour that is also used in the Berlin vernacular, albeit in different contexts, the so-called 'upward staircase contour' which is formed by a lower plateau, a rise and a higher plateau, the Dresden vernacular also uses very salient regionalized variants of such staircase contours: These variants entail upward staircases with, metaphorically speaking, two steps; i.e. after the lower plateau and the rise up to a higher plateau, the pitch rises up again in order to form a third plateau. Depending upon the alignment of the second rise and the third plateau, with only the final unaccented syllable of the intonation phrase or with the nuclear accented syllable and the following tail, the contour needs to be distinguished, yielding either an 'upward staircase with an additional final rise plateau' or a 'double upward staircase'. These two contours are shown to be used in different conversational contexts and in different functions in the Dresden vernacular. - Data for this study come from natural speech by speakers of the Dresden vernacular. The phonetic and phonological analysis of the contour is based on auditive, acoustic-phonetic and phonological methodology; the functional analysis of the utterances with the salient contours relies on the techniques of conversation analysis