The maps x → ax 2 k + b defined over finite fields of characteristic two can be related to the duplication map over binary supersingular elliptic curves. Relying upon the structure of the group of rational points of such curves we can describe the possible cycle lengths of the maps. Then we extend our investigation to the maps x → (ax 2 k + b) −1. We also notice some relations between these latter maps and the polynomials x 2 k +1 + x + a, which have been extensively studied in literature.
The disruption of six novel genes (YDL059c, YDL060w, YDL063c, YDL065c, YDL070w and YDL110c), localized on the left arm of chromosome IV in Saccharomyces cerevisiae, is reported. A PCR-based strategy was used to construct disruption cassettes in which the kanMX4 dominant marker was introduced between two long flanking homology regions, homologous to the promoter and terminator sequences of the target gene (Wach et al., 1994). The disruption cassettes were used to generate homologous recombinants in two diploid strains with different genetic backgrounds (FY1679 and CEN. PK2), selecting for geneticin (G418) resistance conferred by the presence of the dominant marker kanMX4. The correctness of the cassette integration was tested by PCR. After sporulation and tetrad analysis of the heterozygous deletant diploids, geneticin-resistant haploids carrying the disrupted allele were isolated. YDL060w was shown to be an essential gene for vegetative growth. A more detailed phenotypic analysis of the non-lethal haploid deletant strains was performed, looking at cell and colony morphology, growth capability on different media at different temperatures, and ability to conjugate. Homozygous deletant diploids were also constructed and tested for sporulation. Only minor differences between parental and mutant strains were found for some deletant haploids.
In this paper we construct an infinite sequence of binary irreducible
polynomials starting from any irreducible polynomial $f_0 \in \F_2 [x]$. If
$f_0$ is of degree $n = 2^l \cdot m$, where $m$ is odd and $l$ is a
non-negative integer, after an initial finite sequence of polynomials $f_0,
f_1, ..., f_{s}$ with $s \leq l+3$, the degree of $f_{i+1}$ is twice the degree
of $f_i$ for any $i \geq s$.Comment: 7 pages, minor adjustment
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