Fuzzy transform is a new type of function transforms that has been successfully used in different applications. In this paper, we provide a broad prospective on fuzzy transform. Specifically, we show that fuzzy transform naturally appears when, in addition to measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations.
A thioredoxin-like protein (txl) gene was cloned from the bumblebee, Bombus ignitus. The B. ignitus txl (Bitxl) gene spans 1777 bp and consists of three introns and four exons coding for 285 amino acid residues with a conserved active site (CGPC). The deduced amino acid sequence of the Bitxl cDNA was 65% similar to the Drosophila melanogaster txl. Northern blot analysis revealed the presence of Bitxl transcripts in all tissues examined. When H2O2 was injected into the body cavity of B. ignitus workers, Bitxl mRNA expression was up-regulated in the fat body tissue. In addition, the expression levels of Bitxl mRNA in the fat body greatly increased when B. ignitus workers were exposed to low (4°C) or high (37°C) temperatures, or injected with lipopolysaccharide (LPS), which suggests that the Bitxl possibly protects against oxidative stress caused by extreme temperatures and bacterial infection.