On central extensions of simple differential algebraic groups

We consider central extensions $Z\hookrightarrow E\twoheadrightarrow G$ in the category of linear differential algebraic groups. We show that if $G$ is simple non-commutative and $Z$ is unipotent with the differential type smaller than that of $G$, then such an extension splits. We also give a construction of central extensions illustrating that the condition on differential types is important for splitting. Our results imply that non-commutative almost simple linear differential algebraic groups, introduced by Cassidy and Singer, are simple.Comment: 13 page

Extensions of differential representations of SL(2) and tori

Linear differential algebraic groups (LDAGs) measure differential algebraic dependencies among solutions of linear differential and difference equations with parameters, for which LDAGs are Galois groups. The differential representation theory is a key to developing algorithms computing these groups. In the rational representation theory of algebraic groups, one starts with SL(2) and tori to develop the rest of the theory. In this paper, we give an explicit description of differential representations of tori and differential extensions of irreducible representation of SL(2). In these extensions, the two irreducible representations can be non-isomorphic. This is in contrast to differential representations of tori, which turn out to be direct sums of isotypic representations.Comment: 21 pages; few misprints corrected; Lemma 4.6 adde

Hypoxia induces transcription of 6-phosphofructo-2-kinase/fructose-2,6-biphosphatase-4 gene via hypoxia-inducible factor-1α activation

AbstractThe PFKFB4 gene encodes isoenzyme of 6-phosphofructo-2-kinase/fructose-2,6-biphosphatase (PFKFB or PFK-2/FBPase-2) which originally was found in the testes. We have studied hypoxic regulation of PFKFB4 gene in prostate cancer cell line, PC-3, and several other cancer cell lines. It was shown that hypoxia significantly induced PFKFB4 mRNA levels in PC-3 as well as in HeLa, Hep3B and HepG2 cell lines. Hypoxia increased PFKFB4 protein levels also. Moreover, desferrioxamine and cobalt chloride, which are known to mimic hypoxia, also had a stimulatory effect on the expression of PFKFB4 mRNA. In order to investigate the mechanisms of hypoxic regulation of PFKFB4 gene expression, we used dimethyloxalylglycine, which has the ability to mimic effect of hypoxia by significant induction of hypoxia-inducible factor (HIF-1α) protein levels. Our studies showed that PFKFB4 mRNA expression in PC-3, HeLa, Hep3B and HepG2 cell lines was highly responsive to dimethyloxalylglycine, an inhibitor of HIF-1α hydroxylase enzymes, suggesting that the hypoxia responsiveness of this gene is regulated by HIF proteins. To better understand the hypoxic regulation of PFKFB4 gene expression, we isolated genomic DNA, which includes the promoter region of PFKFB4. Cell transfection, deletion and site-specific mutagenesis of the PFKFB4 promoter region indicates that hypoxic induction of PFKFB4 gene expression is mediated by the hypoxia-responsive element (HRE). These experiments identified a HRE 422–429 bp upstream from the translation start site. Thus, our results indicate that testis-specific form of PFKFB or PFK-2/FBPase-2 is also expressed in several cancer cell lines and that hypoxia induces transcription of PFKFB4 gene in these cell lines by HIF-1α dependent mechanism. HRE in 5′-promoter region of PFKFB4 gene mediates hypoxic induction of PFKFB4 gene transcription

Колекція верб (Salix L.) Національного ботанічного саду ім. М.М. Гришка НАН України

The history of creation and perspectives of the development of willows collection in M.M. Gryshko National Botanical Gardens are given. At present time it includes 45 species, forms and hybrids.Викладено історію і перспективи розвитку колекції верб НБС ім. М.М. Гришка НАН України. Нині вона налічує 45 видів, форм та гібридів