Symmetry Groups of AnA_n Hypergeometric Series

Structures of symmetries of transformations for Holman-Biedenharn-Louck $A_n$ hypergeometric series: $A_n$ terminating balanced ${}_4 F_3$ series and $A_n$ elliptic ${}_{10} E_9$ series are discussed. Namely the description of the invariance groups and the classification all of possible transformations for each types of $A_n$ hypergeometric series are given. Among them, a "periodic" affine Coxeter group which seems to be new in the literature arises as an invariance group for a class of $A_n$ ${}_4 F_3$ series

Loss of miR-542-3p enhances IGFBP-1 expression in decidualizing human endometrial stromal cells

Endometrial decidualization represents an essential step for the successful implantation of the embryo; however, the molecular mechanism behind this differentiation process remains unclear. This study aimed to identify novel microRNAs (miRNAs) involved in the regulation of decidual gene expression in human endometrial stromal cells (HESCs). An in vitro analysis of primary undifferentiated and decidualizing HESCs was conducted. HESCs were isolated from hysterectomy specimens from normally cycling premenopausal women with uterine fibroids, who were not on hormonal treatment at the time of surgery. Primary HESCs were expanded in culture and decidualized with 8-bromo-cyclic adenosine monophosphate and medroxyprogesterone acetate. Microarray analysis identified six miRNAs differentially expressed in response to decidualization of HESCs. All but one miRNA were downregulated upon decidualization, including miR-542-3p. We demonstrated that miR-542-3p overexpression inhibits the induction of major decidual marker genes, including IGFBP1, WNT4 and PRL. In addition, miR-542-3p overexpression inhibited the morphological transformation of HESCs in response to deciduogenic cues. A luciferase reporter assay confirmed that the 3′-untranslated region of IGFBP1 mRNA is targeted by miR-542-3p. The results suggest that miR-542-3p plays an important role in endometrial decidualization by regulating the expression of major decidual marker genes

Symmetry Groups of An Hypergeometric Series ⋆

Abstract. Structures of symmetries of transformations for Holman–Biedenharn–Louck An hypergeometric series: An terminating balanced 4F3 series and An elliptic 10E9 series are discussed. Namely the description of the invariance groups and the classification all of possible transformations for each types of An hypergeometric series are given. Among them, a “periodic ” affine Coxeter group which seems to be new in the literature arises as an invariance group for a class of An 4F3 series. Key words: groups multivariate hypergeometric series; elliptic hypergeometric series; Coxete

Raising Operators Of Row Type For Macdonald Polynomials

. We construct certain raising operators of row type for Macdonald's symmetric polynomials by an interpolation method. 1. Introduction Throughout this paper, we denote by J (x; q; t) the integral form of Macdonald's symmetric polynomial in n variables x = (x 1 ; : : : ; xn ) (of type An01 ) associated with a partition ([5]). For each m = 0; 1; 2; : : : , we consider a q-difference operator Bm which should satisfy the following condition: For any partition = ( 1 ; 2 ; : : : ) whose longest part 1 has length m, one has BmJ (x; q; t) = ( J (m;) (x; q; t) if `() ! n; 0 if `() = n; (1.1) where (m; ) = (m; 1 ; 2 ; : : : ) stands for the partition obtained by adding a row of length m to . An operator Bm having this property will be called a raising operator of row type for Macdonald polynomials. With such operators, the Macdonald polynomial J (x; q; t) for a general partition = ( 1 ; 2 ; : : : ; n ) can be expressed as B 1 B 2 : : : B n :1 = J (x; q; t) ( 1 2 : : : n ..