A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.Comment: To appear in Monatshefte f\"ur Mathematik; 11 page

アストロサイトにおける抗うつ薬による塩基性線維芽細胞増殖因子産生機構に関する薬理学的研究

内容の要旨 , 審査の要旨広島大学(Hiroshima University)博士(薬科学)Doctor of Philosophy in Medicinal Sciencedoctora

Optogenetic Control of Subcellular Protein Location and Signaling in Vertebrate Embryos.

This chapter describes the use of optogenetic heterodimerization in single cells within whole-vertebrate embryos. This method allows the use of light to reversibly bind together an "anchor" protein and a "bait" protein. Proteins can therefore be directed to specific subcellular compartments, altering biological processes such as cell polarity and signaling. I detail methods for achieving transient expression of fusion proteins encoding the phytochrome heterodimerization system in early zebrafish embryos (Buckley et al., Dev Cell 36(1):117-126, 2016) and describe the imaging parameters used to achieve subcellular light patterning

SYSTEMS OF SETS OF LENGTHS: TRANSFER KRULL MONOIDS VERSUS WEAKLY KRULL MONOIDS

Transfer Krull monoids are monoids which allow a weak transfer homomorphism to a commutative Krull monoid, and hence the system of sets of lengths of a transfer Krull monoid coincides with that of the associated commutative Krull monoid. We unveil a couple of new features of the system of sets of lengths of transfer Krull monoids over finite abelian groups G, and we provide a complete description of the system for all groups G having Davenport constant D(G) = 5 (these are the smallest groups for which no such descriptions were known so far). Under reasonable algebraic finiteness assumptions, sets of lengths of transfer Krull monoids and of weakly Krull monoids satisfy the Structure Theorem for Sets of Lengths. In spite of this common feature we demonstrate that systems of sets of lengths for a variety of classes of weakly Krull monoids are different from the system of sets of lengths of any transfer Krull monoid