Prime divisors and divisorial ideals

AbstractLet I1,…,Ig be regular ideals in a Noetherian ring R. Then it is shown that there exist positive integers k1,…,kg such that (I1n1 + m1…Igng + mg):(I1m1…Igmg) = I1n1…Igng for all ni≥ki (i = 1,…,g) and for all nonnegative integers m1,...,mg. Using this, it is shown that if Δ is a multiplicatively closed set of nonzero ideals of R that satisfies certain hypotheses, then the sets Ass(R(I1n1…Igng)) equal for all large positive integers n1,...,ng. Also, if R is locally analytically unramified, then some related results for general sets Δ are proved

Ethyl 5-hy­droxy-6-oxo-4-phenyl-5,6-dihydro-4H-cyclo­penta­[b]thio­phene-5-carboxyl­ate

In the title mol­ecule, C16H14O4S, the dihydro­cyclo­penta­thio­phenone ring system is almost planar, with an r.m.s. deviation of 0.060 Å from the best fit plane through all nine non-H atoms. The cyclo­penta­none ring adopts a severely flattened envelope conformation with the C atom carrying the OH and ethylcarboxylate substituents at the flap. This atom lies only 0.185 (3) Å from the plane through the other four C atoms. The phenyl substituent is inclined at 43.37 (5)° to the dihydro­cyclo­penta­thio­phenone mean plane. In the crystal, mol­ecules are linked by pairs of O—H⋯O hydrogen bonds, forming inversion dimers with R 2 2(10) ring motifs. Weak C—H⋯O hydrogen bonds also link mol­ecules into chains along c, while an approximately orthogonal set of C—H⋯O contacts form chains along b, resulting in layers lying parallel to (100). Inversion dimers also form through weaker R 2 2(12) C—H⋯S contacts, which combine with C—H⋯O contacts to form stacks along b

1,4-Bis(iodo­meth­yl)benzene

The centrosymmetric title compound, C8H8I2, was prepared by metathesis from the dibromo analogue. In the crystal structure, weak C—H⋯I inter­actions link the mol­ecules into stacks down the b axis. The structure is further stabilized by short I⋯I contacts [3.8433 (2) Å], forming undulating sheets in the (101) plane

An exploration of the assessment experiences of new academics as they engage with a community of practice in higher education

This paper considers a phenomenological research study that attempted to explore how new academics were introduced to the assessment process within a Higher Education context. Two key educational perspectives have shaped the interpretation of the studies findings. These are Nonaka and Takeuchi’s [Nonaka, I., Takeuchi, H., 1995. The Knowledge Creating Company: How Japanese Companies Create the Dynamics of Innovation. Oxford University Press, New York] model of knowledge conversion and Lave and Wenger’s work on communities of practice (1991, 2002). Three key findings emerged from this work. Firstly, the study highlights a number of issues relating to the types of support and guidance that new academics receive. These were divided into formal and informal types that either promoted conformity or facilitated challenge. Secondly, the study suggests that the ways in which experienced academic staff communicate their assessment knowledge and interact with new academics may require further consideration. Finally, the study raises questions about the type of academic that the organisation would wish to develop

6-Hy­droxy-5,7,8-trimethyl­chroman-2-one

The title compound, C12H14O3, consists of a chromanone unit with an –OH substituent at the 4-position and methyl substituents on the remaining C atoms of the aromatic ring. The fused pyran­one ring adopts a distorted envelope conformation with the methyl­ene group adjacent to the carbonyl carbon as the flap atom. The crystal structure is stabilized by classical O—H⋯O hydrogen bonds and weak C—H⋯O and C—H⋯π inter­actions, generating a three-dimensional network

Gel actuators based on polymeric radicals

Low-voltage electrochemical actuation of radical polymer gels has been demonstrated in an organic electrolyte. Polymer gels were prepared by post-modification of active-ester precursor gels with an amine-functionalised radical. A combination of few-layer graphene and multiwall carbon nanotubes gave high conductivity and improved actuation in the gels, with 32% linear actuation. The actuator system showed good stability over at least 10 cycles, showing its promise. The cycle time was several hours due to mass-transport limited transport of ions and solvent into the device