CONTENTS Introduction 1 1. Notation 3 2. Main definitions and first properties 4 3. Cohomology of line bundles and generalised Kostka-Foulkes polynomials 5 4. The little adjoint module and short q-analogues 11 5. Short Hall-Littlewood polynomials 18 6. Miscellaneous remarks 23 References 25 INTRODUCTION Let G be a semisimple algebraic group with Lie algebra g. We consider generalisations of Lus...

news & views possibilities for such devices in general. In particular, omnidirectional retroreflectors are likely to find use wherever back-reflecting mirrors are required whose alignment is hard to fix. Although perhaps less striking in its physical effect than a perfect lens or an invisibility cloak, the work of Ma et al. demonstrates that other devices hitherto confined to theory can be prac...

Zero curvature formulations are given for the “dual hierarchies” of standard soliton equation hierarchies, recently introduced by Olver and Rosenau, including the physically interesting Fuchssteiner-Fokas-CamassaHolm hierarchy. PACS Numbers: 03.40.Kf, 47.20.Ky, 52.35.Sb Through the years since the discovery of the notion of “integrability” in PDEs, quite a number of integrable PDEs have been di...

In theory, there are analogous transformations of light’s spin and orbital angular momentum [Allen and Padgett, J. Mod. Opt. 54, 487 (2007)]; however, none have been observed experimentally yet. In particular, it is unknown if there exists for the orbital angular momentum of light an effect analogous to the spin angular momentum-based optical rotation; this would manifest itself as a rotation o...

The spectroscopically invisible CuB site of heme­copper oxidases has been studied with hybrid density functional calculations. The site comprises a copper atom ligated to three histidines residues (His­240, His­290, His­291), and a tyrosine residue (Tyr­244) covalently bound to one of the histidines (His­240). Our recent results suggest that this site might dictate proton transfer in cytochrom...

In their opinion article within this issue of Human Reproduction, Polyzos and Sunkara propose to create a new, presumed clinically relevant, ovarian response category (Polyzos and Sunkara, 2015). Today, the poor responder is indisputably recognized as problematic, as the far below average prognosis for live birth, especially in women of higher age, sheds doubt on the added value of assisted rep...

The (2+1)-dimensional “universal” variable separation formula (Tang, Lou and Zhang, Physical Review E 66, 046601 (2002)) is extended to a more general form for some (2+1)-dimensional integrable systems. Various independent arbitrary functions have been included in the extended formula. Starting from the universal formula and its extended form, a new type of solitons, foldons, is studied both an...

Many cancer cells depend on glutamine as they use the glutaminolysis pathway to generate building blocks and energy for anabolic purposes. As a result, glutamine transporters are essential for cancer growth and are potential targets for cancer chemotherapy, with ASCT2 (SLC1A5) being investigated most intensively. Here we show that HeLa epithelial cervical cancer cells and 143B osteosarcoma cell...