The Shi arrangements and the Bernoulli polynomials

The braid arrangement is the Coxeter arrangement of the type $A_\ell$. The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the braid arrangement and their parallel translations. In this paper, we give an explicit basis construction for the derivation module of the cone over the Shi arrangement. The essential ingredient of our recipe is the Bernoulli polynomials.Comment: We fixed a typ

The Primitive Derivation and Discrete Integrals

The modules of logarithmic derivations for the (extended) Catalan and Shi arrangements associated with root systems are known to be free. However, except for a few cases, explicit bases for such modules are not known. In this paper, we construct explicit bases for type $A$ root systems. Our construction is based on Bandlow-Musiker's integral formula for a basis of the space of quasiinvariants. The integral formula can be considered as an expression for the inverse of the primitive derivation introduced by K. Saito. We prove that the discrete analogues of the integral formulas provide bases for Catalan and Shi arrangements

Health-related quality of life after radical cystectomy for bladder cancer in elderly patients with an ileal conduit, ureterocutaneostomy, or orthotopic urinary reservoir: a comparative questionnaire survey

To compare the health-related quality of life of elderly patients after radical cystectomy for bladder cancer in urinary diversion groups: ileal conduit, ureterocutaneostomy, or orthotopic urinary reservoir. The 109 participating elderly patients aged 75 or older completed self-reporting questionnaires: the QLQ-C30, and on satisfaction with urinary diversion methods. Fifty-six patients had undergone constructions for ileal conduit diversion, 31 for ureterocutaneostomy, and 22 for orthotopic urinary reservoir (OUR). The median follow-up period for each group was 4.0 years (range 0.3-11.2), 4.5 years (range 0.3-18.0), and 3.3 years (range 0.3-6.7), respectively. Regardless of the type of urinary diversion, the majority of patients reported having good overall quality of life, although with some problem of pain. No significant differences among urinary diversion subgroups were found in any quality of life area in the QLQ-C30 questionnaire. More patients in the OUR sub-group felt disappointment than those in the ileal conduit or cutaneostomy sub-groups. However, a questionnaire which asked which diversion method would be preferable showed a trend that more patients in the OUR subgroup would have chosen the same one. Health-related quality of life appeared relatively good in these 3 groups. Patient demands and expectations may be so different from the results that the details of each urinary diversion method should be explained thoroughly. OUR construction could be a candidate even for elderly patients

Effects of 3 MeV Proton Irradiation on Superconductivity and CDW in 2H-NbSe2 Single Crystals

Interplay between superconductivity and charge-density wave (CDW) in 2H-NbSe2 single crystals irradiated by 3 MeV protons is studied. Both Tc and TCDW are found to decrease monotonically with the increase in irradiation dose. This behavior is different from electron-irradiated NbSe2, where TCDW is suppressed monotonically with the increase in dose, while Tc shows an initial enhancement before it starts to decrease. We attempt to explain this difference based on the negative pressure effect which has been reported in our previous study on NbSe2 irradiated by heavy ions