Monomial Relization of Crystal Bases for Special Linear Lie Algebras

We give a new realization of crystal bases for finite dimensional irreducible modules over special linear Lie algebras using the monomials introduced by H. Nakajima. We also discuss the connection between this monomial realization and the tableau realization given by Kashiwara and Nakashima.Comment: 15 page

Young Wall Realization of Crystal Bases for Classical Lie Algebras

In this paper, we give a new realization of crystal bases for finite dimensional irreducible modules over classical Lie algebras. The basis vectors are parameterized by certain Young walls lying between highest weight and lowest weight vectors.Comment: 27page

NMR study on the stability of the magnetic ground state in MnCr2{}_2O4{}_4

The canting angles and fluctuation of the magnetic ion spins of spinel oxide MnCr${}_2$O${}_4$ were studied by nuclear magnetic resonance (NMR) at low temperatures, which has a collinear ferrimagnetic order below $T_C$ and a ferrimagnetic spiral order below $T_s < T_C$. Contrary to previous reports, only one spin canting angle of Cr ions was observed. The spin canting angles of Mn and Cr ions in the ferrimagnetic spiral obtained at a liquid-He temperature were 43\,^{\circ} and 110\,^{\circ}, respectively. The nuclear spin-spin relaxation was determined by the Suhl-Nakamura interaction at low temperatures but the relaxation rate $T_2^{-1}$ increases rapidly as the temperature approaches $T_s$. This indicates that the fluctuation of the spiral component becomes faster as the temperature increases but not fast enough to leave an averaged hyperfine field to nuclei in the time scale of nuclear spin precession in the ferrimagnetic phase, which is on the order of $10^{-8}$ s. The spiral volume fraction measured for various temperatures reveals that the collinear and the spiral ferrimagnetic phases are mixed below the transition temperature of the spiral order. The temperature hysteresis in the volume fraction implies that this transition has first-order characteristics.Comment: 13 pages, 5 figure

A rare case of primary malignant small cell carcinoma combined with urothelial cell carcinoma in the ureter

BACKGROUND: Extrapulmonary small cell carcinomas have been reported in a variety of organs, and their incidence in the genitourinary tract is second only to that in the gastrointestinal tract. To date, however, only a few cases of small cell carcinoma of the ureter have been reported. Because the extreme rarity of this type of carcinoma, its clinical behaviour, diagnostic methods, and effective treatment modalities have not yet been determined. CASE PRESENTATION: A 59-year-old man presented with a 1-month history of painless gross haematuria. Urine cytopathology revealed a urothelial carcinoma and computed tomography revealed left hydronephroureterosis with a distal ureteral stone and a mildly enhanced fungating mass just below the stone-impacted site. The preoperative TNM stage was T2N0M0. The patient underwent simultaneous diagnostic ureterorenoscopy and left laparoscopic nephroureterectomy with bladder cuff resection. Gross examination showed a 3.5 × 3.0 × 0.8 cm white, partly yellow mass in the left distal ureter. Light microscopy showed a small cell carcinoma, overlaid on a urothelial carcinoma in situ, invading the ureter and external lateral resection margins. The small cell carcinoma was diffusely positive for neuron-specific enolase, and exhibited focal positivity for CD 56, synaptophysin, chromogranin and cytokeratin 20. The patient was treated with adjuvant chemotherapy, consisting of cisplatin and etoposide, and radiation therapy, and has been well, without evidence of tumour recurrence or metastasis in the 10 months after surgery. CONCLUSION: Small cell carcinoma of the ureter is rare. Although its clinical behaviour and diagnostic modalities have not been determined and it has yet to be diagnosed immunohistopathologically, multimodality treatment including surgery, chemotherapy and radiotherapy may improve patient survival