Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields

summary:It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider this question in an infinite parametric family of number fields. In this paper we consider the infinite parametric family of simplest quartic fields $K$ generated by a root $\xi$ of the polynomial $P_t(x)=x^4-tx^3-6x^2+tx+1$, assuming that $t>0$, $t\neq 3$ and $t^2+16$ has no odd square factors. In addition to generators of power integral bases we also calculate the minimal index and all elements of minimal index in all fields in this family

Book reviews

G. Loebenstein, P. H. Berger, A. A. Brunt and R. H. Lawson (eds): Virus and Virus-like Diseases of Potatoes and Production of Seed-Potatoes. Kluwer Academic Publ., Dordrecht (The Netherlands), 2001, 460 pp. László Nowinszky (ed.): The Handbook of Light Trapping. Savaria University Press, Szombathely, 2003

Efficacy and safety of FOLFIRINOX in locally advanced pancreatic cancer: a single center experience

The management of locally advanced pancreatic cancer (LAPC) is a major challenge. Although new drugs are available for the treatment of metastatic disease, the optimal treatment of non-metastatic cases remains controversial. The role of neoadjuvant therapy is still a question of debate in this setting. The aim of the study was to prospectively collect and analyse data on efficacy and safety of a modified FOLFIRINOX regimen in LAPC patients treated in a single institution. Another major objective was to assess the capability of FOLFIRINOX to render primary non-resectable cancer to resectable. No bolus fluorouracil was given and a 20% dose reduction of oxaliplatin and irinotecan was applied. Primary G-CSF prophylaxis was applied to prevent febrile neutropenia. Thirty-two patients (mean age 60.2 years, range: 40-77 years) have been enrolled into the study. All patients had ECOG performance status of 0 or 1. Best response to therapy was stable disease (SD) or partial regression (PR) in 18 (56.2%) and 6 (18.8%) cases. Two patients (6.3%) underwent surgical resection (100% R0). The most frequent grade 3/4 adverse events were nausea (18.8%), fatigue (12.5%) and diarrhea (12.5%). The incidence of severe neutropenia was 28.1%, with only one documented case of febrile neutropenia. The probability of disease progression was 25% and 50% after 75 and 160 days with 88.4% of possibility of disease progression after 500 days. OS probability was 92.1, 71.5% and 49.5% at 180-, 365 and 540 days. Our data does not support the capability of FOLFIRINOX to render primary non-resectable cancer to resectable. However, due to the high disease control rate observed, FOLFRINOX might be recommended as first line option for the palliative treatment of LAPC. Despite reduced chemotherapy doses significant toxicity has been seen