Reducing the polynomial-like iterative equations order and a generalized Zoltan Boros' problem

We present a technique for reducing the order of polynomial-like iterative equations; in particular, we answer a question asked by Wenmeng Zhang and Weinian Zhang. Our method involves the asymptotic behaviour of the sequence of consecutive iterates of the unknown function at a given point. As an application we solve a generalized problem of Zoltán Boros posed during the 50th ISFE

Expression of angiogenic factors predicts response to chemoradiotherapy and prognosis of oesophageal squamous cell carcinoma

The ability to predict patients' responses to chemoradiotherapy by analyzing pre-treatment biopsy specimens would be valuable for managing oesophageal squamous-cell cancer. To this end, the expression of p53, thymidine phosphorylase and vascular endothelial cell growth factor was analyzed by immunohistochemistry in 52 patients with oesophageal squamous-cell cancer prior to chemoradiotherapy. Treatment consisted of radiotherapy (40 Gy) and 5 day-infusion of 5-Fluorouracil (500 mg m−2 per day) combined with cisplatin (10 mg m−2 per day). Following treatment, imaging and endoscopic reassessment was performed to establish treatment response. Thirty-one patients underwent radical surgery and 21 patients were treated with an additional 20 Gy of radiotherapy. Of the tumours studied, 58% were p53-positive, 40% thymidine phosphorylase-positive and 44% vascular endothelial cell growth factor-positive. A clinical response was observed in 36 patients (69%) and was negatively associated with thymidine phosphorylase expression (P=0.02) and vascular endothelial cell growth factor expression (P<0.001). However, the 5-year survival rate was significantly lower only in patients with vascular endothelial cell growth factor-positive tumours (P=0.037). Multivariate analysis identified vascular endothelial cell growth factor as a significant independent prognostic factor (P=0.0147). These results suggest that expression of angiogenic factors has predictive value for the treatment response and outcome of patients with oesophageal cancer

On a functional equation involving iterates and powers

We present a complete list of all continuous solutions f : (0,+∞)→(0,+∞) of the equation f 2(x) = γ [f (x)]αxβ, where α, β and γ > 0 are given real numbers

Immunostaining of thymidylate synthase and p53 for predicting chemoresistance to S-1/cisplatin in gastric cancer

High expression of thymidylate synthase (TS) and inactivation of p53 are allegedly associated with chemoresistance. The authors evaluated TS and p53 expression in gastric cancer treated with neoadjuvant S-1/cisplatin chemotherapy. Paraffin sections of pretreatment biopsy and surgical specimens from 41 gastric cancers were immunostained for TS and p53 protein after appropriate antigen retrieval. Fifty-one cases without neoadjuvant chemotherapy were also studied. In the pretreatment biopsies, high expression of TS was seen in 8% of the histologic responders, in 28% of the nonresponders and in 31% of the controls. High expression of p53 was observed in 56% of the nonresponders, but in 8% of the responders and in 29% of the controls (P<0.01 and P<0.05, respectively). The TS- and/or p53-high phenotype was seen in 76% of the nonresponders and in 54% of the controls, but in 8% of the responders (P<0.0001 and P<0.005, respectively). The data of the surgical specimens were consistent with those of the pretreatment biopsies. These results suggest that immunostaining for TS and p53 protein is useful for pretreatment selection of gastric cancer patients unresponsive to S-1/cisplatin chemotherapy