Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop

It is provedin this paper that the maximum number of limit cycles of system [formula] is equal to two in the finite plane, where [formula]. This is partial answer to the seventh question in [2], posed by Arnold

Abelian integrals of quadratic hamiltonian vector fields with an invariant straight line

We prove that the lowest upper bound for the number of isolated zeros of the Abelian integrals associated to quadratic Hamiltonian vector fields having a center and an invariant straight line after quadratic perturbations is on

Effect of insulin resistance on gonadotropin and bone mineral density in nondiabetic postmenopausal women

ObjectiveThe effects of insulin resistance (IR) on bone mineral density (BMD) are unclear. This investigation aimed to assess the impact of IR and hyperinsulinemia on bone health. Determine whether IR mediates the link between follicle-stimulating hormone (FSH) and bone mass in nondiabetic postmenopausal women.DesignRetrospective cross-sectional study.SettingHealth checkup center of Hangzhou Women’s Hospital.MethodsThis study comprised 437 nondiabetic postmenopausal women. BMD was evaluated using dual-energy X-rays. Fasting sera were analyzed for insulin and glucose levels, and indicators related to IR were determined. By pathway analysis, we examined the indirect effects of FSH on BMD via the mediators Homeostatic Model Assessment for insulin resistance (HOMA-IR) and fasting insulin (FINS) after correction for confounding factors.ResultAfter adjusting for age and body mass index (BMI) in linear regression, HOMA-IR and FINS were linked with FSH (P<0.05). IR was stronger among women in the normal BMD group than those in the osteoporosis or osteopenia group. In unadjusted models, BMD was greater in those with higher HOMA-IR and FINS (β=0.027, P=0.006 and β=0.033, P=0.003, respectively). After correcting for BMI and other possible variables, these associations remained. In addition, path models for FSH demonstrated a negative association with BMD by HOMA-IR (95% confidence interval [CI]: -0.0174 to -0.0014) and FINS (95% CI: -0.0188 to -0.002).ConclusionGreater IR was associated with increased BMD in nondiabetic postmenopausal women, regardless of BMI and other variables. HOMA-IR or FINS could play a novel mediating role in FSH-induced BMD suppression

Polynomial systems : a lower bound for the weakened 16th Hilbert problem

In this paper we provide the greatest lower bound about the number of (non-infinitesimal) limit cycles surrounding a unique singular point for a planar polynomial differential system of arbitrary degree

Induction of defensive enzymes (isozymes) during defense against two different fungal pathogens in pear calli

Activities of defensive enzymes peroxidase (POD), superoxide dismutase (SOD), catalase (CAT), polyphenol oxidase (PPO) and esterase (EST) and their isozymes in pear calli were studied to reveal their role in the defensive response to different fungal infections and to find some clues to enhance their antimicrobial properties. The results confirm the fact that the activities and isozymes of these five enzymes showed differences in response to different fungal infections. After the inoculation of two different fungi for the same calli, its defensive enzymes’ activities changed relatively when compared with those of the control and in Botryosphaeria berengriana f.sp. piricola (BBP)-infected calli, the enzymes’ activities changed more significantly than those of Monilinia fructigena Honcy (MFH). Meanwhile, more new isozymes were induced by BBP infection. These are in agreement with the fact that the BBP-infected calli decay was slower than that of the MFH. These results suggest that enhancing defensive enzymes’ activities and inducing new isozymes may be related to mitigating pathogen-induced oxidative damage which result in the decrease of calli decay, and this implies that antioxidant defense response may be involved in the mechanisms of plant against fungal pathogen.Keywords: Pear callus, fungi infection, defense enzyme, isozyme, biochemical defense mechanis

The prognostic significance of different proportion of signet-ring cells of colorectal carcinoma

While the prognosis of patients with partial SRCC (PSRCC) has been rarely reported, colorectal signet-ring cell carcinoma (SRCC) has been associated with poor prognosis. The aim of this study was to analyze the prognosis of patients with different SRCC composition and establish a prediction model. A total of 91 patients with SRC component were included in the study. These patients were divided into two groups: SRCC group (SRC composition > 50%; n=41) and partial SRCC (PSRCC) group (SRC composition ≤ 50%; n=50). COX regression model was used to identify independent prognostic factors for overall survival (OS). A predictive nomogram was established and compared with the 7th AJCC staging system. After a median follow-up of 16 months, no significant difference in OS was observed in either group. Preoperative carcinoembryonic antigen (CEA) level, pN stage, M stage, preoperative ileus, and adjuvant chemotherapy were independent prognostic risk factors for OS (p<0.05). A nomogram for predicting the overall survival of colorectal SRCC was established with a C-index of 0.800, and it showed better performance than that of the 7th AJCC staging system (p<0.001). In summary, the ratio of SRC component was not an independent prognostic factor of the OS. Those patients with less than 50% of SRC component should be given the same clinical attention. A predictive nomogram for survival based on five independent prognostic factors was developed and showed better performance than the 7th AJCC staging system. This resulted to be helpful for individualized prognosis prediction and risk assessment