To evaluate and quantify the association between physical activity (PA) and risk of breast cancer. Methods: A systematic review meta-analysis was conducted. The literature was independently and manually searched by 2 reviewers through 3 English databases (PubMed, Embase, and ISI Web of Science) for data till October 2017. The quality of included studies was assessed by the Newcastle-Ottawa Quality Assessment Scale. Fixed-effects models were used to estimate the pooled relative risk and 95% confidence intervals (95% CI). Doseeresponse analysis was chosen for quantifying the association between PA and risk of breast cancer. The Begg test and the Egger test were used to estimate potential publication bias. Heterogeneity between studies was evaluated with I 2 statistics. Results: The meta-analysis included 38 cohort studies published between 1994 and 2017, which included 68 416 breast cancer cases. The overall relative risk (ORR) for breast cancer was 0.87 (95% CI 0.84-0.90). The inverse association was consistent among all subgroup analyses. In subgroup analysis by menopausal status, the ORR of breast cancer was 0.83 (95% CI 0.79-0.87) for premenopausal status and 0.91 (95% CI 0.85-0.97) for postmenopausal status. In subgroup analysis by PA type, the ORR for total activity was 0.87 (95% CI 0.81-0.93), for recreational activity 0.88 (95% CI 0.85-0.91), for occupational activity 0.91 (95% CI 0.84-0.99), and for nonoccupational activity 0.87 (95% CI 0.83-0.92). The risk of breast cancer was significantly lower in people with exposure periods longer than 1 year and less than 5 years (ORR 0.62; 95% CI 0.46-0.78), followed by those with lifetime activity (ORR 0.81; 95% CI 0.69-0.93). The ORR for subjects with body mass index of less than 25 kg/m 2 (0.88; 95% CI 0.83-0.93) was close to that for subjects with body mass index of more than 25 kg/m 2 (0.87; 95% CI 0.77-0.97). A linear relationship was found between breast cancer risk and PA (recreational activity and total activity), and the ORR was reduced by 3% (95% CI 0.95-0.99) for every 10 metabolic equivalent of energy hours per week increment in recreational PA and by 2% (95% CI 0.97-0.99) for every 10 metabolic equivalent of energy hours per week increment in total PA. Conclusions: PA is significantly associated with a decrease in the risk of breast cancer.

In this paper, we give an analogue of the Arzela-Ascoli theorem on time scales. Then, we establish the existence of nonoscillatory solutions to the neutral dynamic equation [x(t) + p(t)x(g(t))] + f (t, x(h(t))) = 0 on a time scale. To dwell upon the importance of our results, three interesting examples are also included.

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In this paper, we consider a class of evolution equations with Hilfer fractional derivative. By employing the fixed point theorem and the noncompact measure method, we establish a number of new criteria to guarantee the existence and uniqueness of mild solutions when the associated semigroup is compact or not.

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