ON CONSERVATIVE APPROXIMATION BY LINEAR POLYNOMIAL OPERATORS AN EXTENSION OF THE BERNSTEIN'S OPERATOR

In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.

Outcomes and complications of operative versus non-operative treatment of acute Achilles tendon rupture： a meta-analysis

Background There is lack of consensus regarding the best option for the treatment of acute Achilles tendon rupture- operation or non-operation. The purpose of this meta-analysis was to identify and summarize the randomized controlled trials comparing the operative and non-operative lines of treatment of acute Achilles tendon ruptures. Methods We searched multiple databases in English （including EMBASE, PubMed, and OVID） and in Chinese （including CNKI, WANFANG, and VIP）, as well as reference lists of articles and main orthopaedic and sports medical journals. Two reviewers independently screened the studies for eligibility, evaluated the quality and extracted data from eligible studies, with confirmation by cross-checking. The major results and conclusions were concluded, and the different complication rates and functional outcomes were compared. Meta-analysis was processed by RevMan 5.0 software. Results Eight randomized controlled trials （RCTs） involving 777 patients met the inclusion criteria. The rerupture rate in non-operative group was significantly higher （Z=3.33, P 〈0.01）. However, the moderate （Z--4.27, P 〈0.01） and minor （Z--5.59, P 〈0.01） complication rate in the operative group were significantly higher. No significant difference in comparing the major and total complication rates. The return to work time in the operative group was shorter （Z=2.65, P 〈0.01）. The inability to return to previous level sporting rate and ankle joint decreased range of motion （ROM） rate showed no significant difference in the two groups. Other functional outcomes were similar in the two groups. Conclusions Operation could significantly reduce the risk of rerupture; however, it was associated with a higher risk of other complications. The functional outcomes were similar in two treatment methods except an earlier return to work in patients treated operatively. Thus operative treatment is preferable for patients with good physical condition. Non-operative treatment is an acceptable alternative especially for the older and patients with lower sporting requirements.

WELL-POSEDNESS OF THE MODEL DESCRIBING A REPAIRABLE,STANDBY,HUMAN & MACHINE SYSTEM

By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.