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Improved Symmetry Property of High Order Weighted Essentially Non-Oscillatory Finite Difference Schemes for Hyperbolic Conservation Laws

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1418-1439页

作者： Wai Sun don Peng Li Kwun Ying Wong Zhen Gao School of Mathematical Sciences Ocean University of ChinaQingdao 266100ShandongChina Department of Mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang 050043HebeiChina N.T.heung Yee Kuk Yuen Long District Secondary School Hong Kong

This study aims to investigate the rapid loss of numerical symmetry for problems with symmetrical initial conditions and boundary conditions when solved by the seventh and higher order nonlinear characteristic-wise weighted essentially non-oscillatory(WENO)finite difference *** the one-dimensional double rarefaction wave problem and the Sedov blast-wave problems,and the twodimensional Rayleigh-Taylor instability(RTI)problem as examples,we illustrate numerically that the sensitive interaction of the round-off error due to the numerical unstable explicit form of the local lower order smoothness indicators in the nonlinear weights definition,which are often given and used in the literature,and the nonlinearity of the WENO scheme are responsible for the rapid growth of asymmetry of an otherwise symmetric *** equivalent but compact and numerical stable compact form of the local lower order smoothness indicators is suggested for delaying the onset of and reducing the magnitude of the symmetry *** benefits of using the compact form of the local lower order smoothness indicators should also be applicable to non-symmetrical strongly non-linear problems in terms of improved numerical stability,reduced rounding errors and increased computational efficiency.

关键词： Weighted essentially non-oscillatory symmetry smoothness indicator hyperbolic conservation laws

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Long-term follow up of endoscopic resection for type 3 gastric NET

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World Journal of Gastroenterology 2013年第46期19卷 8703-8708页

作者： Yong Hwan Kwon Seong Woo Jeon Gwang Ha Kim Jin Il Kim Il-Kwun Chung Sam Ryong Jee heung Up Kim Geom Seog Seo Gwang Ho Baik Kee don Choi Jeong Seop Moon Department of Internal Medicine Kyungpook National University Hospital Department of Internal Medicine Busan National University School of Medicine Department of Internal Medicine Catholic University of Korea College of Medicine Department of Internal Medicine Soonchunhyang University Department of Internal Medicine Inje University Pusan Paik Hospital Department of Internal Medicine Jeju National University School of Medicine Department of Internal Medicine Digestive Disease Research InstituteWonkwang University College of Medicine Department of Internal Medicine Hallym University College of Medicine Department of Internal Medicine University of Ulsan College of MedicineAsan Medical Center Department of Internal Medicine Inje University Seoul Paik Hospital

AIM:To clarify the short and long-term results and to prove the usefulness of endoscopic resection in type 3gastric neuroendocrine tumors(NETs).METHODS:Of the 119 type 3 gastric NETs diagnosed from January 1996 to September 2011,50 patients treated with endoscopic resection were enrolled in this *** endoscopic resection,endoscopic mucosal resection(EMR)or endoscopic submucosal dissection(ESD)was *** efficacy,complications,and follow-up results were evaluated ***:EMR was performed in 41 cases and ESD in 9 *** complete resection was performed in 40 cases(80.0%)and incomplete resection specimens were observed in 10 cases(7 vs 3 patients in the EMR vs ESD group,P=0.249).Upon analysis of the incomplete resection group,lateral or vertical margin invasion was found in six cases(14.6%)in the EMR group and in one case in the ESD group(11.1%).Lymphovascular invasions were observed in two cases(22.2%)in the ESD group and in one case(2.4%)in the EMR group(P=0.080).During the follow-up period(43.73;13-60 mo),there was no evidence of tumor recurrence in either the pathologically complete resection group or the incomplete resection *** recurrence was reported during *** addition,no mortality was reported in either the complete resection group or the incomplete resection group for the duration of the follow-up ***:Less than 2 cm sized confined submucosal layer type 3 gastric NET with no evidence of lymphovascular invasion,endoscopic treatment could be considered at initial treatment.

关键词： Stomach Neuroendocrine tumor Endo-scopic resection Treatment Carcinoid

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