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直接误差估计的一个新方法 被引量:1
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作者 田天海 王能超 《应用数学》 CSCD 北大核心 1989年第3期39-48,共10页
本文利用文[1]的方法进行误差估计产生了严重过估的事实,从而提出了一个估计误差的新方法。通过严格的分析树高定义,给出了绝对误差和相对误差二种形式的误差估计方法,并针对并行算法的特点,给出了向量运算算法的误差估计方法。利用该... 本文利用文[1]的方法进行误差估计产生了严重过估的事实,从而提出了一个估计误差的新方法。通过严格的分析树高定义,给出了绝对误差和相对误差二种形式的误差估计方法,并针对并行算法的特点,给出了向量运算算法的误差估计方法。利用该方法本文给出了几个典型问题的算法的误差估计,结果表明,它和已有的结论是一致的。 展开更多
关键词 直接误差估计 并行算法 向量运算
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MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE
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作者 包康博 梁桂珍 +1 位作者 田天海 张兴安 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期1165-1188,共24页
Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory ca... Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes. 展开更多
关键词 mathematical model drug resistance cancer heterogeneity immune system targeted therapy
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