This article have two parts : g - fixed ideals and some ideas with stable betti numbers on shifting operations 本文分两部分： g -不变理想与移位运算下保持分次betti数不变的一些理想。
2.
According to thinking the joints of plates as elastic boundary supports to plates and by using of the method of separation of variables , betti ' s reciprocal theorem of work , the solution of dynamic equation can be deserved 运用变分法，分离变量法，互等功定理等数学工具求解板的运动方程，可得出弹性地基上考虑接缝传荷能力的道面板在移动荷载下的动力响应(解析解) 。
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From far left : ms grace cheng , ms betti - sue hertz , ms yuko hasagawa , ms may fung , mr roger lai , ms mimi cho museum staff , mr liu xi - lin , mr ou dai - wei , mr zhang hai , mr chui tze - hung , dr mok kar - leung and ms fiona wong 由左后方起：郑婵琦女士betti - sue hertz女士长谷川佑子女士冯美华女士黎日晃先生曹韵雯女士馆员刘曦林先生区大为先生张海先生徐子雄先生莫家良博士及黄丽贞女士。
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When i s is a squarefree strongly stable ideal , ic = i . therefore p and / have the same graded betti numbers , projective dimension and regularity . in this paper , we study the relationship of the betti numbers between ic and i . in section 1 , the concepts of combinatorial shifting and some related results are given ) s为无平方强稳定理想时i ~ c = i ，因而i ~ c和i的分次betti数、投射维数和正则度相同，本文主要研究i为无平方稳定理想时， i ~ c和i之间分次betti数的关系。
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In section 3 , we show that when i is a squarefree stable ideal , shiftij ( i ) and i have the same graded betti numbers , projective dimension and regularity , then ic and i have the same graded betti numbers , projective dimension and regularity . at last we apply the results we obtained to simplicial complexes 在第三节中证明了当i为无平方稳定理想时， shiftij ( i )与i的分次betti数、投射维数和正则度相同，从而i ~ c与i的分次betti数、投射维数和正则度相同，最后将所得结论推广到单纯复形上。
