中文摘要：

为了更深入的研究P53肿瘤抑癌基因，首先我们基于扩展的碱基表C=fD，A，C，O，G，T，P）分别获得了加法运算和乘法运算，然后根据密码子集C^3={XYZ}，定义了汉明距离dH，继而通过加权和改进的汉明距离提出了日H^＊距离．进一步地，我们定义了密码子的外积和H^＊内积。此外，也获得了DNA序列间的H^＊距离dH^＊和H^＊内积（X1Y1Z1，X2Y2Z2）．我们选取了9种与P53肿瘤抑癌基因相关的人类癌症基因序列，并分析了他们的代数结构，获取了如下结果：当0≤dH≤1，我们发现它对任意的氨基酸突变位置没有任何影响，而dH＋和（x1y1z1，X2y2历）对氨基酸突变位置是敏感的，如dH＋，当氨基酸第一位碱基突变时，0．75≥dH＋≥0．25；当氨基酸第二位碱基突变时，3≥dH^＊≥1；当氨基酸第三位碱基突变时，0．08≤dH＋≤0．25；如（X1y1Z1，尥y2历），当氨基酸的第一位或第三位碱基突变时，（X1Y1Z1，X2Y2Z2）值都大于0；而当氨基酸第二位碱基突变时，-2≤（X1Y1Z1，X2Y2Z2）≤4，但其中65．22％都小于或等于0，且氨基酸的理化性质都发生了变化．同时，我们也可认为当（X1Y1Z1，X2Y2Z2）小于或等于0时，第二位碱基将发生变化．通过以上的分析结果可知，较之于汉明距离，H^＊距离及其内积更有利于研究氮基酸的理化性质．这些研究结果不仅有助于更深入的研究基因突变的密码子编码的氨基酸性质，也为人类癌症的预防与控制提供了一些参考．

英文摘要：

To get more insight into the additive and multiplicative operation based on p53 tumor suppressor gene, firstly, the extended base C = {D, A, C, O, G, T, P} were given respectively. And with the codons set C3 = {XYZ}, the Hamming distance dH was defined. Then the H＊-distance was proposed by weighting and improving the Hamming distance. Furthermore, more cross products among these codons and the H＊- inner products were also defined. Besides, between DNA sequences were gained. Then the H＊-distance and the H＊-inner product several human cancers related to p53 tumor suppressor gene were chosen and analyzed by there algebraic structure. The following results had been obtained： When the range of dH/was 1 to 3, we found it no big differences for any mutational position. However, dH＊ and （X1Y1Z1, X2Y2Z2） were sensitive to the mutational position. For dH＊, when the first base mutated, 0.75 〉 dH. ≥ 0.25; When the second base ：mutated, 3≥dH＊ ≥ 1; When the third base mutated, 0.08 ≤ dH＊ ≤ 0.25; For （XIYIZ1, X2Y2Z2）, when the first base or the third base mutated, all of them were greater than 0. In particular, when the second mutated,-2 ≤ （XIY1Z1, X2Y2Z2） ≤ 4, but 65.22% of them were less than or equal to 0, and the physiochemical properties of amino acids were changed. Through above analysis, we knew that the H＊-distance and the H＊-inner product was more useful to the study on the properties of amino acids compm：ed to the Hamming distance. Furthermore, we could say that when the （X1Y1Z1, X2Y2Z2） was less than or equal to 0, the second base mutated. These results were not only important to further study on the amino acids occurring mutation in encoding codons, but also could be as some of human tmnor. guidances for the preventing and controlling