Some Tangles And Solutions Of Its Equations

This paper mainly studies the DNA recombination problem,by the knowledge of tangle discuss how work enzymes on the circular DNA molecules,after DNA molecules can be separated into two complementary tangles,and restructuring a new DNA structure,also is the process of DNA recombination model was constructed.First,tangles are introduced and classified in this article,and defines the two bridge and continued fraction,On the basis of these to construct DNA recombination model,by some theorem and lemma,possible solution of a set of instances is obtained.Such as(1)N(X + T)= 6(1,1);(ii)N(X + R)= b(?,?);(iii)N(X +R+R)= b(?',?').and verify all possible solutions.the product of the second order matrix of rational knot play a big role.The above method is too complicate and a large amount of computation,so study a new method is necessary,application of the two bridge equivalent for subsequent research of new method provide some theoretical basis.rational numbers play a key role on relating the two bridge and rational knot,in order to get the general solution of tangle equations.If b(?,?)isn t chirality,the solution of its mirror image may also is solution of the original equations,and specific instance is given,make the operation more simple.To such as(i)N(X + T)=<1>;(ii)N(+ R)=<x,1>;(+ i)N(X+R+R)=<x,1,1>,this paper summarizes general rule of the tangle equations,let x is odd or even to find the solutions,respectively,all the possible solution of the equations can be gained,and further validate general form of solution.At the same time the following equations is verified:(i)N(X + T7)=<1>;(ii)=<x+R)=<x+1>;(iii)N(X +R + R)=<x,y,1>,among(1)x>1;(2)x,y is(2)positive integer;(3)xy+ 1 is prime number;(4)xy + 2x + 1 is prime number,equations have solutions only when y = 1.Although method of solving the equations is simplifies,but only to certain value is prime,so in the future these problem needs further research.