Two Kinds Of Inverse Spectrum Analysis Of Discrete System

It’s well know in physics, the system consists of n+1spring stiffness k0,k1,…,kn with the point masses m1, m2,…, mn between them is called a mass-spring sys-tem. The system consists of n+1intervals l0,l1,…, ln with the point masses m1, m2,…, mn between them is called a Stieltjes string system. This disser-tation discuss the reconstruction of the mass-spring system and the Stieltjes string based on spectral information. Modify the original mass-spring system, with the eigenvalues of the original and the modify system, and the modify parameters to determine{mi}1n,{ki}1n. Consider the inverse spectral problem for a Stieltjes string system with one-dimensional damping, use the nature of the Stieltjes continued frac-tions, with the eigenvalues of the system to determine the parameters of the system. The main conclusions are as follows:(1) Modify the original mass-spring system(the modify parameters k and m are know), and get a new mass-spring system. Let the eigenvalues {A.,}" of the original system,{μi}1n of the modify system and ξ=k/m satisfy the conditions:λ1<μ1<λ2<…<λq<μq <ξ<μq+1<λq+1<…<λn-1<μn <λn, Then there exist unique sets {mi}1n,{ki}1n.(2) Let l>0be given together with the set of real number0<λ1<λ2<…<λn. Then there exists sets {mk}1n,{lk}0n such that (?)li=l, which generate Stieltjes string with the spectral {λi}1n.(3) Here we consider the inverse problem for a Stieltjes string system with one-dimensional damping. We suppose the string to be thread bearing finite number n1+n2of Point masses. Let the thread consist of two parts. The first part consists of n1+1(n1≥l)intervals lk(k=0,1,…,n1) with the point masses mk (k=1,2,…,n1) between them(lk-1lies to the left from mk and lk lies to the right). The second part consists of n2+1(n2≥1)intervals lk(k=0,1,…,n2) with the point masses lk(k=1,2,…,n2) between them(lk-1lies to the left from mk and lk lies to the right). Thus, the length of the interval between mn1and mn2is ln1+ln2. Let us consider the reconstruction problem of the string which damped at the point of the meeting (the point mass at the point of the meeting is m>0, and α>0is the coefficient of damping). That is, with the spectral information to reconstruct the parameters {mi}1n1,{li}0n1,{mi}1n2,{li}0n2such that(?)li=l,(?)li=l-l...