General Case of n Reactions in Circle

The general case, of which the Krebs cycle with eight reactions in circle is a particular case can be obtained by extension of the expressions derived for three reactions in circle and four reactions in circle. Aliter to this would be the method of eigenvalues and eigenvectors. The cases when A, eigenvalues are imaginary represent situations in the system, when the concentration of the species will exhibit subcritical damped oscillations. These are given by the characteristic equation  

The size of the K matrix depends on the number of reactions in circle. For n reactions in circle K would be an n x n matrix. For the case of the Krebs cycle, it would be an 8 X 8 matrix. 

Upon expansion, an 8th-order polynomial equation in A arises. Eight roots of the polynomial exist. Even if all the values in the characteristic matrix are real, some roots may be complex. When complex roots occur, they appear in pairs. The roots of the polynomial are called eigenvalues of the characteristic matrix. The polynomial equation is called the eigenvalue equation. 

Noting from the product technical brochures, there is significant commercial interest in manufacturing multicomponent copolymers as indicated by BASF, Bayer, etc. Alphamethyl-styrene (AMS) is used as the primary monomer choice. Products that offer higher heat resistance compared with styrene-acrylonitrile (SAN) copolymer can be made by copolymerization of AMS with AN, thereby circumventing the 

Monomer and Polymer Compositions of Samples Used in Tube Polymerization Study AMS (Wt Fraction) AN (Wt Fraction) Sty (Wt Fraction) AMS (Wt Fraction) AN (Wt Fraction) STY (Wt Fraction) 

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