Abstract
The main objective of this paper is to find an analytic expression for the maximum eigenvalue of a special matrix A of order n, with n in the range 2<or=n( infinity . This will be done using a new result which states that if one knows any entry Ckl(j) of any real positive square matrix Cj (where j denotes the number of iterations), then, after taking the thermodynamic limit (lim j to infinity ), the maximum eigenvalue of this matrix is known. The analysis that is presented is of particular interest, because the structure of the above-mentioned matrix A, appears in several problems related to physical and biophysical systems in one dimension, i.e. the one-dimensional fluid model, denaturation of DNA (where loop entropy is taken into account), in the study of the homogeneous island model, etc. As a particular application of this method, the author derives the Takahashi equation of state, which is the more general solution for a one-dimensional fluid model when it is assumed that the interaction potential between nearest-neighbour particles is arbitrary.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
