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This paper surveys results in Spectral Graph Theory and the Inverse Eigenvalue Problem of a Graph , examines the connections between these problems , and presents some new results on construction of a matrix of minimum rank for a given graph having a special form such as a 0,1 - matrix or a generalized Laplacian . In this report we propose a new model to represent spectral functions called the composite model . Nevertheless , many public safety communications systems are not designed to maximize spectral efficiency , and for good reasons . The system 's patented airlink combines adaptive TDD , TDMA ( time division multiple access ) and variable index modulation ( 4 , 16 , or 64 QAM ) to maximize spectral efficiency and provide more throughout per megahertz of spectrum than any other system in the market today . Professional library of pole assignment methods is extended to include spectral and mapping dyadic algorithms and the full-rank algorithms for state and output feedback . System Professional library of pole assignment methods is extended to include spectral and mapping dyadic algorithms and the full-rank algorithms for state and output feedback . The stretched PC data are then projected back into the original channels which are enhanced to maximize spectral sensitivity . Each channel contains a spectral filter , which results in spectral dependence of the output . Discovered by M.G.Krein analogy between polynomials orthogonal on the unit circle and generalized eigenfunctions of certain differential systems is used to obtain some new results in spectral analysis of Sturm-Liouville operators . Some portions of this range will be made available with a cross-dispersing element to maximize spectral coverage at the expense of slit height . Such decay is a technically convenient characterization of localization for it is known to imply spectral localization , absence of level repulsion , dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases . These protocols combine to maximize spectral efficiency and throughput .