Leading eigenvalues

The diffusive random walk of the Helfand moment is mled by a diffusion equation. If the phase-space region is defined by requiring Ga(t) < x/2, the escape rate can be computed as the leading eigenvalue of the diffusion equation with these absorbing boundary conditions for the Helfand moment [37, 39] ... 

First invariant leading eigenvalue of the adjacency matrix A Second invariant leading eigenvalue ofGG matrix... 

The largest eigenvalue of the topological - distance matrix D representing an H-depleted molecular graph was proposed as a molecular descriptor, and was called the leading eigenvalue of the distance matrix [Schultz et al., 1990]. It was found to be a... 

They are the eigenvalues obtained from the Wiener matrix W. In particular, in analogy with the Lovasz-Pelikan index, the 1 Wieuer matrix eigenvalue X] (or Wiener matrix leading eigenvalue) is taken as an alternative descriptor for the molecular... 

Wiener matrix leading eigenvalue Wiener matrix eigenvalue -> eigenvalue-based descriptors (O Wiener matrix eigenvalues)... 

For a large Nt, the trace is dominated by the leading eigenvalue of the transfer matrix Z (af >)NT and the ground-state energy is given by... 

The correlation length can be written in terms of the two leading eigenvalues af 1 and of the transfer matrix... 

The —> leading eigenvalues obtained from the geometric distance/topological distance quotient matrix and its higher order matrices were proposed to describe the sequence. In any case, the degeneracy of this approach still remains large. 

From these 12 matrices, the —> leading eigenvalues were calculated and used for similarity/ diversity analysis. 

Erom these Eudidean-distance matrix, M/M quotient matrix and L/L quotient matrix, —> leading eigenvalues were calculated to perform similarity/diversity analysis. 

The leading eigenvalues of the six matrices were proposed to describe the whole DNA sequence. 

It has been demonstrated that the leading eigenvalue of a symmetric matrix M is bounded from above and from below by its largest and smallest row sum ... 

MaxSp( D)a.nd SpSum ( D) are the leading eigenvalue and the sum of the absolute eigenvalues of the Barysz distance matrix, respectively. 

ND indices are molecular descriptors calculated from augmented matrices P, P, and P where the first two columns contain (1) the square root of the bond vertex degree 8 and (2) the equilibrium electronegativity of atoms [Nie, Dai et al, 2005]. ND indices are the leading eigenvalues of the symmetrized augmented path matrices Mi, M2, and M3 ... 

As a direct consequence, the main frequency which is activated by the noise switches exactly at these values of r to the eigenfrequency of the corresponding leading eigenvalue. In Fig. 5.25(c) the eigenperiods are plotted as black dots in dependence of r. The circles mark the positions of the... 

Figures 7 and 8 for families ofbenzenoid compounds and selected larger benzenoids, respectively. Resonance graphs show interesting regular shapes, while the leading eigenvalue of the graphs represent an index of the benzenoid character of PAH," ...

Table 10. The Normalized Leading Eigenvalue for Linear Chains of Length n (Superimposed on Graphite Lattice) Corresponding to M-trans Conformers and all-cis Conformers...

In order to get more experience with the newly proposed index ( ) we will consider the leading eigenvalue X of D/D matrices for several well-defined mathematical curves. We should emphasize that this approach is neither restricted to curves (chains) embedded on regular lattices, nor restricted to lattices on a plane. However, the examples that we will consider correspond to mathematical curves embedded on the simple square lattice associated with the Cartesian coordinates system in the plane, or a trigonal lattice. The selected curves show visibly distinct spatial properties. Some of the curves considered apparently are more and more folded as they grow. They illustrate the self-similarity that characterizes fractals. " A small portion of such curve has the appearance of the same curve in an earlier stage of the evolution. For illustration, we selected the Koch curve, the Hubert curve, the Sierpinski curve and a portion of another Sierpinski curve, and the Dragon curve. These are compared to a spiral, a double spiral, and a worm-curve. 

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