In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which...

We study the sum ζH(s) = ∑ j E j over the eigenvalues Ej of the Schrˇdinger equation in a spherical domain with Dirichlet walls, threaded by a line of magnetic flux. Rather than using Green’s function techniques, we tackle the mathematically nontrivial problem of finding exact sum rules for the zeros of Bessel functions Jν , which are extremely helpful when seeking numerical approximations to g...

A new formulation of MPCI is proposed. The on-line objective is not to minimize the sum of square errors, but to maximize on-line the sum of the lower bounds on the minimum eigenvalues of the information matrices over finite horizons. In that way, inputs to the process are allowed to excite the process highly enough to generate as much modeling information as possible, while the process goes of...

A new formulation of MPCI is proposed. The on-line objective is not to minimize the sum of square errors, but to maximize on-line the sum of the lower bounds on the minimum eigenvalues of the information matrices over finite horizons. In that way, inputs to the process are allowed to excite the process highly enough to generate as much modeling information as possible, while the process goes of...

In this study, the effective parameters on the inelastic response of asymmetric buildings is evaluated for an ensemble of real Iranian earthquake records by considering soil-structure interaction. Then, the design eccentricity obtained from the inelastic dynamic soil-structure analysis is compared with the design eccentricity of seisimic codes of Iran, ATC-3, New Zeland, Canada, Mexico, Austral...

Graph energy is defined to be the p -norm of adjacency matrix associated graph for = 1 elaborated as sum absolute eigenvalues matrix. The graph’s spectral radius represents matrix’s largest eigenvalue. Applications energies and radii can found in both molecular computing computer science. On similar lines, Inverse Sum Indeg, ( ISI ) energies, constructed. This article’s main focus generalized s...

It is well known that a function can be decomposed uniquely into the sum of an odd and an even function. This notion can be extended to the unique decomposition into the sum of four functions – two of which are even and two odd. These four functions are eigenvectors of the Fourier Transform with four different eigenvalues. That is, the Fourier transform of each of the four components is simply ...

We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [2] where, assuming the stochastic excitation is small, the stability of such systems was computed using a weighted sum of the extended power spectral density over the eigenvalues of the unperturbed operator. In this paper, we show how to convert this to a su...

The incidence energy I E (G) of a graph G, defined as the sum of the singular values of the incidence matrix of a graph G, is a much studied quantity with well known applications in chemical physics. The Laplacian-energy-like invariant of G is defined as the sum of square roots of the Laplacian eigenvalues. In this paper, we obtain the closed-form formulae expressing the incidence energy and th...