We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, max-sum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is intractable, determining optimal values for a part of variables is an interesting possibility. Existing methods are based on different sufficient conditions. We p...

The nullity of a graph G is the multiplicity zero as an eigenvalue its adjacency matrix. An assignment weights to vertices graph, that satisfies sum condition over neighbors each vertex, and uses maximum number independent variables denoted by high weighting graph. This applicable tool used determine Two types graphs are defined, change their nullities studied, namely, G+ab constructed from add...

This paper presents a combinatorial algorithm for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eig...

In terms of damping low frequency oscillation, power system stabilizer(PSS) plays a very key role. However, in terms of PSS capability exploitation, it is quite important to select the suitable parameters assignment. Different from traditional optimization algorithms with eigenvalue analysis based and with system damping ratio as the aim function, in this paper a new PSS parameters method based...

We describe the generic change of the partial multiplicities at a given eigenvalue λ0 of a regular matrix pencil A0 + λA1 under perturbations with low normal rank. More precisely, if the pencil A0 + λA1 has exactly g nonzero partial multiplicities at λ0, then for most perturbations B0 + λB1 with normal rank r < g the perturbed pencil A0 + B0 + λ(A1 + B1) has exactly g − r nonzero partial multip...

The Estabrook-Wahlquist method for establishing the integrability of partial diierential equations is extended to semi-discrete (lattice) systems. If successful, the method construct the linear eigenvalue problem associated with the equation.

In the past few years transmission eigenvalues have become an important area of research in inverse scattering theory with active research being undertaken in many parts of the world. Transmission eigenvalues appear in the study of scattering by inhomogeneous media and are closely related to non-scattering waves. Such eigenvalues provide information about material properties of the scattering m...

This paper presents an analytical model for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalu...

A resonant-state expansion (RSE) for open optical systems with a general frequency dispersion of the permittivity is presented. The RSE of dispersive systems converts Maxwell’s wave equation into a linear matrix eigenvalue problem in the basis of unperturbed resonant states, in this way numerically exactly determining all relevant eigenmodes of the optical system. The dispersive RSE is verified...

Teaching linear algebra routines for computing eigenvalues of a matrix can be well motivated to students using interesting examples. We propose in this paper to use vibrating plates for two reasons: first there are interesting applications, from which we chose the Chladni figures representing sand ornaments which form on a vibrating plate, and the Tacoma bridge, one of the most spectacular brid...