Spectra of digraphs

In this primarily expository paper we survey classical and some more recent results on the spectra of digraphs, equivalently, the spectra of (0,1)-matrices, with emphasis on the spectral radius.     

Towards a spectral theory of graphs based on the signless Laplacian, II

A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This theory is called M-theory. We outline a spectral theory of graphs based on the signless Laplacians Q and compare it with other spectral theories, in particular to those based on the adjacency matrix A and the Laplacian L. As demonstrated in the first part, the Q-theory can be constructed in part using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, common features with L-theory for bipartite graphs, general analogies with A-theory and analogies with A-theory via line graphs and subdivision graphs. In this part, we introduce notions of enriched and restricted spectral theories and present results on integral graphs, enumeration of spanning trees, characterizations by eigenvalues, cospectral graphs and graph angles.     

Solitary waves in Abelian Gauge Theories with strongly nonlinear potentials

We study the existence of radially symmetric solitary waves for a system of a nonlinear Klein–Gordon equation coupled with Maxwell's equation in presence of a positive mass. The nonlinear potential appearing in the system is assumed to be positive and with more than quadratical growth at infinity.     

A Note on degree antiregular graphs

This note proves a conjecture of Merris that the minimal value of entries of the doubly stochastic matrix of the degree antiregular graph E_n of order n ≥ 3 is equal to (l/2(n + l)).     

On the Uniqueness Theorem for Generalized Solutions of Initial-Boundary Problems for the Marguerre—Vlasov Vibrations of Shallow Shells with Clamped Boundary Conditions

The uniqueness theorem for generalized solutions of initial-boundary problems for the Marguerre—Vlasov vibrations of shallow shells with clamped boundary conditions is proved. A unique method developed by the author, based upon a nonstandard treatment of smoothing operators, is applied instead of using an enclosure theorem at the critical values of indices. Accepted 10 November 1997     

High-temperature oxidation studies of cold-sprayed Ni-20Cr and Ni-50Cr coatings on SAE 213-T22 boiler steel

The high-temperature oxidation behavior of cold-sprayed Ni-20Cr and Ni-50Cr coatings on SAE 213-T22 boiler steel has been investigated at 900 °C in air under cyclic heating and cooling conditions for 50 cycles. The kinetics of oxidation of coated and bare boiler steel has been established with the help of weight change measurements. It was observed that all the coated and bare steels obeyed parabolic rate law of oxidation. X-ray diffraction, FE-SEM/EDAX and X-ray mapping techniques were used to analyse the oxidation products of the coated and uncoated boiler steel. The uncoated steel suffered corrosion in the form of intense spalling and peeling of its oxide scale, which was perhaps due to the formation of unprotective Fe₂O₃ oxide scale. Both the coatings showed better resistance to the air oxidation as compared to the uncoated steel. The Ni-50Cr coating was found to be more protective than the Ni-20Cr-coated steel. The formation of oxides and spinels of nickel and chromium may be contributing to the development of air oxidation resistance in the coatings.     

Symmetries of a generic coaction

If B is -algebra of dimension $4\leq n<\infty$ then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say , have the same fusion rules as the ones of SO(3). As consequences, we get (1) a structure result for in the case where B is a matrix algebra (2) if then the dual is not amenable (3) if then the fixed point subfactor has index n and principal graph . Received: 3 December 1998 / in final form: 8 January 1999