Let G be a graph of order n with (0, 1)-adjacency matrix A. An eigenvalue σ of A is said to be an eigenvalue of G, and σ is a main eigenvalue if the eigenspace EA(σ) is not orthogonal to the all-1 vector in IR. Always the largest eigenvalue, or index, of G is a main eigenvalue, and it is the only main eigenvalue if and only if G is regular. We say that G is an integral graph if every eigenvalue...

We extend a result of Coifman and Dahlberg [Singular integral characterizations of nonisotropic H spaces and the F. and M. Riesz theorem, Proc. Sympos. Pure Math., Vol. 35, pp. 231–234; Amer. Math. Soc., Providence, 1979] on the characterization of H spaces by singular integrals of R with a nonisotropic metric. Then we apply it to produce singular integral versions of generalized BMO spaces. Mo...

Abstract. Two optimal monotone integral principles (equivalently for the Laplacian, two sharp iso-weighted-volume inequalities) are established through extending the first and second integral bounds of H. Weinberger for the Green functions (i.e., fundamental solutions) of uniformly elliptic equations in terms of the layer-cake formula, a one-dimensional monotone integral principle, and the isop...

This paper is devoted to the computation of transmission eigenvalues in inverse acoustic scattering theory. problem first reformulated as a two by boundary system integral equations. Next, utilizing Schur complement technique, we develop operator with regularization obtain reduced The Nystrom discretization then used an eigenvalue for matrix. We employ recursive method numerical matrix eigenval...