Recently, in Refs. [1] and [2], calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on stratification and Stieltjes function associated with the network, whereas in the latter one a recursive formula for effective resistances was given based on the Christoffel-Darboux identity. In this paper, evaluation of effec...

To each symmetric n × n matrix W with non-zero complex entries, we associate a vector space N , consisting of certain symmetric n × n matrices. If W satisfies n ∑ x=1 Wa,x Wb,x = nδa,b (a, b = 1, . . . , n), then N becomes a commutative algebra under both ordinary matrix product and Hadamard product (entry-wise product), so that N is the Bose-Mesner algebra of some association scheme. If W sati...

The Kramer–Neugebauer–like transformation is constructed for the stationary axisymmetric D=4 Einstein–Maxwell–dilaton–axion system. This transformation directly maps the dualized sigma–model equations of the theory into the nondualized ones. Also the new chiral 4× 4 matrix representation of the problem is presented. PACS numbers: 04.20.Jb, 03.65.Ca Typeset using REVTEX 1