The notion of Newton–like inequalities is extended and an inductive approach is utilized to show that the generalized Newton–like inequalities hold on elementary symmetric functions with self–conjugate variables in the right half–plane.

Let R be an n by n nontrivial real symmetric involution matrix, that is, R R−1 R / In. An n × n complex matrix A is termed R-conjugate if A RAR, where A denotes the conjugate of A. We give necessary and sufficient conditions for the existence of the Hermitian R-conjugate solution to the system of complex matrix equations AX C andXB D and present an expression of the Hermitian R-conjugate soluti...

We present a residual smoothing algorithm for the complex symmetric conjugate gradients method. As in the real case, the residual smoothing method reproduces the (quasi-minimising) QMR method, and is considerably simpler to compute.

The pure symmetric automorphism group of a finitely generated free group consists of those automorphisms which send each standard generator to a conjugate of itself. We prove that these groups are duality groups.

All symmetric designs are determined for which the automorphism group is 2-transitive on the set of points. This note contains a proof of the following result. Theorem. Let D be a symmetric design with v > 2k such that Aut D is 2-transitive on points. Then D is one o f the following: (i) a projective space; (ii) the unique Hadamard design with v = I 1 and k = 5; (iii) a unique design with v = 1...

In conjugate symmetric data transmission, due to insufficient judgment of congestion during the amount is large and transmission rate low. order improve rate, a control method based on machine learning designed. Firstly, be transmitted tracked determined, then fusion completed according calculation result best tracking signal. According results, framework coding system established, completed. T...