We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for $|q_0|=...=|q_{N-1}|=1$ the quantity $\Phi ={\sum }_{i+k=j+l}\frac{q_i{q}_k}{q_j{q}_l}$ satisfies $\Phi \ge N^2$, with equality if and only if $q=\left(q_i\right)$ is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of $\Phi$, (2) the study of the critical points of $\Phi$, and (3) the computation of the moments of $\Phi$. We explore here these questions,...

Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.

Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of the input-output disturbances. Such an estimate is highly non-linear. Moreover in some realistic situations, the errors cannot be considered as independent by nature. Weakly dependent ($\alpha$- and $\varphi$-mixing) disturbances, which are not necessarily stationary nor identically...

We prove a number of results concerning the large $N$ asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of $N$ of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics of the free...