Al~lract--Motivated by a crucial role blocking zeros play in deciphering the strong stabilizability of a given system, a careful study of blocking zeros is undertaken here. After developing certain properties of blocking zeros and based on the multiplicity structure of invariant zeros, we identify what kind of invariant zeros are blocking zeros. For controllable and observable systems, an invar...

model order reduction is known as the problem of minimizing the -norm of the difference between the transfer function of the original system and the reduced one. in many papers, linear matrix inequality (lmi) approach is utilized to address the minimization problem. this paper deals with defining an extra matrix inequality constraint to guarantee that the minimum phase characteristic of the sys...

One of the most celebrated problem of mathematics is the Riemann hypothesis which states that all the non trivial zeros of the Zeta-function lie on the critical line <(s) = 1/2. Even if this famous problem is unsolved for so long, a lot of things are known about the zeros of ζ(s) and we expose here the most classical related results : all the non trivial zeros lie in the critical strip, the num...

which is valid for any complex s, it follows that ζ(s) has zeros at s = −2,−4, . . . . These zeros are called the “trivial” zeros of ζ(s), to distinguish them from the complex zeros of ζ(s). The zeta-function has also an infinity of complex zeros. It is well-known that all complex zeros of ζ(s) lie in the so-called “critical strip” 0 < σ = R s < 1, and if N(T ) denotes the number of zeros ρ = β...

This survey paper is devoted to inequalities for zeros of algebraic polynomials. We consider the various bounds for the moduli of the zeros, some related inequalities, as well as the location of the zeros of a polynomial, with a special emphasis on the zeros in a strip in the complex plane.

We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to the density of zeros. Zeros away from the a.c. spectrum have limit points mod p and only finitely many of them.

Single-input single-output (SISO), systems with zeros interlacing poles (ZIP) have been extensively studied in the literature and received interest widely. However, ZIP property for multiple-input multiple-output (MIMO), has not pursued sufficiently. In this article, we pursue MIMO link to strict passivity. For class of that admit a symmetric state-space realization, which SISO case is equivale...

he purpose of this study is to demonstrate how we, especially children and adolescents, are influenced by the media; this issue had investigated by analyzing the representation of gender roles in the Game of Thrones Series. There were based on three social learning, socialization and cultivation theories. This research had done a quantitative content analysis. The variables included 20 gender a...

For a given real entire function φ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions Q = (φ/φ) and Q1 = (φ /φ). This connection leads to a proof of the Hawaii conjecture [T.Craven, G.Csordas, and W. Smith, The zeros of derivatives of entire functions and the Pólya-Wiman conjecture, Ann. of Math. (2) 125 (1987), 405–431] stating that th...

We study the Yang-Lee zeros of a random matrix partition function with the global symmetries of the QCD partition function. We consider both zeros in the complex chemical potential plane and in the complex mass plane. In both cases we find that the zeros are located on a curve. In the thermodynamic limit, the zeros appear to merge to form a cut. The shape of this limiting curve can be obtained ...