For the two sixth-order polynomials a(s) and b(s), Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.

We describe the pairs (p, n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.

The Barkhausen pattern from the amorphous alloy Fe21Co64B15 showed high sweep-to-sweep reproducibility for most sweeps when driven slowly over a minor hysteresis loop. Small changes in the maximum applied field led to completely different pulse patterns. When driven near saturation the sweep-to-sweep reproducibility was lost. Large features observed on rapid sweeps were also reproducible, but n...

Recently, geometrically thick disks around black holes have been studied by many authors. I) These models may exist in the inner region of accretion disks and explain the generation of high luminosity and colliminated jets in quasers and active galactic nuclei. In such tori, there is no reason for the rotation law to be Keplerian as pressure force plays a role in the equilibrium structure. Thes...

Beginning with Hermite’s integral representation of the Hurwitz zeta function, we derive explicit expressions in terms of elementary, polygamma, and negapolygamma functions for several families of integrals of the type ∫∞ 0 f(t)K(q, t)dt with kernels K(q, t) equal to ( e2πqt − 1 )−1 , ( e2πqt + 1 )−1 , and (sinh(2πqt))−1.

Simple proofs of the Hermite–Biehler and Routh–Hurwitz theorems are presented. The total nonnegativity of the Hurwitz matrix of a stable real polynomial follows as an immediate corollary. © 2003 Elsevier Inc. All rights reserved. AMS classification: 93D05; 34D99; 12D10; 26C05; 26C10; 30C15; 15A23; 15A48; 15A57

This paper deals with the stability study of polling systems with either finite or infinite (countable) number of stations (queues) and with a finite number of servers that poll (visit) the stations along some random (state-independent) routes. First, we formulate “global” and “local” stability theorems for systems with a single server and with a general stationary ergodic input. Their proofs a...

We present a generalized approach to stability of static equilibria of nonlinearly elastic rods, subjected to general loading, boundary conditions and constraints (of both point-wise and integral type), based upon the linearized dynamics stability criterion. Discretization of the governing equations leads to a non-standard (singular) generalized eigenvalue problem. A new efficient sparse-matrix...

A new variational approach to irreversible thermodynamics has been developed leading to lagrangian equations of evolution. The essential results have been presented recently in the form of a short monograph [l]. Its foundation rests on a fundamental principle of virtual dissipation. Our purpose here is to derive new stability criteria for a steady state evolution based on lagrangian equations i...