In the space of the system parameters, the stability charts are determined for the delayed and damped Mathieu equation defined as ẍ~t!1k ẋ~t!1~d1« cos t!x~t!5bx~t22p! . This stability chart makes the connection between the Strutt-Ince chart of the damped Mathieu equation and the Hsu-Bhatt-Vyshnegradskii chart of the autonomous second order delay-differential equation. The combined charts descri...

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M 12. As a consequence, we confirm for this group the Kimmerle's conjecture on prime graphs.

Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.

We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 3, it may lead to exceptional points depending upon the strength of the coupling parameter ξ. The corresponding Schrödinger equation is also shown to go over to the Mathieu equation asymptotically. The limiting value of...

Many reviews have been written on pre-main-sequence binaries over the past 25 years, e.g., Reipurth (1988), Zinnecker (1989), Mathieu (1994), and Goodwin (2010), and particular mention should be made of IAU Symposium No. 200 (Zinnecker and Mathieu, 2001), which is still today a useful reference. Most recently, Duchêne and Kraus (2013) review the binarity for stars of all masses and ages. Stimul...