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...

Prospects for Xenotransplantation: Identifying psychosocial and pastoral challenges Jochen Sautermeister, Richard Mathieu, Veronika Bogner Chair for Moral Theology, Catholic Theological Faculty, University Munich,

We derive a new Chambers-type formula and prove sharper upper bounds on the measure of spectrum critical almost Mathieu operators with rational frequencies.

Heavy metal pollution limits shouldn't just keep humans safe, but other animals too, say Coline Monchanin and Mathieu Lihoreau

a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...

New, accurate lower and upper bounds for the sum of the generalized Mathieu series ∞ ∑ k=1 2k (k2 + x2) , p > 0,

We propose a homotopy analysis method in combination with Galerkin projections to obtain transition curves of Mathieu-like equations. While constructing homotopy, we think convergence-control parameter as function embedding and call it function. Homotopy provides relation between the parameters Mathieu equation that also includes free arising from generate extra nonlinear algebraic equations us...

So you think you can't dance? (The mysterious case of the guy with two left feet) Mathieu did not just suddenly come to realize this problem, and he did not give up easily. He spent most of his 23 years of life studying music (various instruments , voice) and dance (Latin dance lessons, and he even performed in a dance troupe at a family amusement park!), only to find, time after time, that he ...

In the early 60’s J. B. Keller and D. Levy discovered a fundamental property: instability tongues in Mathieu-type equations lose sharpness with addition of higher-frequency harmonics Mathieu potentials. Twenty years later, V. Arnold similar phenomenon on circle maps (and rediscovered result Levy). this paper we find third class object where type behavior takes place: area-preserving cylinder. l...

OBJECTIVES To report our experience with Mathieu urethroplasty for revision of hypospadias repairs. Mathieu perimeatal-based flap urethroplasty remains a popular technique more than seven decades after its description for single-stage hypospadias repair. The excellent results of primary distal hypospadias repair are well documented, but reports of the results using the technique as a salvage pr...