We studied the amplification of the solution of a Mathieu-like equation with multiplicative white noise. This equation has a periodic varying mass term. The exponents were calculated numerically by solving the stochastic differential equations by symplectic method. It was shown that the exponent increases with a parameter α in the range of large α, where the value of α is determined by the inte...

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

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 ...

We utilize the travelling-wave Ansatz to obtain novel analytical solutions linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in Lorentzian form secondly cosine form. new contain Heun functions first case Mathieu for second case, therefore are highly nontrivial. use these test some non-conventional explicit stable numerical methods agai...

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...

We prove that the the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency.