Diophantine criteria occur naturally in the theory of partial differential equations through the notorious problem of small denominators. An extensive treatment of such problems in the theory of PDEs can be found, e.g., in [6]. In this paper, we are interested in a Diophantine problem related to an inhomogeneous wave equation in n spatial and one temporal dimension with periodic boundary condit...

The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. The interaction of a periodic solitary wave (cnoidal wave) with high frequency radiation of finite energy (L-norm) is studied. It is proved that the interaction of low frequency component (cnoidal wave) and high frequency radiation is weak for finite time in the following sense: the radiation approximately sat...

In [2], two of the authors and W. Meeks found examples of translation-invariant, embedded minimal surfaces with an infinite number of topological ends. For each k > 0, a surfaceMk was constructed, which was invariant with respect to a translation parallel to the x3-axis, and under a rotation group of order k+ 1 around the x3-axis. The method of construction was generalized in [3] to obtain the ...

We show how to stabilize the uniform oscillations of the complex Ginzburg–Landau equation with periodic boundary conditions by means of some global delayed feedback. The proof is based on an abstract pseudo-linearization principle and a careful study of the spectrum of the linearized operator.

The significance of 2π is that it is a cluster point of the length spectrum from the left (t < 2π), as described in more detail below. In brief, the length spectrum is the closure of the set of lengths of periodic geodesics. The number 2π represents the length of the (generalized) geodesic that follows the circumference of the circle. The number 8 is the geodesic that follows a diameter of the ...

We consider one dimensional p-Laplacian eigenvalue problems of the form −∆pu = (λ− q)|u|p−1sgnu, on (0, b), together with periodic or separated boundary conditions, where p > 1, ∆p is the p-Laplacian, q ∈ C1[0, b], and b > 0, λ ∈ R. It will be shown that when p 6= 2, the structure of the spectrum in the general periodic case (that is, with q 6= 0 and periodic boundary conditions), can be comple...

Stopping games (without simultaneous stopping) are sequential games in which at every stage one of the players is chosen, who decides whether to continue the interaction or stop it, whereby a terminal payoff vector is obtained. Periodic stopping games are stopping games in which both of the processes that define it, the payoff process as well as the process by which players are chosen, are peri...

A fricative [s] and an affricate [ts] pronounced by both native Japanese and Korean speakers were analyzed to clarify the effect of the mother language on speech production. It was revealed that Japanese speakers have a clear individual production boundary between [s] and [ts], and that this boundary corresponds to the production boundary of all Japanese speakers. In contrast, although Korean s...

Numerical Investigations on the Thermohydraulic Performance of CrossWavy Channels with Multi-Periodic Boundary Conditions L. X. Du a , T. Ma a , M. Zeng a , Z. X. Guo b & Q. W. Wang a a Key Laboratory of Thermo-Fluid Science and Engineering, MOE, School of Energy and Power Engineering , Xi'an Jiaotong University , Xi'an , Shaanxi , P. R. China b Department of Mechanical and Aerospace Engineerin...