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...

The one-dimensional Dunkl operator Dk with a non-negative parameter k, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of Dk, satisfying this condition is studied. An operational calculus of Mikusiński type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value ...

The modeling of finite-extent semiconductor nanostructures that are embedded in a host material requires a proper boundary treatment for a finite simulation domain. For the study of a self-assembled InAs dot embedded in GaAs, three kinds of boundary conditions are examined within the empirical tight-binding model: ~i! the periodic boundary condition, ~ii! raising the orbital energies of surface...

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the ...

Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for one-dimensional problems and block-Toeplitz–Toeplitzblock matrices for two-dimensional cases. They are computationally intensive to invert especially in the block case. If ...