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...

We establish an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, which could be applied to a large class of Hamiltonian PDEs containing the derivative ∂x in the perturbation. Especially, in this range of application lie a class of derivative nonlinear Schrödinger equations with Dirichlet boundary conditions and perturbed Benjamin-Ono equation with peri...

I present a calculation of the interfacial width within the capillary wave (Gaussian) approximation. The calculation is done on rectangular lattices of size L1 times L2, with periodic boundary conditions.

The U.S. Department of Health and Human Services vision and strategic framework on multiple chronic conditions (MCCs) incorporates recommendations designed to facilitate research that will improve our knowledge about interventions and systems that will benefit individuals with MCCs (or multimorbidity). The evidence base supporting the management of patients with MCCs will be built through inter...

The evidence appears compelling that the microenvironment, and associated biological cellular and molecular factors, may contribute to the progression of a variety of tumors. The effects of the microenvironment may directly influence the plasticity of T cell lineages, which was recently discussed (O'Shea & Paul, 2010 [4]). To review the putative role of the microenvironment in modulating the co...

The nonlinear differential equation x" = f(t, x(t)), f being 22T-periodic in t, is considered for the existence of 27T-periodic solutions. The equation is reduced to an equivalent system of two Hammerstein equations. The case of nonlinear perturbation at resonance is also discussed.