Isochronous centers of Lienard type equations and applications

In this work we study Eq. (E) with a center at 0 and investigate conditions of its isochronicity. When f and g are analytic (not necessary odd) a necessary and sufficient condition for the isochronicity of 0 is given. This approach allows us to present an algorithm for obtained conditions for a point of (E) to be an isochronous center. In particular, we find again by another way the isochrones of the quadratic Loud systems (LD,F). We also classify a 5-parameters family of reversible cubic systems with isochronous centers.     

Corrections to scaling for period doubling

We have studied a multiple scaling which describes corrections to scaling. For the period doubling in one-dimensional dissipative maps, two-dimensional areapreserving maps, and four-dimensional symplectic maps, the multiple scaling is seen to be well-obeyed, and new scaling factors have been found. The multiple scaling is also seen to be a very powerful tool for searching for scaling behavior.     

Minimal periods of semilinear evolution equations with Lipschitz nonlinearity

It is known that any periodic orbit of a Lipschitz ordinary differential equation must have period at least 2π/L, where L is the Lipschitz constant of f. In this paper, we prove a similar result for the semilinear evolution equation du/dt=-Au+f(u): for each α with 0?α?1/2 there exists a constant K_α such that if L is the Lipschitz constant of f as a map from D(A^α) into H then any periodic orbit has period at least K_αL^-1/(1-α). As a concrete application we recover a result of Kukavica giving a lower bound on the period for the 2d Navier-Stokes equations with periodic boundary conditions.     

微扰模型分析长周期光纤光栅薄膜传感器

提出了一种新的基于三层阶跃折射率光纤的微扰模型,分析长周期光纤光栅（Long Period Fiber Grating,LPFG）薄膜传感器,并从β2稳定性定理出发推导出适用于薄膜传感器的微扰公式.该模型不仅能够清晰反映薄膜参量与包层模传播常量变化量之间的关系,而且在计算量和计算难度远低于四层波导模型情况下获得与严格求解结果相当的计算准确度.考虑数值计算本身引入的计算误差,该模型能够满足定性和半定量理论分析需要.最后通过长周期光纤光栅液态水膜的挥发实验对该模型进行了初步验证.     

周期映射单调性的新证法

研究方程d2xdt2 + g(x)= 0 周期解的周期映射,给出了当g(x)为二次多项式时其周期单调的新证法.     

More on the Difference Equation y n + 1 = ( p + y n −1 )/( qy n + y n −1 )

From previous studies of the equation in the title with positive parameters p and q and positive initial conditions we know that if q h 4 p + 1 then the equilibrium is a global attractor. We also know that if q > 4 p + 1 then every solution eventually enters and remains in the interval [ p / q , 1]. In this strip there exists a "unique" prime period two solution that is locally asymptotically stable. In this paper, we provide more insight as to the behavior of solutions of the equation in the title in the strip [ p / q , 1], where a one-dimensional stable manifold lives.     

Comments on the complete generalized fractional Fourier transform

In this research, we thoroughly investigate the complete generalized fractional Fourier transform (CGFRFT) and draw the following conclusions that are different from the original literature: (1) The CGFRFT is not a generalized version, but a special case that ignores the marginal postulate; (2) If the period parameter is not a multiple of four, the CGFRFT can never perform a Fourier transform regardless of the value of the transform order. The simulation results of a rectangular signal support the above conclusions.     

Period doubling cascade in diffusion flames

Here it is shown that chaotic oscillations can appear after a series of period doublings in radiating diffusion flames when the activation temperature is high enough. It is also shown that period doubling cascades appear typically in very small regions and that they may not be observable if one starts with small perturbations of a steady flame.     

Characteristics of terahertz slow-wave system with two-dimensional photonic band-gap structure

A terahertz slow-wave system model consists of a photonic crystal with two-dimensional band-gap structure and a slow-wave plate as its periodic unit. The electromagnetic field in the slow-wave system has been numerically simulated. The dispersion relation and the coupled impedance of the backward wave mode in the system have been calculated for a variety of geometric settings. The results indicate that this model would be a promising candidate for the slow-wave system with single stable backward wave mode.     

p -SOLVABILITY AND A GENERALIZATION OF PRIME GRAPHS OF FINITE GROUPS

Abstract

The real Torelli mapping, from the moduli space of real curves of genus g to the moduli space of g-dimensional real principally polarized abelian varieties, sends a real curve into its real Jacobian. The real Schottky problem is to describe its image. The results contained in the present paper concern hyperelliptic real curves and in particular real curves of genus 2. We exhibit also some counterexamples for the non-hyperelliptic case.