Some Special Pairs of Σ2 e-Degrees

It is shown that there are incomparable Σ₂ e-degrees a, b such that every e-degree strictly less than a is also less than b .     

图灵机设计问题解法的优化

图灵机设计问题的常规解法一般有多个状态和较复杂的δ映像函数．给出了三种优化的解题方法，与常规方法相比用较少的状态数优化了图灵机的设计，达到减少状态的冗余和简化δ映像函数的目的．     

The low<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> and low<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> r. e. degrees are not elementarily equivalent

Jockusch, Li and Yang showed that the Lown and Low1 r.e. degrees are not elementarily equivalent for n > 1. We answer a question they raise by using the results of Nies, Shore and Slaman to show that the Lown and Lowm r.e. degrees are not elementarily equivalent for n > m > 1.     

Selkov模型不同扩散和流速下非Turing不稳定化学反应机制

建立了Selkov模型中间反应物具有不同扩散和不同流速条件下的反应-扩散-流动方程,理论分析了非Turing不稳定形成的条件,求得其参数区间,对Andresen的结论作了拓展.研究还发现,在振荡Hopf区域之外,静止波动(空间周期结构FDS)仍然可以存在.因而,此结构存在的参数空间大于Andresen的结果.同时,还将此种不稳定参数区间与Turing不稳定和差速流动引起不稳定(DIFI)的结果进行了比较,结果发现静态FDS值总是处于DIFI临界曲线相应的最小值之上,这表明动力学机制是由DIFI不稳定造成的,DIFI不稳定区是产生静止波FDS不稳定结构的必要条件.     

Wave features of a hyperbolic reaction–diffusion model for Chemotaxis

The Extended Thermodynamic theory is used to derive a hyperbolic reaction–diffusion model for Chemotaxis. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and nonuniform perturbations. A particular emphasis is given to the occurrence of the Turing bifurcation. The existence of traveling wave solutions connecting the two steady states is investigated and the governing equations are numerically integrated to validate the analytical results. The propagation of plane harmonic waves is analyzed and the stability regions in terms of the model parameters are shown. The frequency dependence of the phase velocity and of the attenuation is also illustrated. Finally, in order to have a measure of the non linear stability, the propagation of acceleration waves is studied, the wave amplitude is derived and the critical time is evaluated.     

Hopf Bifurcation Analysis of a Host-generalist Parasitoid Model with Diffusion Term and Time Delay

In this paper, we studied a delayed host-generalist parasitoid model with Holling II functional response and diffusion term. The Turing instability and local stability are studied. The existence of Hopf bifurcation is investigated, and some explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of center manifold and normal form method. Some numerical simulations are carried out.     

Turing Patterns in a Reaction-Diffusion System

We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.     

Embedding of Countable Orders in Turing Degrees

In their classical papers, Lerman, Lachlan, and Lebeuf developed the embedding method, which provides constructions of initial segments of Turing degrees isomorphic to various partially ordered structures. We analyze this method and prove that there is a nonzero degree below each decreasing chain of degrees uniform in O'. This imposes restrictions on the application of the embedding method.     

实函数的归约性

本文才巴 Ker-IKO 文中实数归约性推广到实函数,讨论了推广后各种归约之间的关系。证明了两种递归实函数定义的等价性。引入了算子图灵机的概念,利用算子图灵机给出了 C[1,0]上的一个分层(不可解度的分层)。证明了该分层有一个子结构与(?)同构。     

Present random computations in a uniform way

Some equivalent definitions for PP are introduced, which allows us to present the randomized complexity classses RP, NP, PP, BPP in a uniform format.