Sharp global well-posedness for KdV and modified KdV on

The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all -based Sobolev spaces where local well-posedness is presently known, apart from the endpoint for mKdV and the endpoint for KdV. The result for KdV relies on a new method for constructing almost conserved quantities using multilinear harmonic analysis and the available local-in-time theory. Miura's transformation is used to show that global well-posedness of modified KdV is implied by global well-posedness of the standard KdV equation.

     

Besov-Morrey spaces: Function space theory and applications to non-linear PDE

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.

     

关于一个素数和一个素数的k次方和问题

设k≥2,且Hk表示一个正整数n的集合,使得该集合中的元素满足a+bk≡n(modq)对任意的q,在模q的既约剩余系中有解,令Dk(N)表示所有的n≤N,且n∈Hk且不能表成p1+p2k=n形式的整数.那么在GRH下, Dk(N)相似文献   

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

关于Logistic模型的倍周期收敛现象

运用实验和归纳的方法 ,讨论了如何利用 Mathematic数学软件观察 Logistic模型的倍周期收敛现象以及对初值的依赖性 ,并从理论上解释了倍周期收敛现象     

Stability of a class of transformations of distribution-valued processes and stochastic evolution equations

Stability of a class of linear transformations of distribution-valued stochastic processes is studied. Two types of applications to convergence of solutions of stochastic evolution equations are given. One of them, for the case of continuous limits, simplifies the tightness problem considerably due to a recent result of Aldous.Centro de Investigación y de Estudios Avanzados.     

乙酰胆碱酯酶电极反应机理

在研究酶电极基础上探讨了电极上的反应机理。以乙酰胆碱酯酶催化活性为基础的抑制型酶电极的电极反应是:1)催化底物水解;2)底物中的I-被氧化为I2;3)底物氯化硫代乙酰胆碱分解产生的硫代胆碱含有的-SH基在银基汞膜电极上与汞生成硫醇汞盐。硫代胆碱在玻碳电极表面的氧化,为具有吸附性的不可逆过程,电极反应的电子转移数n=2,反应速率常数k=0.29s-1。     

Adsorbate motions induced by vibrational mode coupling

Adsorbate motions are discussed with a primary attention focused on the coupling between a vibrational mode excited by ultrafast laser heated hot-electrons or by inelastic tunneling electrons with scanning tunneling microscope and the reaction coordinate (RC) mode. Recent experimental results have demonstrated an efficient reaction pathways involving an indirect excitation of a frustrated translational mode, rather than its direct excitation for adsorbate hopping on surfaces. Elementary processes are briefly described for hopping of CO molecules on a laser heated stepped Pt surface, where excitation of the frustrated rotation mode has been found to plays an indispensable. Calculation of the inelastic tunneling current (ITC) for excitation of the C-O stretch mode of a CO molecule is combined with a theory of anharmonic mode coupling to activate the frustrated translation mode above the barrier. The hopping rate as a function of the bias voltage agrees with the experimental result. An unified theory of single-, and two-electron processes for ITC-induced motions induced by an indirect excitation of the RC-mode via mode coupling is also applied to reproduce a crossover from hopping to desorption of a single NH₃ molecule on Cu(1 0 0) with an increase in the tunneling current.     

Transmutation of 129I, 237Np, 238Pu, 239Pu, and 241Am using neutrons produced in target-blanket system ‘Energy plus Transmutation’ by relativistic protons

Target-blanket facility ‘Energy + Transmutation’ was irradiated by proton beam extracted from the Nuclotron Accelerator in Laboratory of High Energies of Joint Institute for Nuclear Research in Dubna, Russia. Neutrons generated by the spallation reactions of 0.7, 1.0, 1.5 and 2 GeV protons and lead target interact with subcritical uranium blanket. In the neutron field outside the blanket, radioactive iodine, neptunium, plutonium and americium samples were irradiated and transmutation reaction yields (residual nuclei production yields) have been determined using γ-spectroscopy. Neutron field's energy distribution has also been studied using a set of threshold detectors. Results of transmutation studies of ¹²⁹I, ²³⁷Np, ²³⁸Pu, ²³⁹Pu and ²⁴¹Am are presented.