Law of large numbers and central limit theorem for randomly forced PDE's

We consider a class of dissipative PDE's perturbed by an external random force. Under the condition that the distribution of perturbation is sufficiently non-degenerate, a strong law of large numbers (SLLN) and a central limit theorem (CLT) for solutions are established and the corresponding rates of convergence are estimated. It is also shown that the estimates obtained are close to being optimal. The proofs are based on the property of exponential mixing for the problem in question and some abstract SLLN and CLT for mixing-type Markov processes.     

Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders.     

40,48Ca+90,96Zr融合反应的动力学模型研究

应用改进的量子分子动力学模型,在严格挑选初始核考虑弹靶结构效应的基础上,研究了近垒和垒上融合反应^40,48Ca+^90,96Zr. 研究表明: 4个反应的理论计算截面与实验值很好符合; 丰中子反应⁴⁰Ca+⁹⁶Zr的垒下融合截面比其他3个反应有明显增强的现象.为了理解丰中子反应⁴⁰Ca+⁹⁶Zr与⁴⁰Ca+⁹⁰Zr相比垒下融合截面增强,而Ca+⁹⁶Zr垒下融合截面没有明显增强的原因, 进一步分析了484个反应的融合位垒,中子转移与融合位垒的关系、中子转移与Q值的关系,结果表明: 正反应Q值会引起核子(特别是中子)转移的增强,从而导致动力学融合位垒的下降和垒下融合截面增强.     

激光二极管泵浦的高重复频率Nd：YAG激光器

报道两个１．５Ｗ连续激光二极管端面泵浦的声光调ＱＮｄ：ＹＡＧ激光器，输出激光脉冲的最高重复频率为３０ｋＨｚ重复频率１ｋＨｚ时，最窄脉宽为１２ｎｓ，最高峰值功率为１２．１ｋＷ。     

Valence band and chemical interactions of Zn/CdSnAs2 interfaces

X-ray photoelectron spectroscopy (XPS) together with argon ion sputtering was used to investigate the interface of the Zn/CdSnAs₂ system at various temperatures. The formation of an intermediate compound between Zn and As is proposed. The surface enrichment of Cd and Sn at 200 and 400°C is explained in terms of bond breaking and lattice strain theories.NCL Communication No. 4352     

Query complexity,or why is it difficult to separateNP A ∩coNP A fromP A by random oraclesA?

By thequery-time complexity of a relativized algorithm we mean the total length of oracle queries made; thequery-space complexity is the maximum length of the queries made. With respect to these cost measures one can define polynomially time- or space-bounded deterministic, nondeterministic, alternating, etc. Turing machines and the corresponding complexity classes. It turns out that all known relativized separation results operate essentially with this cost measure. Therefore, if certain classes do not separate in the query complexity model, this can be taken as an indication that their relativized separation in the classical cost model will require entirely new principles.A notable unresolved question in relativized complexity theory is the separation of NP^A co NP^A fromP ^A under random oraclesA. We conjecture that the analogues of these classes actually coincide in the query complexity model, thus indicating an answer to the question in the title. As a first step in the direction of establishing the conjecture, we prove the following result, where polynomial bounds refer to query complexity.If two polynomially query-time-bounded nondeterministic oracle Turing machines accept precisely complementary (oracle dependent) languages L^A and {0, 1}^*L^A under every oracle A then there exists a deterministic polynomially query-time-bounded oracle Turing machine that accept L^A. The proof involves a sort of greedy strategy to selecting deterministically, from the large set of prospective queries of the two nondeterministic machines, a small subset that suffices to perform an accepting computation in one of the nondeterministic machines. We describe additional algorithmic strategies that may resolve the same problem when the condition holds for a (1–) fraction of the oracles A, a step that would bring us to a non-uniform version of the conjecture. Thereby we reduce the question to a combinatorial problem on certain pairs of sets of partial functions on finite sets.     

Symmetries and conservation laws of Kadomtsev-Pogutse equations

Kadomtsev-Pogutse equations are of great interest from the viewpoint of the theory of symmetries and conservation laws and, in particular, enable us to demonstrate their potentials in action. This paper presents, firstly, the results of computations of symmetries and conservation laws for these equations and the methods of obtaining these results. Apparently, all the local symmetries and conservation laws admitted by the considered equations are exhausted by those enumerated in this paper. Secondly, we point out some reductions of Kadomtsev-Pogutse equations to more simpler forms which have less independent variables and which, in some cases, allow us to construct exact solutions. Finally, the technique of solution deformation by symmetries and their physical interpretation are demonstrated.     

Solutions rationnelles de certaines équations fonctionnelles

Dans cet article, nous démontrons essentiellement les deux résultats suivants, qui montrent que les solutions séries formelles à coefficients dans de certaines équations fonctionnelles sont rationnelles. Soient tout d'abords un entier naturel non nul, eta _i ,b _i ,(i = 1, , s), 2s nombres complexes, lesa _i étant non nuls. On définit l'ensembleA comme étant l'intersection des parties de , contenant l'origine et stables par toutes les applicationsg _i (x) = a _i x + b _i . On a alors le résultat suivant: Théorème 1.Soient f, R ₁, ,R _s s + 1 fractions rationnelles de (x), régulières à l'origine, et a_i, b_i (i = 1,, s), 2s éléments de . On suppose que les a_i sont non nuls et de module strictement inférieur à un pour tout i = 1,, s. Soit y(x) un élément de [[x]], vérifiant l'équation fonctionnelle

The many limits of mixed means

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a ₀,b ₀ we define

中国的百岁老人研究Ⅲ.百岁老人聚居区——中国长寿之乡的成因和评定

探讨了中国长寿之乡的成因,提出了评定中国长寿之乡的四项指标和六项衡量标准。主张中国长寿之乡应由有资质的学术团体经过认真调查和核实后认定,被命名的长寿之乡应是相当于县(市)或大城市区一级以上的地域,总人口应在10万人以上;该地区每百万人口中应有70位以上百岁老人;并应有反映后备力量和发展速度的指标。