Multi-Model Communication and Data Assimilation for Mitigating Model Error and Improving Forecasts

Models for weather and climate prediction are complex, and each model typi-cally has at least a small number of phenomena that are poorly represented, such as perhaps the Madden-Julian Oscillation (MJO for short) or El Ni\~{n}o-Southern Oscillation (ENSO for short) or sea ice. Furthermore, it is often a very challenging task to modify and improve a complex model without creating new deficiencies. On the other hand, it is sometimes possible to design a low-dimensional model for a particular phenomenon, such as the MJO or ENSO, with significant skill, although the model may not represent the dynamics of the full weather-climate system. Here a strategy is proposed to mitigate these model errors by taking advantage of each model''s strengths. The strategy involves inter-model data assimilation, during a forecast simulation, whereby models can exchange information in order to obtain more faithful representations of the full weather-climate system. As an initial investigation, the method is examined here using a simplified scenario of linear models, involving a system of stochastic partial differential equations (SPDEs for short) as an imperfect tropical climate model and stochastic differential equations (SDEs for short) as a low-dimensional model for the MJO. It is shown that the MJO prediction skill of the imperfect climate model can be enhanced to equal the predictive skill of the low-dimensional model. Such an approach could provide a route to improving global model forecasts in a minimally invasive way, with modifications to the prediction system but without modifying the complex global physical model itself.     

On Representations Associated with Completely n-Positive Linear Maps on Pro-C^＊-Algebras

It is shown that an n × n matrix of continuous linear maps from a pro-C^＊-algebra A to L（H）, which verifies the condition of complete positivity, is of the form [V^＊TijФ（·）V]^n i,where Ф is a representation of A on a Hilbert space K, V is a bounded linear operator from H to K, and j=1,[Tij]^n i,j=1 is a positive element in the C^＊-algebra of all n×n matrices over the commutant of Ф（A） in L（K）. This generalizes a result of C. Y.Suen in Proc. Amer. Math. Soc., 112（3）, 1991, 709-712. Also, a covariant version of this construction is given.     

一类替换环的偏序$K_{0}$-群的无扭性

A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0（R）^＋, i.e., [eR]∧[fR] = 0. In this paper, we shall prove that the K0-group of every orthogonal, IBN2 exchange ring is always torsion-free, which generalizes the main result in [3].     

$W_m$与$P_n$ 的笛卡儿积图的交叉数

Most results on crossing numbers of graphs focus on some special graphs, such as the Cartesian products of small graphs with path, star and cycle. In this paper, we obtain the crossing number formula of Cartesian products of wheel Wm with path Pn, for arbitrary m ≥ 3 and n≥ 1.     

Block Transformation of Hybrid Cellular Automata

By introducing a sequence-block transformation and vector-block transformation, we explore the dynamical properties of hybrid cellular automation (HCA) and hybrid cellular automation with memory (HCAM) in the framework of symbolic dynamics. As the local evolution rules of HCA and HCAM are not-uniform, the new uniform cellular automata (CAs) with multiple states are constructed by specifical the block transformations. Furthermore, because the new CA rules are topologically conjugate with the originals, the complex dynamics of the HCA and HCAM rules can be investigated via the new CA rules.     

Existence of $\mu$-pseudo almost automorphic solutions to abstract partial neutral functional differential equations with infinite delay

In this article, we introduce and investigate the concept of $\mu$-Stepanov-like pseudo almost automorphic functions of class $h$ and class infinity via measure theory. We present new results on completeness and composition theorems for the space of such functions. To illustrate our main results, we provide some applications to an abstract partial neutral functional differential equation with infinite delay.     

Exact Boundary Controllability for the Spatial Vibration of String with Dynamical Boundary Conditions

This paper deals with the spatial vibration of an elastic string with masses at the endpoints. The authors derive the corresponding quasilinear wave equation with dynamical boundary conditions, and prove the exact boundary controllability of this system by means of a constructive method with modular structure.     

新型大溶性大π共轭高分子—聚吡咯—{2,5—[双（对二甲氨基苯甲烯）]}？…

该研究合成了一种新型水溶性大π共轭高分子－聚吡咯－｛２,５－〔二（对二甲氨基苯甲烯）〕｝（ＰＰＤＭＡＢ）,它地强酸的水溶液,在１ｍｏｌ／Ｌ的盐酸中溶解度为０．５～１．０g／１００mＬ,通过ＥＡ、ＸＰＳ、ＦＴ－ＩＲ、ＵＶ－Ｖｉｓ－ＮＩＲ、Ｉｎ－ｓｉｔｕＵＶ－Ｖｉｓ－ＮＩＲ对ＰＰＤＭＡＢ进行了结构表征。通过质子化、碘掺杂、浓硫酸（９８％）掺杂等处理,ＰＰＤＭＡＢ的电导率提高２～４个数量组（＆＝１－＾－７     

HgBa2CuO4+δ中载流子分布的研究

我们根据一种结构分块模型,计算了与超导转变温度Tc密切相关的块之间相互作用能,讨论了HgBa2CuO4 δ中载流子分布对相互作用能的影响.通过计算不同氧缺陷下,空穴在不同平面以及空穴在Cu-O平面不同位置上对相互作用能的影响,研究了它们与超导电性的关联.计算表明,空穴在Cu-O面上的位置不仅明显地影响到相互作用能的大小,而且影响相互作用能随氧含量的变化趋势,该结果为我们了解载流子在Cu-O面上分布是否均匀提供了一定的线索.结果还表明,HgBa2CuO4 δ中的载流子主要分布在Cu-O平面上.