Global well‐posedness of the compressible Euler with damping in Besov spaces

In this paper, we consider the Cauchy problems for compressible Euler equations with damping. In terms of the Littlewood–Paley decomposition and Bony's para‐product formula, we prove the global existence, uniqueness and asymptotic behavior of the solution in the critical Besov space comparing with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

1.3 GHz超导腔磁通排出效应研究

设计并搭建了一套高精度的磁场测量和补偿系统,并结合中国科学院高能物理研究所（IHEP）的2K超导腔垂直测试平台对1.3 GHz 单加速间隙超导腔的磁通排出效应开展了实验研究：利用研制的磁场测量和补偿系统能够精密地测量超导腔赤道位置磁场,并能够将磁场补偿至小于5.0×10⁻⁸ T;并对超导腔不同表面温度梯度下的磁通排出效应进行了测量分析;对钉扎了磁场的超导腔进行了射频性能测试,研究了超导腔电阻对磁通钉扎的敏感度,以及在不同电场梯度下超导腔的表面电阻变化情况。结果表明,研制的高精度磁场测量和补偿系统能够满足超导腔磁通排出研究的需求;高的超导腔表面温度梯度有利于磁通的排出;磁通钉扎电阻的敏感度随着加速电场梯度的增加而增大,导致超导腔的性能下降。此实验研究也为后续超导腔的研制奠定了一定基础。     

Gaussian estimates and regularized groups

We show that if a bounded analytic semigroup on satisfies a Gaussian estimate of order and is the generator of its consistent semigroup on , then generates a -regularized group on where . We obtain the estimate of () and the -independence of , and give applications to Schrödinger operators and elliptic operators of higher order.

     

A splitting preconditioner for saddle point problems

For large sparse systems of linear equations iterative techniques are attractive. In this paper, we study a splitting method for an important class of symmetric and indefinite system. Theoretical analyses show that this method converges to the unique solution of the system of linear equations for all t>0 (t is the parameter). Moreover, all the eigenvalues of the iteration matrix are real and nonnegative and the spectral radius of the iteration matrix is decreasing with respect to the parameter t. Besides, a preconditioning strategy based on the splitting of the symmetric and indefinite coefficient matrices is proposed. The eigensolution of the preconditioned matrix is described and an upper bound of the degree of the minimal polynomials for the preconditioned matrix is obtained. Numerical experiments of a model Stokes problem and a least‐squares problem with linear constraints presented to illustrate the effectiveness of the method. Copyright © 2011 John Wiley & Sons, Ltd.     

A Cross‐Cultural Lesson Comparison on Teaching the Connection Between Multiplication and Division

This study compared one lesson across four U.S. “traditional” textbook series, two U.S. reform‐based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of the lesson across three dimensions (i.e., problem schemata, response requirement, and algebra readiness). In particular, the Chinese lesson's penetrating analysis or explanation of the topic is reflected in its deliberately constructed examples and wide range of problems (pertaining to problem types and difficulty levels) present in the teaching and practice sections of the lesson. None of analyzed U.S. lessons are comparable with the Chinese lesson with respect to the breadth and depth in teaching the topic. A deliberate emphasis, both arithmetically and algebraically, on problem schema acquisition as found in the Chinese lesson represents a promotion of symbolic or higher order of conceptual understanding. The findings are discussed within the context of teaching big ideas through problem schemata acquisition and the importance of symbolic level of conceptual understanding.     

Similarity analysis of DNA sequences based on the EMD method

DNA sequences can be translated into 2D graphs and into numerical sequences; we call the numerical sequences nonlinear signal sequences. We can use the empirical mode decomposition (EMD) method to divide nonlinear signal sequences into a group of well-behaved intrinsic mode functions (IMFs) and a residue, so that we can compare the similarities among DNA sequences conveniently and intuitively. This work tests the method’s suitability by using the mitochondria of four different species.     

MOCVD技术制备的ZnS:Mn电致发光薄膜结晶性及Mn2+分布

本文报导了用MOCVD技术制备的ZnS:Mn电致发光薄膜为立方晶相,结晶取向性好,颗粒大。从高倍率的扫描电镜拍摄的照片观察到薄膜的表面平滑。SIMS测量表明Mn2+在ZnS薄膜纵向分布均匀,但在两侧有起伏,可能的原因是在生长的初终阶段流量的突变使化合物的化学计量比偏离而产生位错,引起原子的局部堆积,并且由于初终阶段ZnS:Mn生长的衬底不同使原子堆积层厚度不同。     

强激光在高Z等离子体中吸收的波长关系

利用“神光Ⅰ”输出的～５００Ｊ、１．０５μｍ，～２００Ｊ、０．５３μｍ激光和“星光Ⅱ”输出的～７０Ｊ、０．３５１μｍ激光，实验研究了激光与金圆盘靶作用产生的等离子体对激光的吸收，获得了激光１０°、４５°入射Ａｕ盘靶吸收的波长关系。实验结果与一维平面等离子体吸收模型计算的结果基本相符。     

金箔靶背侧X光辐射的实验研究

利用星光Ⅱ激光装置钕玻璃三倍频激光辐照金箔靶，实验研究了金箔靶背侧发射的Ｘ光能谱，时间过程和秀过激光能量。结果表明：金箔背侧发的Ｘ光可以作为一种较干净的强Ｘ光射源。     

Viscosity analysis on the Boltzmann equation

This paper is devoted to investigating the asymptotic properties of the renormalized solution to the viscosity equation tfε + v ·▽xfε = Q (fε,fε ) + εΔvfε as ε→ 0+ . We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation in L1 ((0 , T ) × RN × RN ). The proof is based on compactness analysis and velocity averaging theory.