Normal families and exceptional functions

In this paper, we obtain some normality criteria for families of meromorphic functions that concern the exceptional functions of derivatives.     

An algorithm for decomposing a polynomial system into normal ascending sets

We present an algorithm to decompose a polynomial system into a finite set of normal ascending sets such that the set of the zeros of the polynomial system is the union of the sets of the regular zeros of the normal ascending sets.If the polynomial system is zero dimensional,the set of the zeros of the polynomials is the union of the sets of the zeros of the normal ascending sets.     

In situ observation of NaBi(WO4)2 dendrite growth and the study on microstructure of solidification

The dendrite growth process of transparent NaBi(WO₄)₂ with small prandtl and high melting point was studied by using the in-situ observation system. According to the dynamic images and detailed information, there are two kinds of restriction effect on the dendrite growth, the competition between arms and branches and the convection in the melt. The dendrite growth rate was time dependent, and the rate of arm growth reached the maximum 5.8 mm/s in the diffusive-advective region and rapidly decreased in the diffusive-convective region. The growth rate of branch had the same change trends as the arm’s. Based on the EPMA-EDS data of solidification structure of quenched NaBi(WO₄)₂ melt, it was found that there were component differences from stoichiometric concentration in the melt near the interface during the growth process. Supported by the National Natural Science Foundation of China (Grant No. 50331040) and the Innovation Funds from Shanghai Institute of Ceramics, Chinese Academy of Sciences (Grant No. SCX0623)     

Photoluminescence properties of the composite of porous alumina and poly (2,5-dibutoxy-1,4 phenylenevinylene)

The spin coating method was used to assemble polymer (Poly (2,5-dibutoxy-1,4-phenylenevinylene)) (DBO-PPV) into the pores of porous alumina which was prepared by anodization. Four peaks in the photoluminescence (PL) spectra of the composite, with contributions from the DBO-PPV and porous alumina, were found. It was also found that the light emitting from the porous alumina could excite the photoluminescence of DBO-PPV. The nanometer effect of the porous alumina can lead to a blue shift of 90 nm of the PL peaks of DBO-PPV.     

Erratum: Yan Guo. Boltzmann diffusive limit beyond the Navier‐Stokes approximation,Communications on Pure and Applied Mathematics (2006) 59(5) 626‐687

The original article to which this erratum refers was published in Communications on Pure and Applied Mathematics Comm Pure Appl Math(2006)59(5) 626 .     

Christoffel functions and mean convergence for Lagrange interpolation for exponential weights

For exponential weights, a necessary condition of weighted mean convergence for Lagrange interpolation is given.     

Examples of non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property

In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces.     

Markarian 8星系的包层辐射

使用美国甚大天线阵(VLA).对Markarian 8星系进行了多频观测.多频VLA观测表明,Markarian 8星系有三个主要的射电子成份,它们浸在一个弥漫的星系包层中.包层的射电谱是陡的非热谱.本文根据VLA观测确定了包层的物理参量,并讨论了包层中相对论性电子的可能起因.本文估计了包层非热辐射所要求的超新星爆发率.     

Integrability of det▽u and Evolutionary Wente''s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.     

Generation of red light at 660 nm by frequency doubling a Nd:YAG laser with periodically-poled stoichiometric LiTaO<Subscript>3</Subscript>

High power red light was generated from a periodically-poled stoichiometric LiTaO₃ (PPSLT) by single-pass frequency doubling of a diode-side-pumped, Q-switched Nd:YAG laser at 1319 nm. An average power of 2.4 W of the 660 nm red light was obtained at the fundamental power of ∼5.4 W with the conversion efficiency up to 44.4% and with low fluctuation down to 2%. The high efficiency and stability at the red output indicate that it is a practical method to construct a reliable compact red laser. PACS 42.70.Mp; 42.79.Nv; 42.55.Xi