一类六点八边图的图设计

设Kv是一个v个点的完全图，G为Kv的一个不含孤立点的简单子图．Kv的一个G-设计，常记为（v，G，I）-GD，是指一个二元组（X，B），其中x为Kv的顶点集，B是Kv的一些子图（亦称为区组）构成的集合，使得每一个区组与G同构，且Kv的任何一条边恰在B的一个区组中出现．文章讨论了一类六点八边图中尚未解决的3个图G（i=1，2，3）的图设计存在性问题，并证明了（v,Gi，1）-GD（i=1，2，3）存在的必要条件v=0，1（mod16）且v≥16也是充分的．从而给出了这类六点八边图图设计存在的完全解．     

Improvement of xylanase production by Aspergillus niger XY-1 using response surface methodology for optimizing the medium composition

Objective： To study the optimal medium composition for xylanase production by Aspergillus niger XY-1 in solid-state fermentation （SSF）. Methods： Statistical methodology including the Plackett-Burman design （PBD） and the central composite design （CCD） was employed to investigate the individual crucial component of the medium that significantly affected the enzyme yield. Results： Firstly, NaNO3, yeast extract, urea, Na2CO3, MgSO4, peptone and （NH4）2SO4 were screened as the significant factors positively affecting the xylanase production by PBD. Secondly, by valuating the nitrogen sources effect, urea was proved to be the most effective and economic nitrogen source for xylanase production and used for further optimization. Finally, the CCD and response surface methodology （RSM） were applied to determine the optimal concentration of each significant variable, which included urea, Na2CO3 and MgSO4. Subsequently a second-order polynomial was determined by multiple regression analysis. The optimum values of the critical components for maximum xylanase production were obtained as follows： x1 （urea）=0.163 （41.63 g/L）, x2 （Na2CO3）=-1.68 （2.64 g/L）, X3 （MgSO4）= 1.338 （10.68 g/L） and the predicted xylanase value was 14374.6 U/g dry substrate. Using the optimized condition, xylanase production by Aspergillus niger XY-1 after 48 h fermentation reached 14637 U/g dry substrate with wheat bran in the shake flask. Conclusion： By using PBD and CCD, we obtained the optimal composition for xylanase production by Aspergillus niger XY-1 in SSF, and the results of no additional expensive medium and shortened fermentation time for higher xylanase production show the potential for industrial utilization.     

{3,4*} -PBD的存在性

主要解决{3,4^＊}-PBD的存在性问题。当且仅当：（1）v≥4;（2）v=0,1（mod3）且v≠6,7,9时,即{3,4^＊}-PBD存在。     

单纯设计NB〔4，12；v〕的存在性

证明了单纯设计ＮＢ〔４，１２；ｖ〕存在的必要条件同时也是充分的．     

在三层有机薄膜电致发光器件中PBD的空穴限定作用研究

把ＰＢＤ层夹在空穴传输层（ＨＴＬ）和发光层（ＥＭＬ）中间，制备了三层有机薄膜电致发光器件，同时得到了ＨＴＬ和ＥＭＬ的发光，提出了ＰＢＤ的空穴限定作用，并通过与双层器件比较、用光致发光方法以及通过发光与驱动电压的关系得到了证实．     

PBD闭集H0,1(4)\{4}的有限生成集

给出PBD闭集H0,1(4)\{4}的有限生成集Q={5,8,9,12,13,16,17,20,24,28,29,32,33,44,52,68,84,92}.     

A NOTE ON IGDDS

In this note we prove the existance of (u,3,λ)IGD[v,n] and that of (w,4,λ)-IGD[v,n] where w≡1(mod 3),w≠10 or 19,and (v,n)≠(6,1),which generalizes the results of [2],[4] 3nd [5]。