世界各地数学奥林匹克试题摘编

１．ｐ，ｑ是正整数，ｆ是正实数集合到正实数集的一个映射，使得对于任意的正实数ｘ，ｙ，有ｆ（ｘｆ（ｙ））＝ｘｐｙｑ①求证：ｑ＝ｐ２．证取ｘ＝１ｙ，代入①得ｆ（ｙ）＝ｙｑｐ（ｆ（１））１ｐ②再取ｙ＝１，代入②得ｆ（１）＝１，由②得ｆ（ｙ）＝ｙｑｐ③∴ｆ（...     

脱乙酰壳多糖-羧甲基纤维素聚电解质复合物的合成和药物控制释放研究

本文研究合成条件对脱乙酰壳多糖－羧甲基纤维素聚电解质复合物的组成、结构及药物控制释放性能的影响。结果表明，反应介质的ｐＨ值对生成的脱乙酰壳多糖－羧甲基纤维素聚电解质复合物的组成和结构的影响最大，在ｐＨ值５．５合成的脱乙酰壳多糖－羧甲基纤维素聚电解质复合物具有较好的药物控释性能。     

结构描述符正交化及典型相关分析在饱和醇、醚质谱分类中的应用

结构描述符正交化及典型相关分析在饱和醇、醚质谱分类中的应用;饱和醇醚;模式识别;质谱分类变量;块变量;典型相关分析     

RELATIONSHIP BETWEEN THE CHANGES OF THE FAST PHASE OF MILLISECOND DELAYED LIGHT EMISSION AND THE PROTON RELEASED BY THE OXIDATION OF WATER

The phosphorylation uncouplers suppressing the proton gradient across the thylakoidmembrane can also affect the fast phase of millisecond delayed light emission (ms-DLE) atflash light intensity strong enough to saturate the Hill reaction. At the concentration ofsame uncoupling degree, nigericin decreases the fast phase DLE much more than NH_4Cl.Omitting the terminal acceptor in the reaction mixture or adding DBMIB to inhibit PQ oxi-dation diminishes the slow phase DLE and affects the fast phase slightly, while DCMU orHOQNO which inhibits electron transport between PSII and PQ, diminishes both phases ofms-DLE. These results indicate that the proton gradient responsible for the enhancement ofthe fast phase DLE is more intimately linked to the thylakoid membrane, and is mainlyrelated to the proton release from water oxidation and not to the turnover of plastoquinone.     

转基因水稻表达的Bt毒蛋白Cry I Ab溶液构象的研究

用荧光光谱法研究了毒蛋白Cry I Ab在溶液中的构象。结果表明，pH值增大时，毒蛋白的荧光强度也增大，至pH=11时荧光强度已达最大值；甲醇、乙醇及异丙醇等有机溶剂引起毒蛋白荧光发射波长蓝移和荧光强度增大，至有机溶剂的浓度超过某一阈值后荧光发射波长不再蓝移；丙酮能完全猝灭毒蛋白Cry I Ab的荧光，丙烯酰胺能猝灭Cry I Ab86%的荧光，而KI对毒蛋白的荧光无猝灭作用，由此推断Cry I Ab的大部分色氨酸残基位于分子表面富含负电荷的区域中。     

配合物[MnL(2,2''''-bipy)(H2O)]·2H2O的合成及其晶体结构

N-苯基亚氨基二乙酸(H2L),Mn(Ⅱ)和2,2'-联吡啶(2,2'-bipy)在50%甲醇中组装得标题配合物[MnL(2,2'-bipy)(H2O)]·2H2O(1),其结构经IR,元素分析和X-射线单晶衍射表征.1属单斜晶系,空间群P2(1)/n,晶胞参数:a=0.885 9(3)nm,b=1.826 9(6)nm,c=1.385 7(5)nm,β=106.200(6)°,V=2.153 6(13)nm3,Z=4,F(000)=980,Dc=1.457 Mg·m-3.在1的晶体结构中,Mn(Ⅱ)为六配位的畸变八面体构型,其中2,2'-bipy的2个氮原子和羧基的2个氧原子位于赤道平面,L的氮原子和一个配位水分子处于轴向位置.1分子之间存在的氢键与π-π芳香堆积作用将其连接成三维超分子结构.     

A CLUSTER COMPOUND WITH DI-ENDOXYGEN LIGANDS——THE CRYSTAL AND MOLECULAR STRUCTURE OF [Fe(MOS_4O)_2][N(C_2H_5)_4]3

[Fe(MoS_4O)_2] [N(C_2H_3)_4]_3 cluster compound with di-end-oxygen ligands has been prepared and characterized by the X-ray diffraction method. The compound crystallizes in a monoclinic space group P2_1/n with lattice parameters a=13.019(4), b=16.959(5), c=18.234(5), β=97.34(2)(°), Z=4. The final agreement factors are R=0.0740, Rw=0.0598. The terminal bond length, Mo-S_t and bridged one, MO-S_b for the compound are much longer than the counterpart without end-oxygen ligand. It possibly suggests that low valence of molybdenum and smaller electronegativity of sulphur than oxygen lead to the charge transfer as S→Mo→O.     

多目标逐步回归设计在反相色谱三元流动相组分最佳化中的应用

 〕本文首次将多目标优化与逐步回归设计相结合对反相色谱三元流动相的最佳组分进行了选择，并以去痛片组分与内标物的分离为例对方法和编制的程序进行考核。实验证明本方法简易、可靠。     

含氢甲基硅油含氢量的质谱法测定

含氢甲基硅油是高分子量的多聚物，用质谱方法对其Ｓｉ－Ｈ键上的氢含量的测定，仅用测定其分子量的办法不易实现。实验中发现，用其两个碎片离子ＳｉＯ９ＣＨ３）２和ＳｉＯ－ＨＣＨ＾＋３作为代表性离子，以它们的丰度比定出甲基含氢硅油的含氢量「Ｈ」。结果与用化学方法所测值十分接近。     

具有咖啡酰基和没食子酰基的β-二酮酸及喹噁啉酮类HIV整合酶抑制剂的设计合成及其对Cu2+的选择性识别

An efficient procedure for the synthesis of caffeoyl-and galloyl-containing β-diketoacid derivatives linked byarylamide was reported by,in the key step,dissolving the corresponding phenyl methyl ketone in THF/DME in thepresence of NaOMe as base and dimethyl oxalate as oxalylation reagent,and then separating the sodium ketoe-nolate ester.The resulting β-diketoacids underwent further condensation reaction with o-phenylenediamine to gen-erate quinoxalone derivatives in good yield,rather than 2-benzimidazol.The preliminary ion binding properties ofquinoxalone derivatives were also investigated.UV-Vis spectra showed that these compounds could selectively rec-ognize Cu~(2 )ion in ethanol and form a 1∶2 complex.