Fractal drums and then-dimensional modified Weyl-Berry conjecture

In this paper, we study the spectrum of the Dirichlet Laplacian in a bounded (or, more generally, of finite volume) open set R ⁿ (n1) with fractal boundary of interior Minkowski dimension (n–1,n]. By means of the technique of tessellation of domains, we give the exact second term of the asymptotic expansion of the counting functionN() (i.e. the number of positive eigenvalues less than ) as +, which is of the form ^/2 times a negative, bounded and left-continuous function of . This explains the reason why the modified Weyl-Berry conjecture does not hold generally forn2. In addition, we also obtain explicit upper and lower bounds on the second term ofN().     

ULTRASONICALLY DISPERSED POTASSIUM AS DEPROTONATING AND COUPLING AGENT──SYNTHESIS OF 1，6－DINITRILES IN SITU

ＵＬＴＲＡＳＯＮＩＣＡＬＬＹ　ＤＩＳＰＥＲＳＥＤ　ＰＯＴＡＳＳＩＵＭ　ＡＳ　ＤＥＰＲＯＴＯＮＡＴＩＮＧ　ＡＮＤ　ＣＯＵＰＬＩＮＧ　ＡＧＥＮＴ──ＳＹＮＴＨＥＳＩＳ　ＯＦ　１，６－ＤＩＮＩＴＲＩＬＥＳ　ＩＮ　ＳＩＴＵＵＬＴＲＡＳＯＮＩＣＡＬＬＹＤＩＳＰ...     

Re(CO)5Br-catalyzed addition of carboxylic acids to terminal alkynes: a high anti-Markovnikov and recoverable homogeneous catalyst

The addition of carboxylic acids to terminal alkynes is efficiently catalyzed by the early transition-metal complex Re(CO)5Br in toluene or n-heptane at 110 degrees C in an air atmosphere, affording the anti-Markovnikov adducts in good yields with high selectivity. In most cases, the reactions afford unusual Z-adduct predominantly. When n-heptane was used as solvent, Re(CO)5Br can be partly recovered from the reaction mixture.     

Syntheses and structures of magnesium pyridine thiolates--model compounds for magnesium binding in photosystem I

Novel magnesium pyridine-2-thiolates were prepared by using alkane elimination chemistry. The resulting complexes display a metal coordination environment composed of sulfur/nitrogen bonding from the intramolecularly stabilized mercaptopyridine ligand, in addition to coordination by the oxygen centers from two THF donors. The compounds are well-suited model compounds for the magnesium centers in Photosystem I, in which magnesium, situated in the central chlorophyll ligand, is bound to sulfur from a nearby methionine residue. All compounds were characterized by (1)H, (13)C NMR, and IR spectroscopy, in addition to Xray crystallography.     

Phase Selectively Soluble Dendritic Derivative of 4-(Dimethylamino)- pyridine: An Easily Recyclable Catalyst for Baylis-Hillman Reactions

Among the reactions in which C-C bonds are formed, the Baylis-Hillman coupling of aldehydes with α, β-unsaturated carbonylic compounds is currently attracting much interest due to the atom economy, the mild conditions and the generation of functional groups1,2. Furthermore, compared to the Heck, Suzuki and other palladium catalyzed C-C bond forming reaction3, the Baylis-Hillman reaction can be promoted by using organic bases in the complete absence of any metal4. However, almost all the …     

超声波作用下的糖精相转移催化N—苄基化反应的研究

超声波作用下的糖精相转移催化Ｎ－苄基化反应的研究嵇学林刘华黄昆（江苏镇江医学院有机化学教研室镇江２１２００１）关键词超声波相转换催化糖精苄基化有机声化学近年来，由于超声波（Ｕｌｔｒａｓｏｕｎ，缩写Ｕ．Ｓ）在有机合成中应用的不断发展，逐渐形成了一门新兴...     

一锅法制备全乙酰吡喃溴代糖

将未保护的吡喃糖与醋酸酐在分子碘的催化下制得全乙酰吡喃糖 ,随后不经分离直接与溴化氢的冰醋酸溶液( 4 5 %)反应得到全乙酰吡喃溴代糖 .这种一锅法制备全乙酰吡喃溴代糖操作方便 ,收率高 ,经济实用且对环境友好     

Synthesis of Tetra—Schiff Base Macrocyclic Compound Containing Benzo—12—crown—4

Tetra-Schiff base macrocyclic compound containing benzo-12-crown-4 was synthesized via condensation of 2,6-diformyl-4-methyl-phenol with 4′，5′-diaminobenzo-12-C-4 promoted by proton. The compound was characterized by MS,IR ^1HNMR spectroscopy and elemental analysis.     

富勒烯及其衍生物的质谱研究

本文制备了一系列富勒烯及其衍生物，并利用多种质谱技术进行了鉴定、表征、揭示了它们在离子源条件下的稳定性及解规律。这些富勒烯及其省生物在ＦＤＭＳ、ＩＳＭＳ中均得到了较强的准分子离子峰且碎片峰很少。结果表昨ＦＤＭＳ，ＬＳＩＭＳ技术均适于富勒烯及其衍生物的定性分析，是目前富勒烯分析鉴定中较好的方法。     

2-取代亚肼基-1,3-二硫杂环戊烷类化合物的合成及其生物活性研究

以取代苯甲醛、取代吡啶和取代苯甲酸酯等为原料合成了 10种含硫杂环化合物 (其中 2a～ 2g化合物为国内外未见报道 ) .在合成过程中采用了超声波技术 ,极大地缩短了反应时间 ,提高了收率 .所得化合物的结构经IR ,1 HNMR ,MS和元素分析证实 .对其生物活性进行了初步测试 ,结果证明一些化合物具有良好的抑菌或杀菌作用 ,其中 2b ,2c ,2e ,2h ,2i和2j对大肠杆菌 ( 10 40 7号 )的抗菌效果与CET和SMZ相当 ;2b ,2c ,2f对草绿色链球菌 ( 112 3号 )的抗菌效果与CET和SMZ相当 .