Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds

We study the singularities of the exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues of the curvature tensor, and their contribution to the Maslov index of the geodesic is computed explicitly. We prove that degeneracy of conjugate points, which is a phenomenon that can only occur in semi-Riemannian geometry, is caused in the locally symmetric case by the lack of diagonalizability of the curvature tensor. The case of Lie groups endowed with a bi-invariant metric is studied in some detail, and conditions are given for the lack of local injectivity of the exponential map around its singularities.     

Symmetric bi-derivations on prime and semi-prime rings

Summary LetR be a ring. A bi-additive symmetric mappingD(.,.): R × R R is called a symmetric bi-derivation if, for any fixedy R, a mappingx D(x, y) is a derivation. The purpose of this paper is to prove some results concerning symmetric bi-derivations on prime and semi-prime rings. We prove that the existence of a nonzero symmetric bi-derivationD(.,.): R × R R, whereR is a prime ring of characteristic not two, with the propertyD(x, x)x = xD(x, x), x R, forcesR to be commutative. A theorem in the spirit of a classical result first proved by E. Posner, which states that, ifR is a prime ring of characteristic not two andD ₁,D ₂ are nonzero derivations onR, then the mappingx D ₁(D ₂ (x)) cannot be a derivation, is also presented.     

同多酸和杂多酸修饰微电极的电化学研究——Ⅳ.1:2-磷钼杂多酸薄膜修饰碳纤维微电极的制备和电化性质

本文报道了1:12-磷铜杂多酸(PMo_(12)薄膜修饰碳纤维(CF)微电极的制备及其电化学性质。采用简单,快速的浸渍吸附制备的PMo_(12)薄膜修饰CF电极在酸性介质中具有很高的稳定性和氧化还原活性,电解质溶液的pH值和扫描电位范围对PMo_(12)膜的稳定性和电化学性质产生较大的影响。另一方面,PMo_(12)薄膜修饰CF微电极对酸性水溶液中的PMo_(12)和氯酸根离子(ClO)_3~-)的电催化还原作用也进行了描述。     

大环二萜类化合物的研究(Ⅳ)——Isosarcophytol—A前体化合物的合成

Isosarcophytol-A(1)是1982年首次从澳大利亚软珊瑚(Nephthea brassica)中分离鉴定的西松烷型(Cembrane)大环二萜类化合物,其结构为6,10,14-三甲基-3-异丙基-3E,5E,9E,13E-环十四碳四烯-1-醇,是Sarcophytol—A(2)的异构体,但有关1的生物活性试验和全合成研究尚未见报道.我们在前文报道了以低价钛诱导的分子内二羰基偶联为环化方法,完成了天然大环二萜类化合物Cembrene—C的全合成和Sarcophytol—A(2)苄醚衍生物(3)的合成.本文报道以天然法呢醇4为起始原料,经区域选择性氧化、羟醛缩合等六步反应,合成了1的前体化合物11.合成路线如下:     

A spectroscopic study on the 12-heteropolyacids of molybdenum and tungsten (H3PMo12−nWnO40) combined with cetylpyridinium bromide in the epoxidation of cyclopentene

The epoxidation of cyclopentene with hydrogen peroxide catalyzed by 12-heteropolyacids of molybdenum and tungsten (H₃PMo_12−nW_nO₄₀, n = 1–11), 12-tungstophosphoric acid and 12-molybdophosphoric acid combined with cetylpyridinium bromide as a phase transfer reagent was carried out in acetonitrile. Among 13 heteropolyacids investigated, catalyst of H₃PMo₆W₆O₄₀ showed the highest activity, giving a conversion of 60% and a selectivity of 95% in the epoxidation of cyclopentene. The fresh catalysts and the catalysts under reaction condition were characterized by UV–vis, FT-IR and ³¹P NMR spectroscopy, which has revealed that all of the molybdotungstophosphoric acids were degraded in the presence of hydrogen peroxide to form a considerable amount of phosphorus-containing species. The active species resulted from H₃PMo₆W₆O₄₀ are new kinds of phosphorus-containing species, which is different from {PO₄[WO(O₂)₂]₄}³⁻.     

氯化铯和氯化镧溶剂体系及四类新化合物的合成

研究了四元体系ＣｓＣｌ－ＬａＣｌ３－ＨＣｌ－Ｈ２Ｏ（２５℃、「ＨＣｌ」＝１３％（ｗｔ），２３％（ｗｔ）和ＣｓＣｌ－ＬａＣｌ３－ＨＡｃ－Ｈ２Ｏ（３０℃，「ＨＡｃ」＝４２％（ｗｔ））的平衡态的溶度数据，并给出制了相应的溶度图，共得到了ＣｓＣｌ．ＬａＣｌ３．４Ｈ２Ｏ、２ＣｓＣｌ．ＬａＣｌ３．２Ｈ２Ｏ和３ＣｓＣｌ．ＬａＣｌ３．３Ｈ２Ｏ３种化合物。对得到的新相进行了热分析，Ｘ射线粉末衍射及偏光性质的测定，依     

Synthesis of 3β,20S-dihydroxydammar-24-en-12-one 3,20-di-O-β-D-glucopyranoside (chikusetsusaponin-LT8), a glycoside from Panax japonicus

A method for preparative production of 3β,20S-dihydroxydammar-24-en-12-one 3,20-di-O-β-D-glucopyranoside (1), a glycoside from Panax japonicus, chikusetsusaponin-LT₈ was developed. Chemical transformation of betulafolientriol, a component of Betula leaves extract, produced the 12-keto-20S-protopanaxadiol (3β,20S-dihydroxydammar-24-en-12-one) (2), exhaustive glycosylation of which by 2,3,4,6-tetra-O-acetyl-α-D-glucopyranosylbromide (3) under Koenigs—Knorr reaction conditions with subsequent removal of protecting groups formed 3β,20S-dihydroxydammar-24-en-12-one 3,20-di-O-β-D-glucopyranoside (1). The principal glycosylation product was 3β,20S-dihydroxydammar-24-en-12-one 3-O-β-D-glucopyranoside if equimolar amounts of (2) and (3) were used. __________ Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 44–48, January–February, 2006.     

硅钼杂多阴离子薄膜修饰电极的研究和应用——线性扫描伏安法测定水中可溶性硅酸盐

本文研究了以玻碳电极为基体的1:12硅钼杂多酸根(SiMo_(12)O_(40)~(4-)简称12-MSA)修饰电极的制备及其电化学行为,将12-MSA电极应用于线性扫描伏安法测定天然水中可溶性硅酸盐,结果满意.硅浓度在8.0×10~(-7)～1.7×10~(-3)mol/L,相对标准偏差(n=7)为1.85％,加标回收率为98.2％～103.6％,SiMo_(12)电极具有优良的选择性和稳定性。     

Comparative study on the synthesis, photoluminescence and application in InGaN-based light-emitting diodes of TAG:Ce phosphors

Cerium-doped terbium aluminum garnet phosphors, Tb₃Al₅O₁₂:Ce³⁺ (TAG:Ce³⁺), were prepared with different methods: co-precipitation (CP), half dry-half wet (HDHW), sol-combustion (SC) and Pechini method plus conventional solid state reaction (SS) method. Comparative study on the phase-formation, particle size, morphologies and luminescent characteristics of the phosphors synthesized with different methods was carried out by means of XRD, FE-SEM and photoluminescence (PL) analysis and SC method was confirmed by the comparison of the results to be an easy and an effective process for preparing efficient and nano-sized Tb₃Al₅O₁₂:Ce³⁺ phosphors. Various factors influencing particle size, morphology and PL of the phosphors, such as precursor preparation, reaction temperature and heating time, were also investigated. Light-emitting diodes (LEDs) were fabricated with each phosphor and a ∼460 nm emitting InGaN chip. The LEDs from SS, HDHW and CP exhibit strong white emission while those from SC and Pechini emit yellow, revealing that the emission characteristics of LEDs are influenced not only by the morphology and the particle size of the phosphors, but also by the preparing process of the phosphors.