Analogue Models of and for Gravity

Condensed matter systems, such as acoustics in flowing fluids, light in moving dielectrics, or quasiparticles in a moving superfluid, can be used to mimic aspects of general relativity. More precisely these systems (and others) provide experimentally accessible models of curved-space quantum field theory. As such they mimic kinematic aspects of general relativity, though typically they do not mimic the dynamics. Although these analogue models are thereby limited in their ability to duplicate all the effects of Einstein gravity they nevertheless are extremely important—they provide black hole analogues (some of which have already been seen experimentally) and lead to tests of basic principles of curved-space quantum field theory. Currently these tests are still in the realm of gedanken-experiments, but there are plausible candidate models that should lead to laboratory experiments in the not too distant future.     

Synthesis of bioactive indolocarbazoles: synthesis, nucleophilic ring-opening and chiral base desymmetrisation of a cyclic sulfate intermediate

A number of new functionalised bridged indolocarbazole systems have been prepared by ring-opening reactions of a key cyclic sulfate intermediate, prepared from the corresponding diol by the action of sulfuryl diimidazole and DBU. The same cyclic sulfate also undergoes an unprecedented asymmetric rearrangement to a chiral ketone, on treatment with a chiral lithium amide base.     

与q形变玻色算符逆算符相关的相干态及其量子统计性质

讨论了ｑ形变玻色算符的广义逆算符作用于ｑ－相干态所得到的两类量子态的数学及量子统计性质。结果表明，ｑ－相干态的光子激发态不存在压缩但呈现反聚束效应，而ｑ－相干态的光子湮灭态却存在压缩但不呈现反聚束效应。     

A new approach towards peptidosulfonamides: synthesis of potential inhibitors of bacterial peptidoglycan biosynthesis enzymes MurD and MurE

Peptidosulfonamides are an emerging group of peptidomimetics with a variety of applications in medicinal chemistry. We present a novel approach to the synthesis of peptidosulfonamides, and apply it to a series of new potential inhibitors of the bacterial peptidoglycan biosynthesis enzymes MurD and MurE. The synthesis was conducted via N-phthalimido β-aminoethanesulfonyl chlorides, which are new building blocks for the synthesis of peptidosulfonamides. In the most crucial step, sulfonic acids or their sodium salts were converted into the corresponding sulfonyl chlorides using an excess of either SOCl₂ or SOCl₂/DMF, and then coupled to the C-protected amino acid. None of the compounds significantly inhibited MurD, however, some inhibited MurE; one had an IC₅₀ below 200 μM, which constitutes a promising starting point for further development. Molecular modelling simulations were performed on two analogues to investigate the absence of inhibitory activity of the sulfonamide compounds on MurD.     

Simple and convenient synthesis of a fluorinated GM4 analogue

A series of fluorinated galactosides, dodecyl 2-deoxy-2-fluoro-β-d-galactopyranoside (2F Gal), dodecyl 4-deoxy-4-fluoro-β-d-galactopyranoside (4F Gal) and dodecyl 6-deoxy-6-fluoro-β-d-galactopyranoside (6F Gal), was chemically synthesized and introduced to B16 cells to serve as scaffolds for cellular enzyme glycosylation. Results showed that the presence of fluorine exercised significant effects on cell viability. Among the fluorinated galactosides used, 2F Gal was glycosylated to afford a GM4 analogue.     

Does an all-sulphur analogue of heptamolybdate exist?

The complexes [MoX₄]²⁻ (M = Mo; X = O or S) exist as the monomeric tetrahedral species in aqueous alkaline solutions. Acidification of tetraoxomolybdate results in the condensation of the tetrahedral units via a series of polyoxomolybdates leading to the ultimate formation of the trioxide MoO₃. Heptamolybdate [Mo₇O₂₄]⁶⁻ is the first major polyanion of the acidification reaction. In contrast, acidification of tetrathiomolybdates leads to the formation of amorphous molybdenum trisulphide via a dinuclear Mo(V) complex. The formation of the dinuclear Mo(V) complex precludes the formation of any higher nuclearity Mo(VI)-S complexes in aqueous solution. Thus it is shown that the all-sulphur analogue of heptamolybdate [M0₇S₂₄]⁶⁻ does not exist in alkaline medium and also cannot be isolated from aqueous acidic medium     

若干有关欧阳不等式的非线性积分不等式和离散不等式

获得几个非线性的积分不等式及离散不等式．它们和近期Ｐａｃｈｐａｔｅ［１］中欧阳亮不等式［２］的推广有关．作为特殊情形还导出了一些具有幂非线性的新不等式．为说明结果的有用性，讨论了某个非线性差分方程解的有界性．     

Power expansions for the self-similar solutions of the modified Sawada-Kotera equation

The fourth-order ordinary differential equation that defines the self-similar solutions of the Kaup—Kupershmidt and Sawada—Kotera equations is studied. This equation belongs to the class of fourth-order analogues of the Painlevé equations. All the power and non-power asymptotic forms and expansions near points z = 0, z = ∞ and near an arbitrary point z = z ₀ are found by means of power geometry methods. The exponential additions to the solutions of the studied equation are also determined.      

Template atom transfer radical polymerization of a diaminopyrimidine‐derivatized monomer in the presence of a uracil‐containing polymer

Uracil‐derivatized monomer 6‐undecyl‐1‐(4‐vinylbenzyl)uracil and diaminopyrimidine‐derivatized monomer 2,6‐dioctanoylamido‐4‐methacryloyloxypyrimidine (DMP) were synthesized and polymerized by atom transfer radical polymerization (ATRP). A well‐defined, highly soluble, uracil‐containing polymer, poly[6‐undecyl‐1‐(4‐vinylbenzyl)uracil] (PUVU), was prepared in dioxane at 90 °C with CuBr/1,1,4,7,10,10‐hexamethyltriethylenetetramine as the catalyst and methyl α‐bromophenylacetate as the initiator. PUVU was further used as a template for the ATRP of DMP. The enhanced apparent rate constant of the DMP polymerization in the presence of PUVU indicated that the ATRP of DMP occurred along the PUVU template. The template polymerization produced a stable and insoluble macromolecular complex, PUVU/poly(2,6‐dioctanoylamido‐4‐methacryloyloxypyrimidine). An X‐ray diffraction study confirmed that the complex had strandlike domains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6607–6615, 2006