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.      

The Effect of Cyclodextrins on the Photochemical Stability of 7-Amino-4-methylcoumarin in Aqueous Solution

The effect of -, - and -cyclodextrin onthe photochemical stability of 7-amino-4-methylcoumarin (C120)was studied. Using spectroscopic techniques (UV/Vis absorption spectroscopy, fluorescence, fluorescence anisotropy and circular dichroism) combined with HPLC/MS and MS analysis it was demonstrated that addition of -cyclodextrin to the aqueoussolution of C120 markedly inhibits the photodegradation of that dye. This results from theformation of an inclusion complex between C120 and -cyclodextrin.     

Effects of pH and Dye Concentration on the Optical and Structural Properties of Coumarin-4 Dye-Doped SiO2-PDMS Xerogels

Optical and structural properties of coumarin-4 dye-doped SiO₂-PDMS xerogels synthesized by acid catalyzed (one-step) and acid-base catalyzed (two-step) sol-gel routes with varying pH (0.6 to 7) and dye content ( 5 × 10^–4 to 5 × 10^–2 mole) are reported. Spectroscopic methods such as photo-luminescence, FT-IR and FT-Raman were used for characterizations. The acid catalyzed xerogels prepared with pH < 2.5 exhibited two fluorescence peaks, I at 390 nm and II at 480 nm. The acid-base catalyzed xerogels synthesized with pH < 2.5 also exhibited two peaks, I at 400 nm and II at 475 nm. Peak II was not observed for the samples with pH 2.5. This phenomenon was attributed to the existence of pH dependent different forms of coumarin-4 molecule. The concentration-quenching phenomenon was observed for the acid catalyzed xerogels prepared with different dye concentration. TheFT-IR spectra indicated the existence of hydrogen bonds between the carbonyl groups of dye molecules and the silanol groups of gel matrix. The hydrogen bonding was the highest for the samples with the extremity pH, 0.6 and 7, resulting in the highest dye/gel matrix interactions, hence, the highest fluorescence peaks. The Raman studies indicated that the samples prepared with pH < 2.5 possessed relatively more number of 3-membered siloxane rings than 4-membered siloxane rings. The ring statistics was reversed for the samples with pH > 2.5. The number of silanol groups was higher for the samples with pH > 2.5.