On the existence of a crepant resolution of some moduli spaces of sheaves on an abelian surface

Let J be an abelian surface with a generic ample line bundle . For n≥1, the moduli space M_J(2,0,2n) of (1)-semistable sheaves F of rank 2 with Chern classes c₁(F)=0, c₂(F)=2n is a singular projective variety, endowed with a holomorphic symplectic structure on the smooth locus. In this paper, we show that there does not exist a crepant resolution of M_J(2,0,2n) for n≥2. This certainly implies that there is no symplectic desingularization of M_J(2,0,2n) for n≥2. Jaeyoo Choy was partially supported by KRF 2003-070-C00001 Young-Hoon Kiem was partially supported by a KOSEF grant R01-2003-000-11634-0.     

Synchronization optimal networks obtained using local structure information

In this paper, the networks with optimal synchronizability are obtained using the local structure information. In scale-free networks, a node will be coupled by its neighbors with maximal degree among the neighbors if and only if the maximal degree is larger than its own degree. If the obtained coupled networks are connected, they are synchronization optimal networks. The connection probability of coupled networks is greatly affected by the average degree which usually increases with the average degree. This method could be further generalized by taking into account the degree of next-nearest neighbors, which will sharply increase the connection probability. Compared to the other proposed methods that obtain synchronization optimal networks, our method uses only local structure information and can hold the structure properties of the original scale-free networks to some extent. Our method may present a useful way to manipulate the synchronizability of real-world scale-free networks.     

Effects of niobium doping on lead zirconate titanate films deposited by a sol–gel route

Niobium (Nb)-doped lead zirconate titanate (PZT) films have been prepared on platinized silicon substrates using a sol–gel method. The Zr/Ti ratios of the films are 53/47 and 40/60, and the Nb doping level ranges from 0 mol% to 3 mol%. Similar to the cases in bulk ceramics, after the doping with Nb, the remanent polarization P_r, effective transverse piezoelectric coefficients e_31,c and pyroelectric coefficient p of the PZT films increase; but the longitudinal effective piezoelectric coefficient d_33,c remains roughly unchanged. At the optimum Nb doping levels, the observed P_r, −e_31,c and p reach a maximum value of 30 μC/cm², 18 C/m² and 350 μC/m² K, respectively, for the PZT (53/47) films, and 37 μC/cm², 7.9 c/m² and 370 μC/m² K for the PZT (40/60) films. Our results also reveal that there exist linear relations between p, e_31,c/ε_r and P_r.     

Side chain dynamics in unfolded protein states: an NMR based 2H spin relaxation study of delta131delta

NMR relaxation data on disordered proteins can provide insight into both structural and dynamic properties of these molecules. Because of chemical shift degeneracy in correlation spectra, detailed site-specific analyses of side chain dynamics have not been possible. Here, we present new experiments for the measurement of side chain dynamics in methyl-containing residues in unfolded protein states. The pulse schemes are similar to recently proposed methods for measuring deuterium spin relaxation rates in (13)CH(2)D methyl groups in folded proteins.(1) However, because resolution in (1)H-(13)C correlation maps of unfolded proteins is limiting, relaxation data are recorded as a series of (1)H-(15)N spectra. The methodology is illustrated with an application to the study of side chain dynamics in delta131delta, a large disordered fragment of staphylococcal nuclease containing residues 1-3 and 13-140 of the wide-type protein. A good correlation between the order parameters of the symmetry axes of the methyl groups and the backbone (1)H-(15)N bond vectors of the same residue is observed. Simulations establish that such a correlation is only possible if the unfolded state is comprised of an ensemble of structures which are not equiprobable. A motional model, which combines wobbling-in-a-cone and Gaussian axial fluctuations, is proposed to estimate chi(1) torsion angle fluctuations, sigma(chi)()1, of Val and Thr residues on the basis of the backbone and side chain order parameters. Values of sigma(chi)()1 are approximately 10 degrees larger than what has previously been observed in folded proteins. Of interest, the value of sigma(chi)()1 for Val 104 is considerably smaller than for other Val or Thr residues, suggesting that it may be part of a hydrophobic cluster. Notably large (15)N transverse relaxation rates are observed in this region. To our knowledge, this is the first time that side chain dynamics in an unfolded state have been studied in detail by NMR.     

A novel practical cleavage of tert-butyl esters and carbonates using fluorinated alcohols

Thermolytic cleavage of t-butyl esters and t-butyl carbonates was accomplished using TFE (2,2,2-trifluoroethanol) or HFIP (hexafluoroisopropanol) as solvent. Thus, a practical method to cleanly convert t-butyl esters and carbonates into the corresponding carboxylic acids, decarboxylated products, or alcohols in nearly quantitative yields was developed. The product is recovered by a simple solvent evaporation. The practicality of this methodology was demonstrated on alkyl, aryl, and heteroaromatic esters.     

Validation of green‐solvent extraction combined with chromatographic chemical fingerprint to evaluate quality of Stevia rebaudiana Bertoni

An approach that combined green‐solvent methods of extraction with chromatographic chemical fingerprint and pattern recognition tools such as principal component analysis (PCA) was used to evaluate the quality of medicinal plants. Pressurized hot water extraction (PHWE) and microwave‐assisted extraction (MAE) were used and their extraction efficiencies to extract two bioactive compounds, namely stevioside (SV) and rebaudioside A (RA), from Stevia rebaudiana Bertoni (SB) under different cultivation conditions were compared. The proposed methods showed that SV and RA could be extracted from SB using pure water under optimized conditions. The extraction efficiency of the methods was observed to be higher or comparable to heating under reflux with water. The method precision (RSD, n = 6) was found to vary from 1.91 to 2.86% for the two different methods on different days. Compared to PHWE, MAE has higher extraction efficiency with shorter extraction time. MAE was also found to extract more chemical constituents and provide distinctive chemical fingerprints for quality control purposes. Thus, a combination of MAE with chromatographic chemical fingerprints and PCA provided a simple and rapid approach for the comparison and classification of medicinal plants from different growth conditions. Hence, the current work highlighted the importance of extraction method in chemical fingerprinting for the classification of medicinal plants from different cultivation conditions with the aid of pattern recognition tools used.     

Iron(III) Located in the Dinuclear Metallo‐β‐Lactamase IMP‐1 by Pseudocontact Shifts

Heterodinuclear metalloenzymes are an important class of metalloproteins, but determining the location of the different metal ions can be difficult. Herein we present a new NMR spectroscopy method that uses pseudocontact shifts (PCS) to achieve this without assumptions about the coordinating ligands. The approach is illustrated with the dinuclear [FeZn] complex of IMP‐1, which is a prototypical metallo‐β‐lactamase (MβL) that confers resistance to β‐lactam antibiotics. Results from single‐crystal X‐ray diffraction were compromised by degradation during crystallization. With [GaZn]‐IMP‐1 as diamagnetic reference, the PCSs unambiguously identified the iron binding site in fresh samples of [FeZn]‐IMP‐1, even though the two metal centers are less than 3.8 Å apart and the iron is high‐spin Fe³⁺, which produces only small PCSs. [FeZn]‐MβLs may be important drug targets, as [FeZn]‐IMP‐1 is enzymatically active and readily produced in the presence of small amounts of Fe³⁺.     

Synthesis, vacuum ultraviolet and near ultraviolet-excited luminescent properties of GdCaAl3O7: RE (RE=Eu, Tb)

Vacuum ultraviolet (VUV) excitation and photoluminescent (PL) properties of Eu³⁺ and Tb³⁺ ion-doped aluminate phosphors, GdCaAl₃O₇:Eu³⁺ and GdCaAl₃O₇:Tb³⁺ have been investigated. X-ray diffraction (XRD) patterns indicate that the phosphor GdCaAl₃O₇ forms without impurity phase at 900 °C. Field emission scanning electron microscopy (FE-SEM) images show that the particle size of the phosphor is less than 3 μm. Upon excitation with VUV irradiation, the phosphors show a strong emission at around 619 nm corresponding to the forced electric dipole ⁵D₀→⁷F₂ transition of Eu³⁺, and at around 545 nm corresponding to the ⁵D₄→⁷F₅ transition of Tb³⁺. The results reveal that both GdCaAl₃O₇:RE³⁺ (RE=Eu, Tb) are potential candidates as red and green phosphors, respectively, for use in plasma display panel (PDP).