Special Lagrangian Submanifolds with Isolated Conical Singularities. II. Moduli spaces

This is the second in a series of five papers studying special Lagrangiansubmanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds M with singularities x ₁ , ..., x _n locally modelled on specialLagrangian cones C ₁, ..., C _n in ^m with isolated singularities at 0.Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL m-folds X in Mwith conical singularities. We define the moduli space _X of deformations of X in M, and construct a natural topology on it. Then we show that _X is locally homeomorphic to the zeroes of a smooth map : _{X X} between finite-dimensional vector spaces.Here the infinitesimal deformation space _X depends only on the topology of X, and the obstruction space _X only on the cones C ₁, ..., C _n at x ₁, ..., x _n . If the cones C _i are stable then _X is zero, and _X is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M.     

Evolution Equations for Special Lagrangian 3-Folds in C3

This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C ^m . The previous paper (Math. Ann. 320 (2001), 757–797), defined the idea of evolution data, which includes an (m – 1)-submanifold P in R ⁿ , and constructed a family of special Lagrangian m-folds N in C ^m , which are swept out by the image of P under a 1-parameter family of affine maps _t : R ⁿ C ^m , satisfying a first-order o.d.e. in t. In this paper we use the same idea to construct special Lagrangian 3-folds in C³. We find a one-to-one correspondence between sets of evolution data with m = 3 and homogeneous symplectic 2-manifolds P. This enables us to write down several interesting sets of evolution data, and so to construct corresponding families of special Lagrangian 3-folds in C³.Our main results are a number of new families of special Lagrangian 3-foldsin C³, which we write very explicitly in parametric form. Generically these are nonsingular as immersed 3-submanifolds, and diffeomorphic to R³ or ¹× R². Some of the 3-folds are singular, and we describe their singularities, which we believe are of a new kind.We hope these 3-folds will be helpful in understanding singularities ofcompact special Lagrangian 3-folds in Calabi–Yau 3-folds. This will beimportant in resolving the SYZ conjecture in Mirror Symmetry.     

Phenotype and in vitro function of mature MDDC generated from cryopreserved PBMC of cancer patients are equivalent to those from healthy donors

Background  

Monocyte-derived-dendritic-cells (MDDC) are the major DC type used in vaccine-based clinical studies for a variety of cancers. In order to assess whether in vitro differentiated MDDC from cryopreserved PBMC of cancer patients are functionally distinct from those of healthy donors, we compared these cells for their expression of co-stimulatory and functional markers. In addition, the effect of cryopreservation of PBMC precursors on the quality of MDDC was also evaluated using samples from healthy donors.     

Dynamic RHEED observations of the MBE growth of GaAs

Detailed measurements have been made of the specular beam intensity in RHEED patterns from static and growing GaAs surfaces. The basic parameters investigated were substrate temperature and electron beam azimuth. The results have provided further understanding of growth dynamics and surface disorder, respectively. There is a significant trend away from two-dimensional growth at the higher temperatures, which also correspond to more Ga-rich surface structures. Conversely, surface disorder is apparently greater during growth at the lower temperatures, where the structure is As-rich. The static As-stable 2×4 surface is, however, the most ordered and the most closely two-dimensional. It has also been shown that ordered, two-dimensional growth can be initiated from excess Ga adatom populations.     

Exploration for Degradation of Λ Polarization Produced in Relativistic Nucleus Nucleus Collisions

The degradation of Λ transverse polarization produced in S+Pb central collisions at energy 200 GeV per nucleon has been studied in detail. The S+Pb central collision events have been generated using Monte-Carlo generator——LUCIAE at 200 GeV per nucleon. The various factors degrading Λ transverse polarization have been analysed quantitatively. The ratios of Λ′s produced from rescattering, secondary production and decays of Σ, Ξ hyperons to the total measurable Λ′s in experiment have been investigeted and the degradation effect of these Λ on the total polarization has been determined. The simulation and calculation show that above three factors decrease the Λ transverse polarization strongly, however, can not eliminate the polarization completely when the Λ′s are assumed to be produced from hadronic gas in the final state. To explan the experimental data of vanished Λ polarization, it probably needs to consider new mechanisms of Λ production, including a weak effect of QGP formation.     

Benzodiazepine analogues. Part 21. 13C NMR analysis of benzoxathiepine derivatives

The influence of substituents and structure on the 13C NMR spectra of four series of benzoxathiepine derivatives has been investigated. Signal assignments in the 13C NMR spectra have been facilitated by the use of several predictive methods, permitting comparison of their relative efficacy.     

Solubility of benzil in binary alkane + dibutyl ether solvent mixtures. Comparison of predictive expressions derived from the nearly ideal binary solvent model

Experimental solubilities are reported for benzil dissolved in six binary mixtures containing dibutyl ether with hexane, heptane, octane, cyclohexane, methylcyclohexane, and 2,2,4-trimethylpentane at 25°C. Results of these measurements are compared to the predictions of equations developed previously for solubility in systems of nonspecific interactions. The most successful equation in terms of goodness of fit involved a volume fraction average of the excess Gibbs energies relative to the Flory-Huggins model, and predicted the experimental solubilities in the six systems studied to within an overall average absolute deviation of 3.4% and with a maximum deviation of 6.0%.     

Characterisation of selected hypnotic drugs and their metabolites using electrospray ionisation with ion trap mass spectrometry and with quadrupole time-of-flight mass spectrometry and their determination by liquid chromatography-electrospray ionisation-ion trap mass spectrometry

The electrospray ionisation-ion trap mass spectrometry (ESI-MSⁿ) of selected hypnotic drugs, i.e. zopiclone, zolpidem, flunitrazepam and their metabolites have been investigated. Sequential product ion fragmentation experiments (MSⁿ) have been performed in order to elucidate the degradation pathways for the [M+H]⁺ ions and their predominant fragment ions. These MSⁿ experiments show certain characteristic fragmentations in that functional groups are generally cleaved from the ring systems as neutral molecules such as H₂O, CO, CO₂, NO₂, amines and HF. When an aromatic entity is present in a drug molecule together with a nitrogen-containing saturated ring structure as with zopiclone and its N-desmethyl metabolite fragmentation initially occurs at the latter ring with the former being resistant to fragmentation. The structures of fragment ions proposed for ESI-MSⁿ can be supported by electrospray ionisation-quadrupole time-of-flight mass spectrometry (ESI-QTOF-MS).These molecules can be identified and determined in mixtures at low ng/ml concentrations by the application of liquid chromatography (LC)-ESI-MSⁿ which can be used for their analysis in saliva samples.This paper includes a tabulation of mass losses/signals at low m/z values for these hypnotic drugs and many others in recent publications which will be of value in the characterisation of drug metabolites of unknown structure and also natural product pharmaceuticals isolated from plants, etc.