Block thresholding for density estimation: local and global adaptivity

We consider wavelet block thresholding method for density estimation. A block-thresholded density estimator is proposed and is shown to achieve optimal global rate of convergence over Besov spaces and simultaneously attain the optimal adaptive pointwise convergence rate as well. These results are obtained in part through the determination of an optimal block length.     

Enantioselective synthesis of the carbacephem antibiotic loracarbef via Mitsunobu and Dieckmann cyclization from an unnatural amino acid

The nucleus of the carbacephem antibiotic loracarbef was synthesized in a highly efficient and enantioselective fashion from 2S,3S-2-amino-3-hydroxy-6-heptenoic acid (AHHA), which was derived from enzyme-catalyzed condensation of glycine and 4-pentenaldehyde. The bicyclic framework of this compound was established through sequential Mitsunobu reaction and aldol condensations.     

Angular correlations in the decaysB→VV using heavy quark symmetry

We calculate branching ratios and the polarization in the decay ofB mesons to two vector mesons using heavy quark symmetries to evaluate the current matrix elements.     

A comparison study on multivariant and univariant finite elements for three-dimensional incompressible viscous flows

In this paper, four quadratic hexahedron elements are considered and assessed for analysis of an incompressible viscous flow underlying the mixed finite element method. We classify the investigated elements as multivariant and univariant finite elements. With the same number of pressure unknowns, multivariant elements are more constrained when the number of elements per side is larger than 10, as compared with that of continuous pressure elements. In multivariant eléments, the coding is complicated by the appearance of restricted degrees of freedom at mid-face and mid-edge nodes. The comparison consequently should be made via numerical example against the analytical problem.     

Tau functions for the Dirac operator on the Poincaré disk

In this paper we define tau functions for holonomic fields associated with the Dirac operator on the Poincaré disk. The deformation analysis of the tau functions is worked out and in the case of the two point function, the tau function is expressed in terms of a Painlevé function of type VI.     

A curve fitting signal processing scheme for a white-light interferometric system with a synthetic source

A white-light interferometric system, which comprises two Michelson interferometers linked by a 100 μm diameter core multimode step index fibre has been investigated, where a signal processing scheme, using curve fitting, has been introduced to suppress the noise induced in the system. The theoretical resolution of such a sensor with the use of an appropriate curve fitting signal processing scheme has been discussed. The experimental results obtained show the short term repeatability (to three standard deviations) to be better than 5 nm after signal processing, under conditions where the fibre is constantly vibrated in a known and reproducible way.     

Can Gravitons be Detected?

Freeman Dyson has questioned whether any conceivable experiment in the real universe can detect a single graviton. If not, is it meaningful to talk about gravitons as physical entities? We attempt to answer Dyson’s question and find it is possible concoct an idealized thought experiment capable of detecting one graviton; however, when anything remotely resembling realistic physics is taken into account, detection becomes impossible, indicating that Dyson’s conjecture is very likely true. We also point out several mistakes in the literature dealing with graviton detection and production.