Non-relativistic conformal symmetries in fluid mechanics

The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schrodinger group, which also involves, in addition, Schrodinger expansions. While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally invariant relativistic theory, the recently discussed conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry. This is explained by the subtleties of the non-relativistic limit.

A discrete square global grid system based on the parallels plane projection

Knowledge Innovation Project of Chinese Academy of Sciences [KZCX3-SW-347]; National Science Fund for Distinguished Young Scholar [40225004]

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two-dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area-preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.

Lanthanide-hinged calixarene bicapsules: Discrete hexanuclear Ln(III)/phenanthroline/p-sulfonatocalix[4]arene oligomers (Ln = Gd, Tb)

The dumbbell-like calixarene bicapsule in two novel Ln(III)-C4AS compounds was found to be a hexanuclear Ln(III)/phenanthroline/p-sulfonatocalix[4]arene oligomer. The magnetic and luminescent properties of these compounds were examined.

Assembly of 'discrete' (H2O)(16) water clusters within a supramolecular compound of calixarene

A 'discrete' (H2O)(16) cluster, featuring four basic cyclic nine-membered rings and a twelve-membered ring, illustrates a new mode of supramolecular association of water molecules.

Observation of Slow Magnetic Relaxation in Discrete Dysprosium Cubane

A discrete dysprosium cubane has been prepared and structurally characterized Slow relaxation of magnetization in this complex is observed, which may stimulate further investigations into the dynamics of magnetization in lanthanide clusters with different topologies.

The first discrete mixed-valence hexadecavanadate host shell cluster anions: hydrothermal synthesis, structure and characterization of [V16O38(Cl)](8-)

A new compound, [NH4](2)[Zn(phen)(3)](2)[Zn(phen)(2)(H2O)(2)][V16O38(Cl)] (.) 5H(2)O (1), was synthesized in the hydrothermal condition. The "naked" [V16O38(Cl)](8-) is the first observation with host shell structure in polyoxovanadate chemistry.

Discrete wavelets transform for signal denoising in capillary electrophoresis with electrochemiluminescence detection

Discrete wavelets transform (DWT). was applied to noise on removal capillary electrophoresis-electrochemiluminescence (CE-ECL) electropherograms. Several typical wavelet transforms, including Haar, Daublets, Coiflets, and Symmlets, were evaluated. Four types of determining threshold methods, fixed form threshold, rigorous Stein's unbiased estimate of risk (rigorous SURE), heuristic SURE and minimax, combined with hard and soft thresholding methods were compared. The denoising study on synthetic signals showed that wave Symmlet 4 with a level decomposition of 5 and the thresholding method of heuristic SURE-hard provide the optimum denoising strategy. Using this strategy, the noise on CE-ECL electropherograms could be removed adequately. Compared with the Savitzky-Golay and Fourier transform denoising methods, DWT is an efficient method for noise removal with a better preservation of the shape of peaks.

Vertical distribution of bacterial and archaeal communities along discrete layers of a deep-sea cold sediment sample at the East Pacific Rise (similar to 13 degrees N)

The community structure and vertical distribution of prokaryotes in a deep-sea (ca. 3,191 m) cold sediment sample (ca. 43 cm long) collected at the East Pacific Rise (EPR) similar to 13 degrees N were studied with 16SrDNA-based molecular analyses. Total community DNA was extracted from each of four discrete layers EPRDS-1, -2, -3 and -4 (from top to bottom) and 16S rDNA were amplified by PCR. Cluster analysis of DGGE profiles revealed that the bacterial communities shifted sharply between EPRDS-1 and EPRDS-2 in similarity coefficient at merely 49%. Twenty-three sequences retrieved from DGGE bands fell into 11 groups based on BLAST and bootstrap analysis. The dominant groups in the bacterial communities were Chloroflexi, Gamma proteobacteria, Actinobacterium and unidentified bacteria, with their corresponding percentages varying along discrete layers. Pairwise Fst (F-statistics) values between the archaeal clone libraries indicated that the archaeal communities changed distinctly between EPRDS-2 and EPRDS-3. Sequences from the archaeal libraries were divided to eight groups. Crenarchaea Marine Group I (MGI) was prevalent in EPRDS-1 at 83%, while Uncultured Crenarchaea group II B (UCII B) abounded in EPRDS-4 at 61%. Our results revealed that the vertically stratified distribution of prokaryotic communities might be in response to the geochemical settings and suggested that the sampling area was influenced by hydrothermalism. The copresence of members related to hydrothermalism and cold deep-sea environments in the microbial community indicated that the area might be a transitional region from hydrothermal vents to cold deep-sea sediments.