Parameter Estimation for Observed Diffusions in Manifolds

Following the procedure described by Elworthy (1982) and Ikeda& Watanabe (1981) we construct the solution of stochasticdifferential equations (SDEs) in manifolds. We take such SDEsto describe parametrized completely observed stochastic systemsand manifold-valued state processes. The likelihood functionfor the system parameter is computed by two methods: the firstapplies to the case of parallelizable manifolds; the secondapplies to the general case, here the solution of the systemSDE is constructed in the orthonormal frame bundle of the manifold.Two examples are given.     

Crystal Structure of catena-[（Tetrakis-μ2-acetato-μ2-4,4＇-bipyridine） dicopper（Ⅱ）] Acetonitrile Solvate

1 INTRODUCTION Much attention has been paid to 1D, 2D and 3D coordination polymers because they can meet the need of functional materials with desired structures and properties[1～5]. One strategy in the design and synthesis of coordination architectures is the buil- ding-block approach. Commonly, bi- or multidentate organic ligands containing N[6, 7] or O[8, 9] atoms have ever been used in the construction. In our cur- rent work, we have selected melamine ligand as the main building bl…     

Characterization of tectoRNA assembly with cationic conjugated polymers

Association between RNAs with preprogrammed molecular recognition units can be quantified by using cationic, water-soluble conjugated polymers. The method uses a fluorophore-labeled probe RNA (RNA-F*), which is treated with a target structure (RNA-T). Heterodimer formation, (RNA-T/RNA-F*), increases the total negative charge on the F*-bearing macromolecule and reduces the number of negatively charged molecules (relative to unbound RNA-T+ RNA-F*). On the basis of electrostatic interactions, we anticipated more effective binding between CCP and (RNAT/RNA-F*), a reduction of the average CCP- - -F* distance, and more effective FRET upon excitation of the conjugated polymer. The resulting signals benefit from the optical amplification characteristic of emissive conjugated polymers. Solution dissociation constants can be determined by monitoring F* intensity changes as a function of [RNA-F*] and the ratio: [I(T) - I(NB)]/I(NB), where I(T) and I(NB) are the F* intensities in the presence of the target RNA (RNA-T) and a nonbinding RNA (RNA-NB), respectively, while keeping the concentration of the conjugated polymer constant. By focusing on [I(T) - I(NB)]/I(NB) as a function of RNA concentration, one can detect the concentration range wherein increased fluorescence is the result of dimerization.     

Revisions of P-1 Space Groups to Higher Symmetry Space Groups

The space groups of 244 crystal structures originally reported as P-1 are revised to space groups of higher symmetry. The largest number involves revisions to P2/c and C2/c.     

Anaerobic Respiration on Self-Doped Conjugated Polyelectrolytes: Impact of Chemical Structure

We probe anaerobic respiration of bacteria in the presence of conjugated polyelectrolytes (CPEs). Three different CPEs were used to probe how structural variations impact biocurrent generation from Shewanella oneidensis MR-1. For the self-doped anionic CPE only, absorption spectroscopy shows that the addition of S. oneidensis MR-1 leads to the disappearance of the polaron (radical cation) band at >900 nm and an increase in the band at 735 nm due to the neutral species, consistent with electron transfer from microbe to polymer. Microbial three-electrode electrochemical cells (M3Cs) show an increase in the current generated by S. oneidensis MR-1 with addition of the self-doped CPE relative to other CPEs and controls. These experiments combined with in situ cyclic voltammetry suggest that the doped CPE facilitates electron transport to electrodes and reveal structure–function relationships relevant to developing materials for biotic/abiotic interfaces.     

Space Group of Aquaimidazolemaleatozinc, [(H2O)(C3H4N2)(O2CCH=CHCO2Zn)]n

The space group of [(H2O)(C3H4N2)(O2CCH=CHCO2Zn)]n, which was originally described in the acentric Pc space group (Liu et al., Chin. J. Struct. Chem. 2004, 23, 160～163), is re-described in the centric P21/c space group.The crystal structure of (H2O)(C3H4N2)O2C-CH=CHCO2Zn was refined in the acentric Pc space group on 266 variables to R = 0.037 for the 1926 of the 2067 obeying the I > 2σ criterion[1]. The structure is better described in the centric P21/c space group (Table 1) as the two indepen-dent formula units are related by a center of symmetry. The 21 screw axis is must be pre-sent, as noted from the systematically absent 0k0 (k = 2n + 1) reflections in the 3302 reflections that were simulated[2, 3] from the published cell dimensions and atomic coordinates. Crystallo-graphica[4] estimates the hemisphere of reflections to be 3302, so that only a little more than the minimum monoclinic data must have been collec-ted in the study. A revision from Pc to P21/c is not particularly common[5] as the P21/c space group is uniquely determined from systematic absences. The polymeric chain propagates linearly along the c-axis of the unit cell (Fig. 1).     

Real meromorphic functions and linear differential polynomials

We determine all real meromorphic functions f in the plane such that f has finitely many zeros, the poles of f have bounded multiplicities, and f and F have finitely many non-real zeros, where F is a linear differential polynomial given by F = f (k) +Σk-1j=0ajf(j) , in which k≥2 and the coefficients aj are real numbers with a0≠0.