An efficient Pd-catalyzed copper and amine free coupling reaction of acetylene and aryl bromides was achieved with calcium carbide as an acetylene source, using inorganic base and easily prepared, air-stable aminophosphine ligand in common organic solvents, providing symmetric diaryl ethynes in one-pot with yields ranged from moderate to excellent.

Given a selfadjoint random variable x 0 and a unitary random variable u, different from Haar unitary, free from the free circular Brownian motion c t and the free multiplicative Brownian motion b t , we use the Hamilton-Jacobi method to compute the Brown measures of free circular Brownian motion x 0 + c t and the free multiplicative Brownian motion ub t with probabilistic initial point, extending the recent work [13] by Driver-Hall-Kemp. We find that the supports of the Brown measures are related to the subordination functions of the free additive and multiplicative convolutions. The density of the Brown measure of x 0 + c t is constant along the vertical direction in the additive case, and the density of the Brown measure of ub t has the form, in polar coordinates, of (1/r 2 )w t (θ). The densities of the Brown measures are closely related to the laws of x 0 + s t and uu t , where s t is the free semicircular Brownian motion and u t is the free unitary Brownian motion, both freely independent of x 0 and u.

CdTe nanocrystals (NCs) were prepared and modified in aqueous solution by using 3-mercaptopropionic acid (MPA). Compared with previous fluorescent sensors based on organic fluorophores, these NCs have the following merits. First, they are sensitive and the synthetic procedure is simple; second, they have narrow, tunable, symmetric emission spectra and are photochemically stable. The applicability of these NCs to the determination of Cu(II) ions was studied successfully. Maximum fluorescence intensity was produced at pH 7.8, with excitation and emission wavelengths at 365 and 532 nm, respectively. Under optimal conditions, linear relationships were found between the relative fluorescence intensity and the concentration of Cu(II) ions in the range 0-256 ng ml(-1) and the limit of detection was 0.19 ng ml(-1). This method was applied to determine real samples successfully. In addition, the quenching mechanism is also described.

CdTe nanocrystals as fluorescent sensors for Hg2+ ions were synthesized. These nanocrystals were highly sensitive for Hg2+ ions and the selectivity was found to be Hg2+ > Cu2+ > other representative heavy metal ions. Moreover, they bear the following merits. First, they are easily synthesized; second, they have a narrow, tunable, symmetric emission spectrum.

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