Counting Simsun Permutations by Descents

We count in the present work simsun permutations of length n by their number of descents. Properties studied include the recurrence relation and real-rootedness of the generating function of the number of n-simsun permutations with k descents. By means of generating function arguments, we show that the descent number is equidistributed over n-simsun permutations and n-André permutations. We also compute the mean and variance of the random variable X _n taking values the descent number of random n-simsun permutations, and deduce that the distribution of descents over random simsun permutations of length n satisfies a central and a local limit theorem as n ?? +???.     

Facile patterning of upconversion NaYF4:Yb,Er nanoparticles

Different kinds of highly ordered patterns of NaYF(4):Yb,Er nanoparticles on gold substrates were fabricated using a simple method combining micro-contact printing and "breath figures" techniques. Ordered arrays of water droplets were first formed in the hydrophilic regions of patterned self-assembled monolayers (SAMs). This was subsequently submerged in a chloroform solution of NaYF(4):Yb,Er nanoparticles. The particles were spontaneously assembled at the interface of chloroform/water droplet surface, leading to different kinds of uniform patterns after solvent evaporation. The structures of NaYF(4):Yb,Er particles patterns depended on the dimension of the substrate, the concentration of the NaYF(4):Yb,Er nanoparticles and the water condensation process.     

Franck-Condon simulation, including anharmonicity, of the photodetachment spectrum of P2H(-): restricted-spin coupled-cluster single-double plus perturbative triple and unrestricted-spin coupled-cluster single-double plus perturbative triple -F12x potential energy functions of P2H and P2H(-)

Geometry optimization and harmonic vibrational frequency calculations have been carried out on the X?(2)A(') state of P(2)H and the X?(1)A(') state of P(2)H(-) using the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] and explicitly correlated unrestricted-spin coupled-cluster single-double plus perturbative triple excitation [UCCSD(T)-F12x] methods. For RCCSD(T) calculations, basis sets of up to the augmented correlation-consistent polarized valence quintuple-zeta (aug-cc-pV5Z) quality were employed, and contributions from extrapolation to the complete basis set limit and from core correlation of the P 2s(2)2p(6) electrons were also included. For UCCSD(T)-F12x calculations, different atomic orbital basis sets of triple-zeta quality with different associated complementary auxiliary basis sets and different geminal Slater exponents were used. When the P 2s(2)2p(6) core electrons were correlated in these F12x calculations, appropriate core-valence basis sets were employed. In addition, potential energy functions (PEFs) of the X?(2)A(') state of P(2)H and the X?(1)A(') state of P(2)H(-) were computed at different RCCSD(T) and UCCSD(T)-F12x levels, and were used in variational calculations of anharmonic vibrational wavefunctions, which were then utilized to calculate Franck-Condon factors (FCFs) between these two states, employing a method which includes allowance for anharmonicity and Duschinsky rotation. The photodetachment spectrum of P(2)H(-) was then simulated using the computed FCFs. Simulated spectra obtained using the RCCSD(T)/aug-cc-pV5Z and UCCSD(T)-F12x(x = a or b)/aug-cc-pCVTZ PEFs are compared and found to be essentially identical. Based on the computed FCFs, a more detailed assignment of the observed vibrational structure than previously reported, which includes "hot bands," has been proposed. Comparison between simulated and available experimental spectra has been made, and the currently most reliable sets of equilibrium geometrical parameters for P(2)H and its anion have been derived. The photodetachment spectrum of P(2)D, yet to be recorded, has also been simulated.     

Practical manganese-catalysed highly enantioselective cis-dihydroxylation of electron-deficient alkenes and detection of a cis-dioxomanganese(V) intermediate by high resolution ESI-MS analysis

A practical protocol has been developed for asymmetric cis-dihydroxylation of electron-deficient alkenes with Oxone catalysed by a manganese complex bearing a chiral tetradentate N(4)-donor ligand affording cis-diols in up to 95% yield with up to 96% ee. Analysis of the reaction mixture by high resolution ESI-MS revealed the formation of a cis-dioxomanganese(V) intermediate.     

A versatile palladium catalyst system for Suzuki-Miyaura coupling of alkenyl tosylates and mesylates

A general and effective palladium system for Suzuki-Miyaura coupling of alkenyl electrophiles under mild reaction conditions is reported. With the Pd(OAc)(2)/CM-phos system, a variety of alkenyl tosylates are coupled well with ArB(OH)(2). Moreover, the first successful examples of using alkenyl mesylates in alkenylation are also described.     

Free surface Nvier-Stokes flows with simultaneous heat transfer and solidification/melting

A mathematical model to analyse some key aspects of the metal cast process is described involving the filling of the mould by liquid metal and simultaneously, undergoing both cooling and solidification (re-melting) phase change. A computational solution procedure based upon a finite volume discretisation approach, on both structured and unstructured meshes, is described. The overall flow solution procedure is based on the pressure correction algorithm SIMPLE suitably adapted to: (a) solve for the free surface with minimal smearing by the SEA algorithm, and (b) solve for the solidification/melting phase change using an enthalpy conservation algorithm developed by Voller, but with its root in the work of Crank many years ago.Dedicated to Professor J. Crank on the occasion of his 80th birthday     

Intracavity-frequency-doubling of a 946 nm Nd:YAG laser with cadmium mercury thiocyanate crystal

We report the intracavity-frequency-doubling of a 946 nm Nd:YAG laser with a CMTC crystal at room temperature. A cw output power of 1.64 mW of blue light at 473 nm is obtained. To our knowledge, this is the first time that CMTC crystal has been used to frequency double a 946 nm Nd:YAG laser.     

Synthesis, characterization and preliminary toxicity assays of NIR-active Au-silicate nanoparticles through a sol-gel processing

Monodisperse Au-silicate nanoparticles (10.7±1.6 nm in diameter) were prepared by reduction of aqueous solution containing 2 mM HAuCl₄ with sodium citrate (1 wt.%) in a hydrosol, in which small clusters of silicate formed by hydrolysis and polymerization of 3-aminopropyltrimethoxysilane (APTMS). APTMS covalently linked to reduced gold particles through its -NH₂ end-group. UV-vis spectra of the obtained Au-silicate nanoparticles showed a peak at ∼690 nm due to the interface effects between the Au and the silicate matrix. The Au-silicate nanoparticles exhibited near-IR (NIR) sensitivity. Cytotoxicity and limited hemocompatibility in vitro for the prepared Au-silicate nanoparticles were also investigated. It was shown that at lower concentration (<1 μg/ml), the Au-silicate nanoparticles were biocompatible without causing any cytotoxicity and hemolysis.