Preface in dedication to Professors Yong Jin and Zhiqing Yu

This special issue of China PARTICUOLOGY is dedicated to Professors Yong Jin and Zhiqing Yu of Tsinghua University, China, to celebrate over five decades of their careers in chemical engineering research and education.……     

A construction of codimension three arithmetically Gorenstein subschemes of projective space

This paper presents a construction method for a class of codimension three arithmetically Gorenstein subschemes of projective space. These schemes are obtained from degeneracy loci of sections of certain specially constructed rank three reflexive sheaves. In contrast to the structure theorem of Buchsbaum and Eisenbud, we cannot obtain every arithmetically Gorenstein codimension three subscheme by our method. However, certain geometric applications are facilitated by the geometric aspect of this construction, and we discuss several examples of this in the final section.

     

On the notion of relative property (T) for inclusions of von Neumann algebras

We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras recently defined by the second author is equivalent to a weaker property, in which no “continuity constants” are required. The proof is by contradiction and uses infinite products of completely positive maps, regarded as correspondences.     

Modelling of Threshold and Extraction Efficiency in Pr3+ ZBLAN Upconversion Fibre Lasers Using Two-Photon Pumping

We model the steady-state threshold and extracted power of a two-photon incoherently pumped upconversion fibre laser. Our threshold analysis is entirely analytic, and along with this derivation we obtain an analytic threshold cutback formula. This takes a particularly simple form when the ground state pump absorption follows exponential absorption. We also numerically simulate the extracted laser power. The experiment which we simulate is upconversion in Pr³⁺ doped ZBLAN fibre lasing at 491 nm and pumped with 1017 nm and 835 nm diode lasers. Our formulas and simulations are mutually consistent and agree with the experiment to within 10%.     

Change in Preservice Teachers' Beliefs: An Evaluation of a Mathematics Methods Course

This study investigated and evaluated the potential impact of an elementary mathematics methods course in promoting teacher beliefs and attitudes that are consistent with the underlying philosophy of current reform efforts in mathematics education. Using the Mathematics Beliefs Instrument (MBI; Hart, 2002 ), data from 89 preservice teachers were used to evaluate the course. Findings from the study suggest a positive relationship between participating in the mathematics methods course and change in teacher beliefs and attitudes. This study also provided additional validation of the MBI.     

Single-neutron states in (101)Sn

The first data on the relative single-particle energies outside the doubly magic (100)Sn nucleus were obtained. A prompt 171.7(6) keV gamma-ray transition was correlated with protons emitted following the beta decay of (101)Sn and is interpreted as the transition between the single-neutron g(7/2) and d(5/2) orbitals in (101)Sn. This observation provides a stringent test of current nuclear structure models. The measured nug(7/2)-nud(5/2) energy splitting is compared with values calculated using mean-field nuclear potentials and is used to calculate low-energy excited states in light Sn isotopes in the framework of the shell model. The correlation technique used in this work offers possibilities for future, more extensive spectroscopy near (100)Sn.     

A concise synthesis of the Pennsylvania Green fluorophore and labeling of intracellular targets with O6-benzylguanine derivatives

We report improved syntheses of the Pennsylvania Green and 4-carboxy-Pennsylvania Green fluorophores; the latter compound was prepared from methyl 4-iodo-3-methylbenzoate in a three-pot process (32% overall yield). Chinese hamster ovary cells expressing O6-alkylguanine-DNA alkyltransferase fusion proteins were treated with Pennsylvania Green and Oregon Green linked to O6-benzylguanine (SNAP-Tag substrates). Analysis of living cells by confocal microscopy revealed that Pennsylvania Green derivatives exhibit substantially higher cell permeability than analogous Oregon Green-derived molecular probes.     

Systematically convergent correlation consistent basis sets for molecular core-valence correlation effects: the third-row atoms gallium through krypton

The family of correlation consistent polarized valence basis sets has been extended in order to account for core-core and core-valence correlation effects within the third-row, main group atoms gallium through krypton. Construction of the basis sets is similar to that of the atoms boron through argon, where either the difference between core-correlated and valence-only correlation energies were calculated via configuration interaction (CISD) computations on the ground electronic states of the atoms (named cc-pCVnZ) or the sets were optimized with respect to the core-valence correlation energy and a small weight of core-core correlation energy (cc-pwCVnZ). Due to the correlation of 3d orbitals, added shells of higher angular momentum exponents compared to the valence sets are necessary to describe the core region. The pattern of added core-correlating functions is (1s1p1d1f) for double-zeta, (2s2p2d2f1g) for triple-zeta, (3s3p3d3f2g1h) for quadruple-zeta, and (4s4p4d4f3g2h1i) for quintuple-zeta. Atomic and molecular results show good convergence to the CBS limit, with the cc-pwCVnZ sets showing improved convergence compared to the cc-pCVnZ ones for molecular core-valence correlation effects. After testing the basis sets on the homonuclear diatomics Ga2-Kr2 with coupled cluster wave functions, it is concluded that a treatment of core-valence correlation effects is essential for high-accuracy ab initio investigations of third-row-containing molecules. Though the basis sets are optimal for 3s3p3d correlation, preliminary atomic and molecular results show the basis sets to be efficient with respect to 3d-only correlation, and these potentially could be used with 3d-only correlation for more qualitative studies on larger species.     

Inorganic metallodielectric materials fabricated using two single-step methods based on the Tollen's process

Two methods for preparing polycrystalline silver shells on colloidal silica spheres are reported. These do not include the use of organic ligands or metal seeding steps and are based on the Tollen's process for silvering glass. Reaction parameters such as temperature and reactant concentrations are adjusted to slow the reaction kinetics, which we find leads to preferential silver growth on the spheres. The resulting shells are polycrystalline and granular, showing highly uniform sphere coverage. Surface morphologies range from sparsely interconnected grains for shells approximately 20 nm thick, to complete (yet porous) shells of interconnected silver clusters which are up to approximately 140 nm in thickness. The extinction spectra of the core-shell materials are markedly different from those of smooth continuous shells, showing clear evidence that the granular shell geometry influences the plasmon resonance of the composite system. Spheres coated with shells 20-40 nm thick are also suitable for colloidal crystallization. Monolayers of self-assembled spheres with long-range ordering are demonstrated.