A duality property of an uncountable product of $${\mathbb{Z}}$$

We construct a quotient group of an uncountable product of integers which is not Pontryagin reflexive.     

Parity alternation of ground-state P(n)(-) and P(n)(+) (n = 3-15) phosphorus clusters

The ground-state structures of neutral, cationic, and anionic phosphorus clusters P(n), P(n)(+), and P(n)(-) (n = 3-15) have been calculated using the B3LYP/6-311+G* density functional method. The P(n)(+) and P(n)(-) (n = 3-15) clusters with odd n were found to be more stable than those with even n, and we provide a satisfactory explanation for such trends based on concepts of energy difference, ionization potential, electron affinity, and incremental binding energy. The result of odd/even alternations is in good accord with the relative intensities of cationic and anionic phosphorus clusters observed in mass spectrometric studies.     

Topological structures of tetrahedral (Td and T) fullerenes with hexagonal and triangular faces and their vibration and NMR spectra

On analyzing the topological structures of the three types of tetrahedral fullerenes (which consist only of triangles and hexagons), (1) C _n (T _d ,n=12h ²; h=1,2,…), (2) C _n (T _d ,n=4h ²;h=1,2,…), and (3) C _n (T,n=4(h ²+hk+k ²);h>k,h,k=1,2,…), we have obtained theoretically the Infrared and Raman active modes by means of the derived formulas for the decomposition of their nuclear motions into irreducible representations, and the ¹³C NMR spectra with natural abundance for ¹³C by using the distribution functions for all of the tetrahedral (T _d and T) fullerenes, respectively. Received: 25 May 1998 / Accepted: 30 July 1998 / Published online: 23 November 1998     

Vibrational spectra of icosahedral (Ih and I) fullerenes

On the bases of the topological structures of the three big classes of icosahedral fullerenes: (1) C_n(I_h, n=60h²; h=1, 2,…), (2) C_n(I_h, n=20h²; h=1, 2,…), and (3) C_n(I, n=20(h²+hk+k²), h>k; h, k=1, 2,…), we derived formulas for the decomposition of their nuclear motions into irreducible representations. Hence, we obtained the infrared and Raman active modes for all of the icosahedral (I_h and I) fullerenes theoretically. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 113–117, 1998     

Durable Mesenchymal Stem Cell Labelling by Using Polyhedral Superparamagnetic Iron Oxide Nanoparticles

Small polyhedral superparamagnetic iron oxide (SPIO) nanoparticles (<10 nm) coated with a thin layer of silica were prepared (SPIO@SiO₂ and SPIO@SiO₂‐NH₂). Surface modification of the small polyhedral silica‐coated SPIO nanoparticles with amines led to substantially higher mesenchymal stem cell (MSC) labelling efficiency without the use of additional transfecting agents. Therefore, amine surface‐modified nanoparticles (SPIO@ SiO₂‐NH₂) appeared to be the preferred candidate for MSC labelling. In vitro studies demonstrated that controlled labelling of SPIO@SiO₂ and SPIO@SiO₂‐NH₂ did not cause MSC death or proliferation inhibition. MSCs labelled with SPIO@SiO₂‐NH₂ nanoparticles retained differentiation potential and showed osteogenic, adipogenic and chondrogenic differentiations. The noncytotoxic polyhedral SPIO@SiO₂‐NH₂ nanoparticle‐labelled MSCs were successfully implanted in rabbit brain and erector spinae muscle, and demonstrated long‐lasting, durable MRI labelling efficacy after 8–12 weeks.     

Passive guiding and sorting of small particles with optical binding forces

We demonstrate the possibility of serially guiding and sorting nanometer-sized particles without the use of any external control. The working principle is based on an equilibrium between scattering and binding forces, the latter depending on the properties of the particles. A configuration is proposed that utilizes this property and is shown to efficiently sort small particles as function of their size.     

Morphology-directed synthesis of Co3O4 nanotubes based on modified Kirkendall effect and its application in CH4 combustion

We reported the morphology-directed synthesis of Co(3)O(4) nanotubes via interfacial reaction of NaOH with pre-fabricated CoC(2)O(4)·2H(2)O nanorods based on modified Kirkendall effect. The as-obtained Co(3)O(4) nanotubes showed excellent activity and durability in catalytic combustion of CH(4).