A note on traversing specified vertices in graphs embedded with large representativity

A graph G is said to have property P(2,k) if given any k+2 distinct vertices a,b,v₁,…,v_k, there is a path P in G joining a and b and passing through all of v₁,…,v_k. A graph G is said to have property C(k) if given any k distinct vertices v₁,…,v_k, there is a cycle C in G containing all of v₁,…,v_k. It is shown that if a 4-connected graph G is embedded in an orientable surface Σ (other than the sphere) of Euler genus eg(G,Σ), with sufficiently large representativity (as a function of both eg(G,Σ) and k), then G possesses both properties P(2,k) and C(k).     

A self-adaptive moving mesh method for the Camassa-Holm equation

A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points.     

Two-dimensional crystal growth and stacking of bis(phthalocyaninato) rare earth sandwich complexes at the 1-phenyloctane/graphite interface

Initial stages of two-dimensional crystal growth of the double-decker sandwich complex Lu(Pc*)2 [Pc* = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato] have been studied by scanning tunneling microscopy at the liquid/solid interface between 1-phenyloctane and highly oriented pyrolytic graphite. High-resolution images strongly suggest alignment of the double-decker molecules into monolayers with the phthalocyanine rings parallel to the surface. Domains were observed with either hexagonal or quadrate packing motifs, and the growing interface of the layer was imaged. Molecular resolution was achieved, and the face of the phthalocyanine rings appeared as somewhat diffuse circular features. The alkyl chains are proposed to be interdigitating to maintain planar side-by-side packing.     

Optical resolution via catalytic generation of chiral auxiliary

A new catalytic method for separating enantiomers of racemic compounds is proposed. Catalytic asymmetric addition of racemic trans-2-substituted cyclohexanols to imines provided diastereomeric mixtures of aminals, and the subsequent separation of the enantiomers by silica-gel column chromatography and the hydrolysis of the aminals produced the alcohols in an optically active form.     

Electronic absorption and emission spectra of Alq3 in solution with special attention to a delayed fluorescence

Tris(8-quinolinolato)aluminum(III) (Alq₃) shows electronic absorption bands at 378, 360 (in a 1:1 mixed solvent of methanol and ethanol (ME) at 77 K), 334, 316, 300, 263, 255.8, and 233 nm in ethanol at room temperature. According to the polarized fluorescence excitation spectrum together with MO calculations, for instance, the 360 nm band is assigned to an LL CT transition (an intramolecular charge transfer transition between two ligands), and the 378 nm band to an LM/ML CT one (an intramolecular charge transfer transition between ligand and metal). Alq₃ shows a broad fluorescence band peaking at around 478 nm in the ME matrix at 77 K. The emission spectrum measured with a phosphoroscope has two emission bands at 567 and 478 nm. The 567 nm band accompanies vibronic bands at 578 and 605 nm, being safely assigned to a phosphorescence of Alq₃. The lifetimes of the 478 and 567 nm bands are both 5.4 ms. The lifetime of the 478 nm band together with the band position and its band shape indicate that this band can be assigned to a delayed fluorescence.     

Diode-pumped 65 fs Kerr-lens mode-locked Yb(3+):Lu(2)O(3) and nondoped Y(2)O(3) combined ceramic laser

Diode-pumped Kerr-lens mode-locked laser operation of Yb(3+):Lu(2)O(3) and nondoped Y(2)O(3) combined ceramics has been achieved; 65 fs pulses with an average power of 320 mW under 5 W of pump power were obtained at the center wavelength of 1032 nm. The spectral bandwidth and the time bandwidth product were 18.9 and 0.345 nm, respectively. To our knowledge, this is the first demonstration of a Kerr-lens mode-locked laser operation based on Yb(3+):Lu(2)O(3) ceramic.     

Spectral coherent-state quantum cryptography

A novel implementation of quantum-noise optical cryptography is proposed, which is based on a simplified architecture that allows long-haul, high-speed transmission in a fiber optical network. By using a single multiport encoder/decoder and 16 phase shifters, this new approach can provide the same confidentiality as other implementations of Yuen's encryption protocol, which use a larger number of phase or polarization coherent states. Data confidentiality and error probability for authorized and unauthorized receivers are carefully analyzed.     

Structural-Deformation-Energy-Modulation Strategy in a Soft Porous Coordination Polymer with an Interpenetrated Framework

To achieve unique molecular-recognition patterns, a rational control of the flexibility of porous coordination polymers (PCPs) is highly sought, but it remains elusive. From a thermodynamic perspective, the competitive relationship between the structural deformation energy (E_def) of soft PCPs and the guest interaction is key for selective a guest-triggered structural-transformation behavior. Therefore, it is vital to investigate and control E_def to regulate this competition for flexibility control. Driven by these theoretical insights, we demonstrate an E_def-modulation strategy via encoding inter-framework hydrogen bonds into a soft PCP with an interpenetrated structure. As a proof of this concept, the enhanced E_def of PCP enables a selective gate-opening behavior toward CHCl₃ over CH₂Cl₂ by changing the adsorption-energy landscape of the compounds. This study provides a new direction for the design of functional soft porous materials.     

Albidosides H and I,two new triterpene saponins from the barks of Acacia albida Del. (Mimosaceae)

Two new triterpene saponins, albidosides H (1) and I (2), along with the three known saponins were isolated from the barks of Acacia albida. Their structures were elucidated on the basis of extensive 1D- and 2D-NMR studies and mass spectrometry. Albidosides H (1) and I (2) were assayed for their cytotoxicity against HeLa and HL60 cells using MTT method.     

Selective epitaxial growth by UHV-CVD using Si2H6 and Cl2

The conditions under which selective epitaxial growth (SEG) is achieved in UHV-CVD with Si₂H₆ are determined by the amount of Si₂H₆ molecules being supplied, and there is a critical gas supply amount (F_c) beyond which SEG will break down and lose its selectivity. The value of F_c is itself determined by two factors, growth temperature and the material used for masking, i.e. SiO₂, Si₃N₄. We found that this limiting factor of F_c was increased through the addition of a small amount of Cl₂, and that after such addition, the resulting decrease in growth rate is minimal.