Dirac's Condition for Completely Independent Spanning Trees

Two spanning trees T₁ and T₂ of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T₁ and T₂ are internally disjoint. In this article, we show two sufficient conditions for the existence of completely independent spanning trees. First, we show that a graph of n vertices has two completely independent spanning trees if the minimum degree of the graph is at least . Then, we prove that the square of a 2‐connected graph has two completely independent spanning trees. These conditions are known to be sufficient conditions for Hamiltonian graphs.     

Measurement of speed of sound in poly(lactic acid)-clay composite

We measured longitudinal speed of sound for matrix[poly(lactic acid)]-additive(clay particles) composite rectangular-solid specimen prepared by injection molding. It was found that the speed of sound measured in the direction along the longer side of the specimen was the highest at the middle of the specimen. This trend corresponded with that for crystallinity determined through differential scanning calorimetry (DSC). A cross section view of the specimen parallel to its longer side showed that there was a transverse flow trace of resin in the vicinity of the injection gate while the flow trace along the direction of the longer side spread wider as getting far from the gate toward the middle of the specimen. The high crystallinity appeared in the middle of the specimen was inferred to come from the promotion of crystallization by molecular orientation induced with the above flow trace parallel to the direction along the longer side of the specimen.     

Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube

A Talbot-Lau interferometer using two-dimensional gratings and a conventional x-ray tube has been used to investigate a phase-contrast imaging technique that is sensitive to phase gradients in two orthogonal directions. Fourier analysis of Moiré fringe patterns was introduced to obtain differential phase images and scattering images from a single exposure. Two-dimensional structures of plastic phantoms and characteristic features of soft tissue were clearly obtained at 17.5 keV. The phase-stepping technique was also examined to investigate the spatial resolution of different phase retrieval methods. In the presented setup we found that the choice of phase retrieval method made little difference in image blur, and a large effective source size was found to give a high intensity in the image plane.     

Fabrication of silver nanoparticles deposited on boehmite sol for surface enhanced Raman scattering

The composite consisting of silver nanoparticles deposited on boehmite hybrid was synthesized by NaBH₄ reduction technique. The morphology of the composite was studied by TEM, UV/Vis spectrophotometer and particle sizer. The size of the silver nanoparticles deposited on the surface of the boehmite ranged from 10 nm to 100 nm. The contact of silver nanoparticles increased by means of deposition of silver nanoparticles on the boehmite sol and the aggregation of the composites. This leads to the appearance of a shoulder at 450 nm in the UV-Vis absorption spectra with the addition of 0.15 mg and 1.5 mg boehmite. It was found that the intensity of the SERS in the case of the composite was higher than for silver colloids consisting of a concentration of silver greater than 3.2 mM.     

Novel oligonucleotide carrier as scavenger for reactive oxygen species

A novel oligonucleotide carrier which can scavenge ROS is described. The synthesized graft polymer is composed of a PEG segment and a TEMPO‐containing hydrophobic segment for scavenging ROS. This graft polymer can form a PIC through electrostatic interaction with oligonucleotides such as siRNA. The amount of ROS was monitored by fluorescence measurements using H₂DCFDA as a probe, and it was confirmed that the ROS level was effectively suppressed. The cellular uptake of PIC containing the fluorescence‐labeled oligonucleotide was evaluated by fluorescence microscopy. Delivered siRNA suppressed the expression of the mRNA. The prepared graft copolymer is thus a promising candidate as a novel oligonucleotide carrier which also reduces ROS damage generated by cationic polymer carriers.

     

The fast multipole method on parallel clusters,multicore processors,and graphics processing units

In this article, we discuss how the fast multipole method (FMM) can be implemented on modern parallel computers, ranging from computer clusters to multicore processors and graphics cards (GPU). The FMM is a somewhat difficult application for parallel computing because of its tree structure and the fact that it requires many complex operations which are not regularly structured. Computational linear algebra with dense matrices for example allows many optimizations that leverage the regular computation pattern. FMM can be similarly optimized but we will see that the complexity of the optimization steps is greater. The discussion will start with a general presentation of FMMs. We briefly discuss parallel methods for the FMM, such as building the FMM tree in parallel, and reducing communication during the FMM procedure. Finally, we will focus on porting and optimizing the FMM on GPUs.     

Symmetry and broken symmetry in molecular orbital description of unstable molecules IV: comparison between single- and multi-reference computational results for antiaromtic molecules

First principle calculations of the effective exchange integrals (J) in the Heisenberg model for diradical species are presented for both symmetry-adapted multi-reference (MR) and single-reference broken-symmetry (BS) methods. The Mukherjee-type state-specific MR coupled cluster singles and doubles (MkCCSD) method with several different reference orbitals including BS natural orbitals is used to calculate the singlet?Ctriplet energy gaps (S?CT energy gap or 2J) and diradical characters for the antiaromatic molecules [a cyclopropenyl anion (CPA), b cyclobutadiene (CBD), and c cyclopentadienyl cation (CPC)], the cyclobutadiene derivatives with polar substitutents [d aminocyclobutadiene (ACBD), e formylcyclobutadiene (FCBD), and f 1-amino-2-formyl-cyclobutadiene (AFCBD)] and finally the cyclobutadine derivatives with radical substitutents [g 1,2-bis(methylene)cyclobutadiene (1,2-BMCBD) and h 1,3-bis(methylene)cyclobutadiene (1,3-BMCBD)]. For the BS methods, the spin-unrestricted Hartree?CFock based CCSD (UHF-CCSD), the CCD with the spin-unrestricted Brueckner determinant (UBD), and BS density functional theory (UDFT) computations are performed. Comparison between MkCCSD and the UHF-CCSD results indicates that spin-contamination of UHF-CCSD solutions still remains. In comparison with UHF-CCSD, the UBD results show that spin-contamination involved in BS solutions is greatly suppressed. To eliminate the spin contamination, an approximate spin-projection (AP) scheme is applied to the BS solutions. The AP procedure with the use of the expectation value of the total-spin operator corresponding to UHF-CCSD and UBD results yields good agreement with the MkCCSD results. As for the AP correction of the UDFT methods, three different computational schemes for predicting the expectation value of the total-spin operator are examined. Systematic comparisons between these methods are presented for the S?CT energy gaps (2J). Implications of the present computational results have been discussed in relation to the design of magnetic oligomers and polymers.     

Singlet�Ctriplet energy gap for trimethylenemethane, oxyallyl diradical, and related species: single- and multireference computational results

We have investigated the through-bond exchange interactions in three non-Kekulé hydrocarbon diradicals on the basis of single- and multireference coupled cluster and related broken-symmetry (BS) methods. The singlet?Ctriplet energy gap (S-T gap) and diradical characters for these species are evaluated. It is found that the spin contamination involved in the BS solutions is non-negligible and the approximate spin-projection method greatly improves the usual BS solutions. As for Mukherjee??s state-specific multireference coupled cluster (MkMRCC) computations, the size-consistent correction with the UHF localized natural orbitals (ULO) is useful to obtain the qualitatively correct 2J values.     

Highly transparent and flexible field emission devices based on single-walled carbon nanotube films

Single-walled carbon nanotubes (SWNTs) have been used successfully to fabricate highly transparent and flexible field emission displays (FEDs). Field emission measurements indicated that SWNTs films have great potential to work as building blocks for next generation transparent and flexible FEDs.