Bounding the Size of Equimatchable Graphs of Fixed Genus

A graph G is said to be equimatchable if every matching in G extends to (i.e., is a subset of) a maximum matching in G. In an earlier paper with Saito, the authors showed that there are only a finite number of 3-connected equimatchable planar graphs. In the present paper, this result is extended by showing that in a surface of any fixed genus (orientable or non-orientable), there are only a finite number of 3-connected equimatchable graphs having a minimal embedding of representativity at least three. (In fact, if the graphs considered are non-bipartite, the representativity three hypothesis may be dropped.) The proof makes use of the Gallai-Edmonds decomposition theorem for matchings.      

Magneto‐Structural Correlations in a 1,3,2‐Dithiazolyl Radical Crystal,BBDTA⋅GaBr4: Structure and Magnetic Properties of its Three Polymorphs

Three attractions in one cage : Various magnetic networks are formed in the three polymorphs of an organic magnet, BBTDA(=benzo[1,2‐d:4,5‐d′]bis[1,3,2]dithiazole)?GaBr₄. The three phases show quite different magnetic behaviors in spite of having the same chemical formula. Their magnetic differences originate from the relative configuration of the neighboring organic radical molecules in their crystals.

     

Alkylation of aromatic compounds with multi-component Lewis acid catalysts of ZnCl2 and ionic liquids with different organic cations

Alkylation of aromatic compounds with various alkylating agents such as benzyl chloride, benzyl alcohol and isopropyl chloride were investigated using ZnCl₂ based ionic liquid (ILs) Lewis acid catalysts. Multi-component Lewis acid catalysts of ZnCl₂ and ionic liquids such as 1-butyl-3-methylimidazolium bromide, 1-butylpyridinium bromide, cholin chloride and tetrabutylammonium bromide were prepared, supported on silica gel, and compared for alkylation reactions with various alkylating agents. Among the IL-based catalysts, 1-butyl-3-methyl imidazolium-bromide-ZnCl₂ and 1-butylpyridinium bromide-ZnCl₂ are highly active.     

Copper(I) complexes with fluorinated hydrotris(pyrazolyl)borate: Influence of electronic effects on their structure,physicochemical properties,and reactivity

Copper(I) coordination complexes of the anionic fluorinated ligand, hydrotris(3-trifluoromethyl-5-methyl-1-pyrazolyl)borate (L0f⁻), i.e. the copper(I) carbonyl complex, [Cu^I(L0f)(CO)] (1), the copper(I) triphenylphosphine complex, [Cu^I(L0f)(PPh₃)] (2), the copper(I) acetonitrile complex, [Cu^I(L0f)(NCMe)] (3), and the corresponding copper(I) triphenylphosphine complex with hydrotris(3,5-diisopropyl-1-pyrazolyl)-borate anion (L1⁻), i.e. [Cu^I(L1)(PPh₃)] (4), were synthesized in order to investigate the influence of the electron-withdrawing groups on the pyrazolyl rings. The structures of complexes 1, 2, and 4 were determined by X-ray crystallography. While X-ray crystallography did not show definitive trends in terms of copper(I) atom geometry, the clear influence of the electronic structure of the pyrazolyl rings is observed by spectroscopic techniques, namely, IR and multinuclear NMR spectroscopy. Finally, the relative stability of the copper(I) complexes is discussed.     

Polymer electrolytes based on vinyl ethers with various EO chain length and their polymer electrolytes cross-linked by electron beam irradiation

Polymer electrolytes based on vinyl ethers with various ethyleneoxy (EO) chain length (poly-1a (m?=?3), poly-1b (m?=?6), poly-1c (m?=?10), and poly-1d (m?=?23.5)) with lithium bis(trifluoromethanesulfonimide) (LiTFSI) were prepared, and effect of pendant EO chain length in the polymers on electrochemical and thermal properties was investigated. Glass transition temperature (T _g) of all polymer electrolytes increased linearly with an increase in salt concentrations. Ionic conductivities of the polymer electrolytes increased with an increase in the pendant EO chain length of the polymers at the constant [Li]/[O] ratio, but in the polymer electrolyte of the poly-1d (m?=?23.5) with the longest pendant EO chain length, ionic conductivity decreased in the low temperature range of ?20 to 10 °C due to the crystallization of the pendant EO chain. The highest ionic conductivity, 1.23?×?10^?4 S/cm at 30 °C, was obtained in the polymer electrolyte of the poly-1c (m?=?10) with pendant EO chain length of 10 at the [Li]/[O] ratio of 1/20. It was found that the cross-linking of the polymer electrolyte, composed of poly-1c (m?=?10) with LiTFSI at the [Li]/[O] ratio of 1/28, by electron beam (EB) irradiation may improve the mechanical property without affecting ionic conductivity, thermal property, and oxidation stability. Polymer electrolytes based on poly-1a (m?=?3), poly-1b (m?=?6), poly-1c (m?=?10), and poly-1d (m?=?23.5) and cross-linked polymer electrolytes were electrochemically stable until 4 V and thermally stable around 300 °C.     

Two-photon-excited fluorescence from silicate glass containing tantalum ions pumped by a near-infrared femtosecond pulsed laser

We report a novel phenomenon in sodium-calcium-silicate glass doped with Ta(5+). Under irradiation with a 780 nm femtosecond pulsed laser, strong blue emission centered at about 420 nm could be observed. The spectral characteristics are similar to those pumped by ultraviolet photons. The log-log correlation between integrated emission intensity and pump power reveals that a two-photon absorption process is involved in the phenomenon. It is suggested that the presence of localized Ta(5+)5d(0) energy levels is responsible for the appearance of the blue emission. The results indicate that transition metal ions without d electrons play an important role in fields of optics when embedded into glass hosts.     

Dynamic nuclear polarization properties of nitroxyl radicals used in Overhauser-enhanced MRI for simultaneous molecular imaging

DNP parameters relevant to Overhauser-enhanced magnetic resonance imaging (OMRI) are reported for a few nitroxyl radicals and their corresponding (15)N and (2)H enriched analogues, used in simultaneous imaging by OMRI. DNP enhancement was measured at 14.529 mT, using a custom-built scanner operating in a field-cycled mode, for different concentrations, ESR irradiation times and RF power levels. DNP enhancements increased with agent concentration up to 2.5 mM and decreased above 3 mM, in tune with ESR line broadening measured at X-band as a function of the agent concentration. The proton spin-lattice relaxation times (T(1)) measured at very low Zeeman field (14.529 mT) and the longitudinal relaxivity parameters were estimated. The relaxivity parameters were in good agreement with those independently computed from the linear region of the concentration dependent enhancement. The leakage factor showed an asymptotic increase with increasing agent concentration. The coupling parameters of (14)N- and (15)N-labeled carbamoyl-PROXYL showed the interaction between the electron and nuclear spins to be mainly dipolar in origin. Upon (2)H labeling, about 70% and 40% increases in enhancement for (15)N- and (14)N-labeled nitroxyl agents were observed, respectively. It is envisaged that the results reported here may enable better understanding of the factors determining DNP enhancement to design suitable 'beacons' for simultaneous molecular imaging by OMRI.     

Linearly polarized 100-kW-Peak-power pulsed fiber laser with a novel master oscillator

We report progress in the design and fabrication of a monolithic, linearly polarized, pulsed, Yb-doped fiber laser. This laser has a peak power of more than 100 kW, a tunable repetition rate from 100 kHz to 1 MHz, a tunable pulse duration from 2 ns to 2.5 μs, and a diffraction-limited, linearly polarized output beam with a mean power of 21 W and a wavelength of 1064 nm. A seed source that consists of a microchip Nd:YVO₄ laser and an electro optic deflector is developed. Using this source, the repetition rate and pulse duration are varied independently of each other. In addition, an excellent pulse-to-pulse repeatability is achieved.     

Separation‐free single‐base extension assay with fluorescence resonance energy transfer for rapid and convenient determination of DNA methylation status at specific cytosine and guanine dinucleotide sites

A separation‐free single‐base extension (SBE) assay utilizing fluorescence resonance energy transfer (FRET) was developed for rapid and convenient interrogation of DNA methylation status at specific cytosine and guanine dinucleotide sites. In this assay, the SBE was performed in a tube using an allele‐specific oligonucleotide primer (i.e., extension primer) labeled with Cy3 as a FRET donor fluorophore at the 5′‐end, a nucleotide terminator (dideoxynucleotide triphosphate) labeled with Cy5 as a FRET acceptor, a PCR amplicon derived from bisulfite‐converted genomic DNA, and a DNA polymerase. A single base‐extended primer (i.e., SBE product) that was 5′‐Cy3‐ and 3′‐Cy5‐tagged was formed by incorporation of the Cy5‐labeled terminator into the 3′‐end of the extension primer, but only if the terminator added was complementary to the target nucleotide. The resulting SBE product brought the Cy3 donor and the Cy5 acceptor into close proximity. Illumination of the Cy3 donor resulted in successful FRET and excitation of the Cy5 acceptor, generating fluorescence emission from the acceptor. The capacity of the developed assay to discriminate as low as 10% methylation from a mixture of methylated and unmethylated DNA was demonstrated at multiple cytosine and guanine dinucleotide sites.     

A new constitutive analysis of hexagonal close-packed metal in equal channel angular pressing by crystal plasticity finite element method

Most of hexagonal close-packed (HCP) metals are lightweight metals. With the increasing application of light metal products, the production of light metal is increasingly attracting the attentions of researchers worldwide. To obtain a better understanding of the deformation mechanism of HCP metals (especially for Mg and its alloys), a new constitutive analysis was carried out based on previous research. In this study, combining the theories of strain gradient and continuum mechanics, the equal channel angular pressing process is analyzed and a HCP crystal plasticity constitutive model is developed especially for Mg and its alloys. The influence of elevated temperature on the deformation mechanism of the Mg alloy (slip and twin) is novelly introduced into a crystal plasticity constitutive model. The solution for the new developed constitutive model is established on the basis of the Lagrangian iterations and Newton Raphson simplification.