The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity

In this article, we study the existence of a 2‐factor in a K_{1, n}‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K_{1, n}‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K_{1, n}‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K_{1, n}‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K_{1, n}‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K_{1, n}‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011     

A numerical study on extinction behaviour of laminar micro-diffusion flames

We conducted a numerical study on the fluid dynamic, thermal and chemical structures of laminar methane–air micro flames established under quiescent atmospheric conditions. The micro flame is defined as a flame on the order of one millimetre or less established at the exit of a vertically-aligned straight tube. The numerical model consists of convective–diffusive heat and mass transport with a one-step, irreversible, exothermic reaction with selected kinetics constants validated for near-extinction analyses. Calculations conducted under the burner rim temperature 300 K and the adiabatic burner wall showed that there is the minimum burner diameter for the micro flame to exist. The Damköhler number (the ratio of the diffusive transport time to the chemical time) was used to explain why a flame with a height of less than a few hundred microns is not able to exist under the adiabatic burner wall condition. We also conducted scaling analysis to explain the difference in extinction characteristics caused by different burner wall conditions. This study also discussed the difference in governing mechanisms between micro flames and microgravity flames, both of which exhibit similar spherical flame shape.     

Electrical properties and emission mechanisms of Zn-doped β-Ga2O3 films

We study the electrical properties and emission mechanisms of Zn-doped β-Ga₂O₃ film grown by pulsed laser deposition through Hall effect and cathodoluminescence which consist of ultraviolet luminescence (UV), blue luminescence (BL) and green luminescence (GL) bands. The Hall effect measurements indicate that the carrier concentration increases from 7.16×10¹¹ to 6.35×10¹² cm⁻³ with increasing a nominal Zn content from 3 to 7 at%. The UV band at 272 nm is not attributed to Zn dopants and ascribed as radiative electron transition from conduction band to a self-trapped hole while the BL band is attributable to defect level related to Zn dopant. The BL band has two emission peaks at 415 and 455 nm, which are ascribed to the radiative electron transition from oxygen vacancy (V_O) to valence band and recombination of a donor–acceptor pair (DAP) between V_O donor and Zn on Ga site (Zn_Ga) acceptor, respectively. The GL band is attributed to the phonon replicas’ emission of the DAP. The acceptor level of Zn_Ga is estimated to be 0.26 eV above the valence band maximum. The transmittance and absorption spectra prove that the Zn-doped β-Ga₂O₃ film is a dominantly direct bandgap material. The results of Hall and cathodoluminescence measurements imply that the Zn dopant in β-Ga₂O₃ film will form an acceptor Zn_Ga to produce p-type conductivity.     

Low Power Penalty Operation of a Wide Input Dynamic Range Cross-Phase Modulation Wavelength Converter

We successfully demonstrated low power penalty operation of a cross-phase modulated (XPM) wavelength converter using a semiconductor optical amplifier (SOA) power equalizer. We also clarified the SOA equalizing level for more adaptive wavelength conversion and achieved a power penalty of less than 1 dB over the wide input dynamic range of 15 dB.     

On the ‐boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer

In this paper, we prove the ‐boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer with resolvent parameter , where , and our boundary conditions are nonhomogeneous Neumann on upper boundary and Dirichlet on lower boundary. We want to emphasize that we can choose 0 < ? < π ∕ 2 and γ₀ > 0 arbitrarily, although usual parabolic theorem tells us that we must choose a large γ₀ > 0 for given 0 < ? < π ∕ 2. We also prove the maximal L_p ? L_q regularity theorem of the nonstationary Stokes problem as an application of the ‐boundedness. The key of our approach is to apply several technical lemmas to the exact solution formulas of a resolvent problem. The formulas are obtained through the solutions of the ODEs, in the Fourier space, driven by the partial Fourier transform with respect to tangential space variable . Copyright © 2014 John Wiley & Sons, Ltd.     

Quasi-two-dimensional Fermi surfaces and coherent interlayer transport in KFe₂As₂

We report the results of the angular-dependent magnetoresistance oscillations (AMROs), which can determine the shape of bulk Fermi surfaces (FSs) in quasi-two-dimensional (Q2D) systems, in a highly hole-doped Fe-based superconductor KFe2As2 with Tc ≈ 3.7 K. From the AMROs, we determined the two Q2D FSs with rounded-square cross sections, correspond to 12% and 17% of the first Brillouin zone. The rounded-squared shape of the FS cross section is also confirmed by the analyses of the interlayer transport under in-plane fields. From the obtained FS shape, we infer the character of the 3d orbitals that contribute to the FSs.     

Closure, stability and iterated line graphs with a 2-factor

We consider 2-factors with a bounded number of components in the n-times iterated line graph Lⁿ(G). We first give a characterization of graph G such that Lⁿ(G) has a 2-factor containing at most k components, based on the existence of a certain type of subgraph in G. This generalizes the main result of [L. Xiong, Z. Liu, Hamiltonian iterated line graphs, Discrete Math. 256 (2002) 407-422]. We use this result to show that the minimum number of components of 2-factors in the iterated line graphs Lⁿ(G) is stable under the closure operation on a claw-free graph G. This extends results in [Z. Ryjá?ek, On a closure concept in claw-free graphs, J. Combin. Theory Ser. B 70 (1997) 217-224; Z. Ryjá?ek, A. Saito, R.H. Schelp, Closure, 2-factors and cycle coverings in claw-free graphs, J. Graph Theory 32 (1999) 109-117; L. Xiong, Z. Ryjá?ek, H.J. Broersma, On stability of the hamiltonian index under contractions and closures, J. Graph Theory 49 (2005) 104-115].     

Effects of substrate temperature upon the properties of ZnMgTe layer grown by MOVPE

The effects of substrate temperature upon the optical property, composition and surface morphology have been investigated on nominally undoped Zn_1−xMg_xTe layers grown on (1 0 0) ZnTe substrates by atmospheric pressure metal organic vapor phase epitaxy (MOVPE). It was found that Mg composition increases with decreasing substrate temperature. The result of low temperature photoluminescence (PL) measurement suggests that the optical quality of Zn_1−xMg_xTe layers becomes better with decreasing substrate temperature. On the other hand, there is a narrow range of optimal substrate temperature for a smooth surface morphology. For all the layers, a two-mode behavior with ZnTe- and MgTe-like longitudinal optical phonon modes was confirmed by Raman scattering.     

Reporting of quantitative oxygen mapping in EPR imaging

Oxygen maps derived from electron paramagnetic resonance spectral-spatial imaging (EPRI) are based upon the relaxivity of molecular oxygen with paramagnetic spin probes. This technique can be combined with MRI to facilitate mapping of pO(2) values in specific anatomic locations with high precision. The co-registration procedure, which matches the physical and digital dimensions of EPR and MR images, may present the pO(2) map at the higher MRI resolution, exaggerating the spatial resolution of oxygen, making it difficult to precisely distinguish hypoxic regions from normoxic regions. The latter distinction is critical in monitoring the treatment of cancer by radiation and chemotherapy, since it is well-established that hypoxic regions are three or four times more resistant to treatment compared to normoxic regions. The aim of this article is to describe pO(2) maps based on the intrinsic resolution of EPRI. A spectral parameter that affects the intrinsic spatial resolution of EPRI is the full width at half maximum (FWHM) height of the gradient-free EPR absorption line in frequency-encoded imaging. In single point imaging too, the transverse relaxation times (T(2)(?)) limit the resolution since the signal decays by exp(-t(p)/T(2)(?)) where the delay time after excitation pulse, t(p), is related to the resolution. Although the spin densities of two point objects may be resolved at this separation, it is inadequate to evaluate quantitative changes of pO(2) levels since the linewidths are proportionately affected by pO(2). A spatial separation of at least twice this resolution is necessary to correctly identify a change in pO(2) level. In addition, the pO(2) values are blurred by uncertainties arising from spectral dimensions. Blurring due to noise and low resolution modulates the pO(2) levels at the boundaries of hypoxic and normoxic regions resulting in higher apparent pO(2) levels in hypoxic regions. Therefore, specification of intrinsic resolution and pO(2) uncertainties are necessary to interpret digitally processed pO(2) illustrations.     

Amphoteric poly(vinyl alcohol) gel as a force generator: Observation of microporous gel formation with cryo-SEM

Amphoteric PVA hydrogels were made from mixed aqueous solutions of poly(acrylic acid), poly(allylamine) hydrochloride and poly(vinyl alcohol) by repetitive freezing and thawing. The hydrogen bond induced gelation produced an elastic and tough microporous hydrogel which generated tension as high as 0.3MPa corresponding to the solvent exchange from water to acetone. In this paper we show the microscopic structure of hydrogels determined by means of cryo-SEM technique and X-ray analysis.