X-ray Crystallographic Observation of Chiral Transformations within a Metal–Peptide Pore

Porous metal complexes enable single-crystal X-ray crystallographic observation of included guests or reaction intermediates through simple soaking with the guests/substrates. Previous studies on this technique have often encountered difficulties in the observation of chiral structures because the host frameworks had no chirality. We synthesized a new metal–peptide porous complex through a folding-and-assembly strategy and utilized the chiral pore for trapping chiral guests. Chiral alcohols and ketones were successfully included within the pore. Crystallographic analyses clearly revealed not only their chemical structures but also chiral transformation events within the pore such as fixed conformations or an unstable hemiacetal formation.     

Doppler-limited dye laser excitation spectroscopy of the HSO radical

The cw dye laser excitation spectrum of the vibronic transition of the HSO radical was observed between 16 420 and 16 520 cm⁻¹ with Doppler-limited resolution, 0.03 cm⁻¹. The HSO radical was produced by reaction of discharged oxygen with H₂S or CH₃SH. The observed spectra were assigned to 751 transitions of the K′_a ← K″_a = 2 ← 3, 1 ← 2, 0 ← 1, 1 ← 0, 2 ← 1, and 3 ← 2 subbands, and were analyzed to determine rotational constants, centrifugal distortion constants, and spin-rotation interaction constants with good precision. The signs of the spin-rotation interaction constants were determined for both the upper and the lower state from the observed spectra. The band origin obtained is 16 483.0252 (2.5σ = 0.0013) cm⁻¹. The molecular constants which were determined reproduce the observed transitions with an average deviation of 0.0045 cm⁻¹.     

Scharlemann-Thompson Invariant for Knots with Unknotting Tunnels and the Distance of (1,1)-Splittings

Scharlemann and Thompson introduced an invariant (K,) Q/2Z forthe pair of a knot K in the 3-sphere and an unknotting tunnel for K. The paper studies the relationship between the invariant(K, ) of a (1,1)-knot and the distance of its (1,1)-splittingintroduced by the author.     

Growth process of TiC clusters from Ti nanoparticles with evaporated carbon layer

Titanium carbide formation by the solid–solid reaction on the surface of Ti nanoparticles was studied in situ using a high-resolution transmission electron microscope with a heating stage. The cross-sectional image of the Ti surface was clearly observed. Vacuum-deposited carbon covered the whole the surface of Ti nanoparticles in spite of the partly evaporation on the nanoparticle surface. The diffusion of the carbon atoms inside the Ti nanoparticles depended on the size of the nanoparticles. When the Ti nanoparticle diameter was less than 30 nm, carbon atoms diffused into the Ti nanoparticle and formed TiC. The superstructure of the Ti nanoparticles was observed, which revealed the growth process of TiC to be the diffusion of carbon atoms. For Ti nanoparticles with diameter larger than 30 nm it was observed that diffusion of Ti atoms into the carbon layer was dominant, which resulted in formation of TiC in the carbon layer at the surface of Ti nanoparticles.     

On Closed Orbits of Morse-Smale Flows on 3-Manifolds

Any link in a 3-manifold is the closed orbits of a non-singularMorse-Smale flow after taking the split sum with the unlinkand the connected sum with S² x S¹s. Current address: Department of Mathematics, University of Toronto,Toronto, Ontario M5S 1A1, Canada     

Hypergeometric Polynomials and Integer Programming

We examine connections between A-hypergeometric differential equations and the theory of integer programming. In the first part, we develop a hypergeometric sensitivity analysis for small variations of constraint constants with creation operators and b-functions. In the second part, we study the indicial polynomial (b-function) along the hyperplane xi=0 via a correspondence between the optimal value of an integer programming problem and the roots of the indicial polynomial. Gröbner bases are used to prove theorems and give counter examples.     

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.     

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.