The qq-log-convexity of Domb's polynomials

In this paper, we prove the $q$-log-convexity of Domb's polynomials, which was conjectured by Sun in the study of Ramanujan-Sato type series for powers of $\pi$. As a result, we obtain the log-convexity of Domb's numbers. Our proof is based on the $q$-log-convexity of Narayana polynomials of type $B$ and a criterion for determining $q$-log-convexity of self-reciprocal polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:1308.273

On the qq-log-convexity conjecture of Sun

In his study of Ramanujan-Sato type series for $1/\pi$, Sun introduced a sequence of polynomials $S_n(q)$ as given by $$S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k,$$ and he conjectured that the polynomials $S_n(q)$ are $q$-log-convex. By imitating a result of Liu and Wang on generating new $q$-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the $q$-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture

Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and 3-rarefaction wave to the inflow problem is described and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier-Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the degeneracies of the transonic boundary layer solution and the wave interactions in the superposition wave.Comment: 27 page

Lead halide perovskite nanowires stabilized by block copolymers for Langmuir-Blodgett assembly

The rapid development of solar cells based on lead halide perovskites (LHPs) has prompted very active research activities in other closely-related fields. Colloidal nanostructures of such materials display superior optoelectronic properties. Especially, one-dimensional (1D) LHPs nanowires show anisotropic optical properties when they are highly oriented. However, the ionic nature makes them very sensitive to external environment, limiting their large scale practical applications. Here, we introduce an amphiphilic block copolymer, polystyrene-block-poly(4-vinylpyridine) (PS-P4VP), to chemically modify the surface of colloidal CsPbBr3 nanowires. The resulting core-shell nanowires show enhanced photoluminescent emission and good colloidal stability against water. Taking advantage of the stability enhancement, we further applied a modified Langmuir-Blodgett technique to assemble monolayers of highly aligned nanowires, and studied their anisotropic optical properties. [Figure not available: see fulltext.]

Significant improvement of activation energy in MgB2/Mg2Si multilayer films

We obtained a MgB2/Mg2Si multilayer structure by sequentially switching a stoichiometric MgB2 target and a Si target during off-axis pulsed-laser deposition. The transmission-electron-microscopic cross-sectional image of the resulting film exhibits a layered structure with each MgB2 layer being 40–50 nm thick and the Mg2Si interlayers about 5 nm thick. A clearly enhanced anisotropy in the irreversibility lines and the vortex activation energy was observed. Pinning and the flux flow activation energy are significantly increased in parallel applied fields

Characterization of DNA unwinding properties of three N-terminal fragments of RecQ5β helicase

RecQ5β is one member of the human RecQ family helicases that belong to superfamily 2 (SF2) and are critical for the maintenance of genomic stability. Here, the DNA unwinding kinetics of three N-terminal fragments of RecQ5β helicase, RecQ5β1-467, RecQ5β1-567 and RecQ5β1-662, were studied with stopped-flow method based on fluorescence resonance energy transfer (FRET). Under single-turnover kinetic conditions, we found that both the unwinding amplitude and rate increased with the increase of the 3’-tail length of the DNA substrate for each fragment. The maximum amplitudes were 73.5, 57.6 and 35.5% for RecQ5β1-467, RecQ5β1-567 and RecQ5β1-662, respectively. Obviously, the unwinding amplitude decreased with the increase of the fragment length. For each RecQ5β fragment, when the 3’-tail length of the DNA substrates was short, essentially only one slow unwinding process occurred. When the 3’-tail length was increased, the unwinding amplitude of the fast unwinding process increased obviously; that is, the RecQ5β-catalyzed DNA unwinding depended on the 3’-tail length of the DNA substrate. It indicates that RecQ5β molecules are cooperative in DNA unwinding. This is an interesting new feature for a SF2 helicase.Key words: RecQ5β helicase, stopped-flow technique, fluorescence resonance energy transfer (FRET), DNA unwinding kinetics

Superconductivity, critical current density, and flux pinning in MgB_{2-x}(SiC)_{x/2} superconductor after SiC nanoparticle doping

We investigated the effect of SiC nano-particle doping on the crystal lattice structure, critical temperature T_c, critical current density J_c, and flux pinning in MgB_2 superconductor. A series of MgB_{2-x}(SiC)_{x/2} samples with x = 0 to 1.0 were fabricated using in-situ reaction process. The contraction of the lattice and depression of T_c with increasing SiC doping level remained rather small due to the counter-balanced effect of Si and C co-doping. The high level Si and C co-doping allowed the creation of intra-grain defects and highly dispersed nano-inclusions within the grains which can act as effective pinning centers for vortices, improving J_c behavior as a function of the applied magnetic field. The enhanced pinning is mainly attributable to the substitution-induced defects and a local structure fluctuations within grains. A pinning mechanism is proposed to account for different contributions of different defects in MgB_{2-x}(SiC)_{x/2} superconductors.Comment: 7 pages, 8 figure