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

Investigation of motor topologies for SMC application

Soft magnetic composite (SMC) materials possess a number of unique properties and have undergone a significant development in the past decade. Based on the experiences on SMC materials and SMC electrical machines from our research group and other researchers, this paper reviews the investigation on motor topologies for SMC application. Both successful experiences and existing difficulties are analyzed and discussed. It is found that the application of SMC is preponderant in small permanent magnet motors with complex topologies and 3D magnetic flux. Possible further work required for commercial success of SMC machines is proposed

Comparative study of in situ and ex situ MgB2 films deposited by pulsed laser deposition

Two types of MgB2 films were prepared by pulsed laser deposition (PLD) with in situ and ex situ annealing processes respectively. Significant differences in properties between the two types of films were found. The ex situ MgB2 film has a Tc of 38.1K, while the in situ film has a depressed Tc of 34.5K. The resistivity at 40K for the in situ film is larger than that of the ex situ film by a factor of 6. The residual resistivity ratios (RRR) are 1.1 and 2.1 for the in situ and ex situ films respectively. The Jc-H curves of the in situ film show a much weaker field dependence than those of the ex situ film, attributable to stronger flux pinning in the in situ film. The small-grain feature and high oxygen level may be critical for the significant improvement of Jc in the in situ annealed MgB2 film.Comment: 6 pages, 6 figure

Stochastic Resolution of Identity for Real-Time Second-Order Green's Function: Ionization Potential and Quasi-Particle Spectrum.

We develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons

Nature of band-gap states in V-doped TiO2 revealed by resonant photoemission

Band-gap states in V-doped TiO2 have been studied by photoemission spectroscopy over a range of photon energies encompassing the Ti 3p and V 3p core thresholds. The states show resonant enhancement at photon energies significantly higher than found for Ti 3d states introduced into TiO2 by oxygen deficiency or alkalimetal adsorbates. This demonstrates that the gap states relate to electrons trapped on dopant V cations rather than host Ti cations

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