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

Surface phase separation in nanosized charge-ordered manganites

Recent experiments showed that the robust charge-ordering in manganites can be weakened by reducing the grain size down to nanoscale. Weak ferromagnetism was evidenced in both nanoparticles and nanowires of charge-ordered manganites. To explain these observations, a phenomenological model based on surface phase separation is proposed. The relaxation of superexchange interaction on the surface layer allows formation of a ferromagnetic shell, whose thickness increases with decreasing grain size. Possible exchange bias and softening of the ferromagnetic transition in nanosized charge-ordered manganites are predicted.Comment: 4 pages, 3 figure

Truncated α1-antitrypsin as an infection biomarker for Severe Acute Respiratory Syndrome (SARS)

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Sintering-Induced Phase Transformation of Nanoparticles: A Molecular Dynamics Study

Sintering-induced phase transformation of TiO2 nanoparticles is investigated systematically via molecular dynamics simulation. Upon defining a coordination number and bond angle distribution criteria, local phase information is identified for each individual Ti atom originating from amorphous or crystal structure as well as three TiO2 polymorphs, anatase, brookite, and rutile. Size-dependent structures of nanoparticles lead to different dynamics of the sintering-induced phase transformation. Grain boundaries that form between nanoparticles during sintering trigger the nucleation and growth of new phases. During the sintering of two equal-sized core–shell anatase nanoparticles, crystal core regions melt with the temperature increase and the surface energy decrease in the microcanonical (NVE) ensemble. The new phase that develops from the grain boundary spreads into the destroyed core regions in stages, forming a new larger spherical nanoparticle with an ordered atomic arrangement. During the sintering of two unequal-sized nanoparticles (amorphous and core–shell anatase), atoms from the amorphous nanoparticle first nucleate to form crystal anatase in the contact region, and a grain boundary is then developed between the original core region and the newly formed anatase crystal. After that, phase transformation follows much the same route as the equal-sized case from anatase to brookite

Fast Synthesis Algorithm for Uniformly Spaced Circular Array with Low Sidelobe Pattern

© 2018 ACES. In this paper, a highly efficient approach is proposed to synthesize the low sidelobe pattern of uniformly spaced circular array. The proposed approach can be generalized to deal with the pattern synthesis for the circular array with directional elements. Numerical examples are given to verify the effectiveness and advantage of this approach