Interlacing Log-concavity of the Boros-Moll Polynomials

We introduce the notion of interlacing log-concavity of a polynomial sequence $\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$ interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\geq 0$. Interlacing log-concavity is stronger than the log-concavity. We show that the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a sufficient condition for interlacing log-concavity which implies that some classical combinatorial polynomials are interlacing log-concave.Comment: 10 page

In-plane ferromagnetism in charge-ordering Na0.55CoO2Na_{0.55}CoO_2

The magnetic and transport properties are systematically studied on the single crystal $Na_{0.55}CoO_2$ with charge ordering and divergency in resistivity below 50 K. A long-range ferromagnetic ordering is observed in susceptibility below 20 K with the magnetic field parallel to Co-O plane, while a negligible behavior is observed with the field perpendicular to the Co-O plane. It definitely gives a direct evidence for the existence of in-plane ferromagnetism below 20 K. The observed magnetoresistance (MR) of 30 % at the field of 6 T at low temperatures indicates an unexpectedly strong spin-charge coupling in triangle lattice systems.Comment: 4 pages, 5 figure

Oxygen Isotope Effect on the Spin State Transition in (Pr0.7_{0.7}Sm0.3_{0.3})0.7_{0.7}Ca0.3_{0.3}CoO3{_3}

Oxygen isotope substitution is performed in the perovskite cobalt oxide (Pr$_{0.7}$Sm$_{0.3}$)$_{0.7}$Ca$_{0.3}$CoO${_3}$ which shows a sharp spin state transition from the intermediate spin (IS) state to the low spin (LS) state at a certain temperature. The transition temperature of the spin state up-shifts with the substitution of $^{16}O$ by $^{18}$O from the resistivity and magnetic susceptibility measurements. The up-shift value is 6.8 K and an oxygen isotope exponent ($\alpha_S$) is about -0.8. The large oxygen isotope effect indicates strong electron-phonon coupling in this material. The substitution of $^{16}$O by $^{18}$O leads to a decrease in the frequency of phonon and an increase in the effective mass of electron ($m$$^\ast$), so that the bandwidth W is decreased and the energy difference between the different spin states is increased. This is the reason why the $T_s$ is shifted to high temperature with oxygen isotopic exchange.Comment: 4 pages, 3 figure