Symmetrizability of differential equations having orthogonal polynomial solutions

AbstractWe show that if a linear differential equation of spectral type with polynomial coefficients LN[y](x) = ∑i=0Nli(x) = λny(x) has an orthogonal polynomial system of solutions, then the differential operator LN[·] must be symmetrizable. We also give a few applications of this result

Melting of Charge/Orbital Ordered States in Nd1/2_{1/2}Sr1/2_{1/2}MnO3_3: Temperature and Magnetic Field Dependent Optical Studies

We investigated the temperature ($T=$ 15 $\sim$ 290 K) and the magnetic field ($H=$ 0 $\sim$ 17 T) dependent optical conductivity spectra of a charge/orbital ordered manganite, Nd$_{1/2}$Sr$_{1/2}$MnO$_3$. With variation of $T$ and $H$, large spectral weight changes were observed up to 4.0 eV. These spectral weight changes could be explained using the polaron picture. Interestingly, our results suggested that some local ordered state might remain above the charge ordering temperature, and that the charge/orbital melted state at a high magnetic field (i.e. at $H=$ 17 T and $$ 4.2 K) should be a three dimensional ferromagnetic metal. We also investigated the first order phase transition from the charge/orbital ordered state to ferromagnetic metallic state using the $T$- and $H$% -dependent dielectric constants $\epsilon_1$. In the charge/orbital ordered insulating state, $\epsilon_1$ was positive and $d\epsilon_1/d\omega \approx 0$. With increasing $T$ and $H$, $\epsilon_1$ was increased up to the insulator-metal phase boundaries. And then, $\epsilon_1$ abruptly changed into negative and $d\epsilon_1/d\omega >0$, which was consistent with typical responses of a metal. Through the analysis of $\epsilon_1$ using an effective medium approximation, we found that the melting of charge/orbital ordered states should occur through the percolation of ferromagnetic metal domains.Comment: submitted to Phys. Rev.

Cryptococcal Meningoencephalitis Presenting as Cerebell itis - A case report -

, , We herein report an elderly patient with cryptococcosis in the nervous system who presented with cerebellar dysfunction and showed cerebellar parenchymal lesion with adjacent focal meningeal enhancement on the brain CT and the serial brain MRls. The cerebellar lesion suggests cryptococcal inflammatory reaction or a cerebellar infarction from the arteritis of a branch of the left superior cerebellar artery. This clinical and neuroimaging finding of cerebellitis has not been reported in cryptococcosis. We think cryptococcosis would be included in the differential diagnosis of cerebellitis

Competition of charge, orbital, and ferromagnetic correlations in layered manganites

The competition of charge, orbital, and ferromagnetic interactions in layered manganites is investigated by magneto-Raman scattering spectroscopy. We find that the colossal magnetoresistance effect in the layered compounds results from the interplay of the orbital and ferromagnetic double-exchange correlations. Inelastic scattering by charge-order fluctuations dominates the quasiparticle dynamics in the ferromagnetic-metal state. The scattering is suppressed at low frequencies, consistent with the opening of a charge-density wave pseudogap.Comment: 10 pages, 4 figure

Temperature-dependent Raman spectroscopy in BaRuO3_3 systems

We investigated the temperature-dependence of the Raman spectra of a nine-layer BaRuO$_3$ single crystal and a four-layer BaRuO$_3$ epitaxial film, which show pseudogap formations in their metallic states. From the polarized and depolarized spectra, the observed phonon modes are assigned properly according to the predictions of group theory analysis. In both compounds, with decreasing temperature, while $A_{1g}$ modes show a strong hardening, $E_g$ (or $E_{2g}$) modes experience a softening or no significant shift. Their different temperature-dependent behaviors could be related to a direct Ru metal-bonding through the face-sharing of RuO$_6$. It is also observed that another $E_{2g}$ mode of the oxygen participating in the face-sharing becomes split at low temperatures in the four layer BaRuO$_3$. And, the temperature-dependence of the Raman continua between 250 $\sim$ 600 cm$^{-1}$ is strongly correlated to the square of the plasma frequency. Our observations imply that there should be a structural instability in the face-shared structure, which could be closely related to the pseudogap formation of BaRuO$_3$ systems.Comment: 8 pages, 6 figures. to be published in Phys. Rev.

Exclusive electroproduction of K+ Lambda and K+ Sigma^0 final states at Q^2 = 0.030-0.055 (GeV/c)^2

Cross section measurements of the exclusive p(e,e'K+)Lambda,Sigma^0 electroproduction reactions have been performed at the Mainz Microtron MAMI in the A1 spectrometer facility using for the first time the Kaos spectrometer for kaon detection. These processes were studied in a kinematical region not covered by any previous experiment. The nucleon was probed in its third resonance region with virtual photons of low four-momenta, Q^2= 0.030-0.055 (GeV/c)^2. The MAMI data indicate a smooth transition in Q^2 from photoproduction to electroproduction cross sections. Comparison with predictions of effective Lagrangian models based on the isobar approach reveal that strong longitudinal couplings of the virtual photon to the N* resonances can be excluded from these models.Comment: 16 pages, 7 figure

On the effects of the magnetic field and the isotopic substitution upon the infrared absorption of manganites

Employing a variational approach that takes into account electron-phonon and magnetic interactions in $La_{1-x}A_xMnO_3$ perovskites with $0<x<0.5$, the effects of the magnetic field and the oxygen isotope substitution on the phase diagram, the electron-phonon correlation function and the infrared absorption at $x=0.3$ are studied. The lattice displacements show a strong correlation with the conductivity and the magnetic properties of the system. Then the conductivity spectra are characterized by a marked sensitivity to the external parameters near the phase boundary.Comment: 10 figure

Synchronization and resonance in a driven system of coupled oscillators

We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective synchronization of the system, is derived; it is found that the total order parameter decreases monotonically with noise, indicating overall suppression of synchronization. Still, for large coupling strengths, there exists an optimal noise level at which the periodic (ac) component of the order parameter reaches its maximum. The response of the phase velocity is also examined and found to display resonance behavior.Comment: 17 pages, 3 figure

Molecular and functional expression of anion exchangers in cultured normal human nasal epithelial cells

AIMS: Anions have an important role in the regulation of airway surface liquid (ASL) volume, viscosity and pH. However, functional localization and regulation of anion exchangers (AEs) have not been clearly described. The aim of this study was to investigate the regulation of AE mRNA expression level in accordance with mucociliary differentiation and the functional expression of AEs cultured normal human nasal epithelial (NHNE) cells. METHODS: Nasal mucosal specimens from three patients are obtained and serially cultured cells are subjected to morphological examinations, RT-PCR, Western blot analysis and immunocytochemistry. AE activity is assessed by pHi measurements. RESULTS: Expression of ciliated cells on the apical membrane and expression of MUC5AC, a marker of mucous differentiation, increased with time. AE2 and SLC26A4 mRNA expression decreased as mucociliary differentiation progressed, and AE4, SLC26A7 and SLC26A8 mRNA expression increased on the 14th and 28th day after confluence. Accordingly, AE4 protein expression also progressively increased. AE activity in 100 mM K(+) buffer solutions was nearly twofold higher than that in 5 mM K(+) buffer solutions. Moreover, only luminal AE activity increased about fourfold over the control in the presence of 5 microM forskolin. In the presence of 100 microM adenosine-5'-triphosphate (ATP) which evokes intracellular calcium signalling through activation of purinergic receptors, only luminal AE activity was again significantly increased. On the other hand, 500 microM 4,4'-diisothiocyanostilbene-2,2'-disulfonic acid (DIDS), an inhibitor of most SLC4 and SLC26AE isoforms, nearly abolished AE activity in both luminal and basolateral membranes. We found that AE activity was affected by intracellular cAMP and calcium signalling in the luminal membrane and was DIDS-sensitive in both membranes of cultured NHNE cells. CONCLUSION: Our findings through molecular and functional studies using cultured NHNE cells suggest that AEs may have an important role in the regulation of ASL.ope

The Plasma Environment of Comets

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138863/1/rog199129s2976.pd