Bounding sup-norms of cusp forms of large level

Let f be an $L^2$-normalized weight zero Hecke-Maass cusp form of square-free level N, character $\chi$ and Laplacian eigenvalue $\lambda\geq 1/4$. It is shown that $\| f \|_{\infty} \ll_{\lambda} N^{-1/37}$, from which the hybrid bound $\|f \|_{\infty} \ll \lambda^{1/4} (N\lambda)^{-\delta}$ (for some $\delta > 0$) is derived. The first bound holds also for $f = y^{k/2}F$ where F is a holomorphic cusp form of weight k with the implied constant now depending on k.Comment: version 3: substantially revised versio

On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Modest-2: A Summary

This is a summary paper of MODEST-2, a workshop held at the Astronomical Institute ``Anton Pannekoek'' in Amsterdam, 16-17 December 2002. MODEST is a loose collaboration of people interested in MOdelling DEnse STellar systems, particularly those interested in modelling these systems using all the available physics (stellar dynamics, stellar evolution, hydrodynamics and the interplay between the three) by defining interfaces between different codes. In this paper, we summarize 1) the main advances in this endeavour since MODEST-1; 2) the main science goals which can be and should be addressed by these types of simulations; and 3) the most pressing theoretical and modelling advances that we identified.Comment: Accepted by New Astronom

Non-volatile molecular memory elements based on ambipolar nanotube field effect transistors

We have fabricated air-stable n-type, ambipolar carbon nanotube field effect transistors (CNFETs), and used them in nanoscale memory cells. N-type transistors are achieved by annealing of nanotubes in hydrogen gas and contacting them by cobalt electrodes. Scanning gate microscopy reveals that the bulk response of these devices is similar to gold-contacted p-CNFETs, confirming that Schottky barrier formation at the contact interface determines accessibility of electron and hole transport regimes. The transfer characteristics and Coulomb Blockade (CB) spectroscopy in ambipolar devices show strongly enhanced gate coupling, most likely due to reduction of defect density at the silicon/silicon-dioxide interface during hydrogen anneal. The CB data in the ``on''-state indicates that these CNFETs are nearly ballistic conductors at high electrostatic doping. Due to their nanoscale capacitance, CNFETs are extremely sensitive to presence of individual charge around the channel. We demonstrate that this property can be harnessed to construct data storage elements that operate at the few-electron level.Comment: 6 pages text, 3 figures and 1 table of content graphic; available as NanoLetters ASAP article on the we

Investigation of the crystallization process of CSD-ErBCO on IBAD-substrate via DSD approach

REBa$_{2}$Cu$_{3}$O$_{7-δ}$ (REBCO, RE: rare earth, such as Y and Gd) compounds have been extensively studied as a superconducting layer in coated conductors. Although ErBCO potentially has better superconducting properties than YBCO and GdBCO, little research has been made on it, especially in chemical solution deposition (CSD). In this work, ErBCO films were deposited on IBAD (ion-beam-assisted-deposition) substrates by CSD with low-fluorine solutions. The crystallization process was optimized to achieve the highest self-field critical current density (J$_{c}$) at 77 K. Commonly, for the investigation of a CSD process involving numerous process factors, one factor is changed keeping the others constant, requiring much time and cost. For more efficient investigation, this study adopted a novel design-of-experiment technique, definitive screening design (DSD), for the first time in CSD process. Two different types of solutions containing Er-propionate or Er-acetate were used to make two types of samples, Er-P and Er-A, respectively. Within the investigated range, we found that crystallization temperature, dew point, and oxygen partial pressure play a key role in Er-P, while the former two factors are significant for Er-A. DSD revealed these significant factors among six process factors with only 14 trials. Moreover, the DSD approach allowed us to create models that predict J$_{c}$ accurately. These models revealed the optimum conditions giving the highest J$_{c}$ values of 3.6 MA/cm$^{2}$ for Er-P and 3.0 MA/cm$^{2}$ for Er-A. These results indicate that DSD is an attractive approach to optimize CSD process

Electrically Driven Light Emission from Individual CdSe Nanowires

We report electroluminescence (EL) measurements carried out on three-terminal devices incorporating individual n-type CdSe nanowires. Simultaneous optical and electrical measurements reveal that EL occurs near the contact between the nanowire and a positively biased electrode or drain. The surface potential profile, obtained by using Kelvin probe microscopy, shows an abrupt potential drop near the position of the EL spot, while the band profile obtained from scanning photocurrent microscopy indicates the existence of an n-type Schottky barrier at the interface. These observations indicate that light emission occurs through a hole leakage or an inelastic scattering induced by the rapid potential drop at the nanowire-electrode interface.Comment: 12 pages, 4 figure

A log-quadratic relation for predicting supermassive black hole masses from the host bulge Sersic index

We reinvestigate the correlation between black hole mass and bulge concentration. With an increased galaxy sample, updated estimates of galaxy distances, black hole masses, and Sersic indices `n' - a measure of concentration - we perform a least-squares regression analysis to obtain a relation suitable for the purpose of predicting black hole masses in other galaxies. In addition to the linear relation, log(M_bh) = 7.81(+/-0.08) + 2.69(+/-0.28)[log(n/3)] with epsilon_(intrin)=0.31 dex, we investigated the possibility of a higher order M_bh-n relation, finding the second order term in the best-fitting quadratic relation to be inconsistent with a value of zero at greater than the 99.99% confidence level. The optimal relation is given by log(M_bh) = 7.98(+/-0.09) + 3.70(+/-0.46)[log(n/3)] - 3.10(+/-0.84)[log(n/3)]^2, with epsilon_(intrin)=0.18 dex and a total absolute scatter of 0.31 dex. Extrapolating the quadratic relation, it predicts black holes with masses of ~10^3 M_sun in n=0.5 dwarf elliptical galaxies, compared to ~10^5 M_sun from the linear relation, and an upper bound on the largest black hole masses in the local universe, equal to 1.2^{+2.6}_{-0.4}x10^9 M_sun}. In addition, we show that the nuclear star clusters at the centers of low-luminosity elliptical galaxies follow an extrapolation of the same quadratic relation. Moreover, we speculate that the merger of two such nucleated galaxies, accompanied by the merger and runaway collision of their central star clusters, may result in the late-time formation of some supermassive black holes. Finally, we predict the existence of, and provide equations for, a relation between M_bh and the central surface brightness of the host bulge

Strong rejuvenation in a chiral-glass superconductor

The glassy paramagnetic Meissner phase of a Bi$_2$Sr$_2$CaCu$_2$O$_x$ superconductor ($x$ = 8.18) is investigated by squid magnetometry, using ``dc-memory'' experiments employed earlier to study spin glasses. The temperature dependence of the zero-field-cooled and thermo-remanent magnetization is recorded on re-heating after specific cooling protocols, in which single or multiple halts are performed at constant temperatures. The 'spin' states equilibrated during the halts are retrieved on re-heating. The observed memory and rejuvenation effects are similar to those observed in Heisenberg-like spin glasses.Comment: REVTeX 4 style; 5 pages, 5 figure

The genetic contribution of the NO system at the glutamatergic post-synapse to schizophrenia : further evidence and meta-analysis

NO is a pleiotropic signaling molecule and has an important role in cognition and emotion. In the brain, NO is produced by neuronal nitric oxide synthase (NOS-I, encoded by NOS1) coupled to the NMDA receptor via PDZ. interactions; this protein-protein interaction is disrupted upon binding of NOS1 adapter protein (encoded by NOS1AP) to NOS-I. As both NOS1 and NOS1AP were associated with schizophrenia, we here investigated these genes in greater detail by genotyping new samples and conducting a meta-analysis of our own and published data. In doing so, we confirmed association of both genes with schizophrenia and found evidence for their interaction in increasing risk towards disease. Our strongest finding was the NOS1 promoter SNP rs41279104, yielding an odds ratio of 1.29 in the meta-analysis. As findings from heterologous cell systems have suggested that the risk allele decreases gene expression, we studied the effect of the variant on NOS1 expression in human post-mortem brain samples and found that the risk allele significantly decreases expression of NOS1 in the prefrontal cortex. Bioinformatic analyses suggest that this might be due the replacement of six transcription factor binding sites by two new binding sites as a consequence of proxy SNPs. Taken together, our data argue that genetic variance in NOS1 resulting in lower prefrontal brain expression of this gene contributes to schizophrenia liability, and that NOS1 interacts with NOS1AP in doing so. The NOS1-NOS1AP PDZ interface may thus well constitute a novel target for small molecules in at least some forms of schizophrenia. PostprintPeer reviewe