On a nonlinear recurrent relation

We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.Comment: to appear in Journal of Statistical Physic

Water productivity in Zhanghe Irrigation System: issues of scale

Irrigation systemsWater productivityReservoirsWater useWater stressWater conservationRicePaddy fieldsCrop yield

The Nullity of Bicyclic Signed Graphs

Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs (including simple bicyclic graphs) of order n with nullity n-5

An investigation into the feasibility of myoglobin-based single-electron transistors

Myoglobin single-electron transistors were investigated using nanometer- gap platinum electrodes fabricated by electromigration at cryogenic temperatures. Apomyoglobin (myoglobin without heme group) was used as a reference. The results suggest single electron transport is mediated by resonant tunneling with the electronic and vibrational levels of the heme group in a single protein. They also represent a proof-of-principle that proteins with redox centers across nanometer-gap electrodes can be utilized to fabricate single-electron transistors. The protein orientation and conformation may significantly affect the conductance of these devices. Future improvements in device reproducibility and yield will require control of these factors

Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-modules to the category of A_1^(1)-modules of critical level. Using this approach, we prove the irreducibility of a family of A_1^(1)-modules at the critical level. As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give a natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations.Comment: 21 pages, Late

Superconductivity at 41 K and its competition with spin-density-wave instability in layered CeO1−x_{1-x}Fx_xFeAs

A series of layered CeO$_{1-x}$F$_x$FeAs compounds with x=0 to 0.20 are synthesized by solid state reaction method. Similar to the LaOFeAs, the pure CeOFeAs shows a strong resistivity anomaly near 145 K, which was ascribed to the spin-density-wave instability. F-doping suppresses this instability and leads to the superconducting ground state. Most surprisingly, the superconducting transition temperature could reach as high as 41 K. The very high superconducting transition temperature strongly challenges the classic BCS theory based on the electron-phonon interaction. The very closeness of the superconducting phase to the spin-density-wave instability suggests that the magnetic fluctuations play a key role in the superconducting paring mechanism. The study also reveals that the Ce 4f electrons form local moments and ordered antiferromagnetically below 4 K, which could coexist with superconductivity.Comment: 4 pages, 5 figure

Anomalous metallic state of Cu0.07_{0.07}TiSe2_2: an optical spectroscopy study

We report an optical spectroscopy study on the newly discovered superconductor Cu$_{0.07}$TiSe$_2$. Consistent with the development from a semimetal or semiconductor with a very small indirect energy gap upon doping TiSe$_2$, it is found that the compound has a low carrier density. Most remarkably, the study reveals a substantial shift of the "screened" plasma edge in reflectance towards high energy with decreasing temperature. This phenomenon, rarely seen in metals, indicates either a sizeable increase of the conducting carrier concentration or/and a decrease of the effective mass of carriers with reducing temperature. We attribute the shift primarily to the later effect.Comment: 4 figures, 4+ page

Infrared spectroscopy of the charge ordering transition in Na0.5_{0.5}CoO2_2

We report infrared spectra of a Na$_{0.5}$CoO$_2$ single crystal which exhibits a sharp metal-insulator transition near 50 K due to the formation of charge ordering. In comparison with x=0.7 and 0.85 compounds, we found that the spectral weight associated with the conducting carriers at high temperature increases systematically with decreasing Na contents. The charge ordering transition only affects the optical spectra below 1000 cm$^{-1}$. A hump near 800 cm$^{-1}$ develops below 100 K, which is accompanied by the appearance of new lattice modes as well as the strong anti-resonance feature of phonon spectra. At lower temperature $T_{co}$, an optical gap develops at the magnitude of 2$\Delta\approx3.5k_BT_{co}$, evidencing an insulating charge density wave ground state. Our experimental results and analysis unequivocally point towards the importance of charge ordering instability and strong electron-phonon interaction in Na$_x$CoO$_2$ system.Comment: 4 pages, 3 figure