In situ scanning tunneling microscopy imaging of mercury film electrodeposited on Ir(1 1 1)

In situ scanning tunneling microscopy (STM) was used to examine multilayer Hg film electrodeposited on a well-ordered Ir(1 1 1) single crystal electrode in 0.1 M HClO₄ + 1 mM Hg(ClO₄)₂. Topography STM scans showed that the Ir(1 1 1) – supported Hg film electrode contained well-defined terraces separated by monatomic steps (Δz = 2.3 Å). The STM’s tip could be used to induce local dissolution of the Hg deposit under proper operating conditions and the depth of the etched pit informed directly the thickness of Hg deposit. Although in situ STM imaging with a tungsten tip could not result in atomic structure of bare Hg film in 0.1 M HClO₄, it discerned highly ordered iodine adlayers, represented by a (2 × 8√3)rect – I structure, on the Hg film in solution containing potassium iodide. These STM results suggested that the Hg substrate could have an ordered atomic structure.     

Ordered molecular assemblies of substituted bis(phthalocyaninato) rare earth complexes on Au(111): in situ scanning tunneling microscopy and electrochemical studies

Substituted bis(phthalocyaninato) rare earth complexes ML2 (M = Y and Ce; L = [Pc(OC8H17)8]2, where Pc = phthalocyaninato) were adsorbed onto single crystalline Au(111) electrodes from benzene saturated with either YL2 or CeL2 complex at room temperature. In situ scanning tunneling microscopy (STM) and cyclic voltammetry (CV) were used to examine the structures and the redox reactions of these admolecules on Au(111) electrodes in 0.1 mol dm(-3) HClO4. The CVs obtained with YL2- and CeL2-coated Au(111) electrodes respectively contained two and three pairs of redox peaks between 0 and 1.0 V (versus reversible hydrogen electrode). STM molecular resolution revealed that YL2 and CeL2 admolecules were imaged as spherical protrusions separated by 2.3 nm, which suggests that they were oriented with their molecular planes parallel to the unreconstructed Au(111)-(1 x 1). Both molecules when adsorbing from approximately micromolar benzene dosing solutions produced mainly ordered arrays characterized as (8 x 5 radical3)rect (theta = 0.0125). The redox reactions occurring between 0.2 and 1.0 V caused no change in the adlayer, but they were desorbed or oxidized at the negative and positive potential limits. The processes of adsorption and desorption at the negative potentials were reversible to the modulation of potential. Electrochemical impedance spectroscopy (EIS) and CV measurements showed that YL2 and CeL2 adlayers could block the adsorption of perchlorate anions and mediating electron transfer at the Au(111) electrode, leading to the enhancement of charge transfer for the ferro/ferricyanide redox couple.     

Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons

We consider the dynamics of N boson systems interacting through a pair potential N ^?1 V _a (x _i ?x _j ) where V _a (x)=a ^?3 V(x/a). We denote the solution to the N-particle Schrödinger equation by Ψ _{N, t} . Recall that the Gross-Pitaevskii (GP) equation is a nonlinear Schrödinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if u _t solves the GP equation, then the family of k-particle density matrices solves the GP hierarchy. Under the assumption that a=N ^?? for 0N→∞ the limit points of the k-particle density matrices of Ψ _{N, t} are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by ∫V(x)dx. The uniqueness of the solutions of this hierarchy remains an open question.     

Likelihood Inferences for High-Dimensional Factor Analysis of Time Series With Applications in Finance

This article investigates likelihood inferences for high-dimensional factor analysis of time series data. We develop a matrix decomposition technique to obtain expressions of the likelihood functions and its derivatives. With such expressions, the traditional delta method that relies heavily on score function and Hessian matrix can be extended to high-dimensional cases. We establish asymptotic theories, including consistency and asymptotic normality. Moreover, fast computational algorithms are developed for estimation. Applications to high-dimensional stock price data and portfolio analysis are discussed. The technical proofs of the asymptotic results and the computer codes are available online.     

Stability of coulomb systems with magnetic fields

The ground state energy of an atom in the presence of an external magnetic filedB (with the electron spin-field interaction included) can be arbitrarity negative whenB is arbitrarily large. We inquire whether stability can be restored by adding the self energy of the field, B ². For a hydrogenic like atom we prove that there is a critical nuclear charge,z _c , such that the atom is stable forz<z _c and unstable forz>z _c .Work partically supported by U.S. National Scinece Foundation grant DMS-8405264 during the author's stay at the Institute for Advanced Study, Princeton, NJ, USAWork partially supported by U.S. National Science Foundation grant PHY-8116101-A03Work partially supported by U.S. and Swiss National Science Foundation Cooperative Science Program INT-8503858. Current address: Institut f. Mathematik, FU Berlin, Arnimallee 3, D-1000 Berlin 33     

A sharp polynomial estimate of positive integral points in a 4‐dimensional tetrahedron and a sharp estimate of the Dickman‐de Bruijn function

The estimate of integral points in right‐angled simplices has many applications in number theory, complex geometry, toric variety and tropical geometry. In [24], [25], [27], the second author and other coworkers gave a sharp upper estimate that counts the number of positive integral points in n dimensional () real right‐angled simplices with vertices whose distance to the origin are at least . A natural problem is how to form a new sharp estimate without the minimal distance assumption. In this paper, we formulate the Number Theoretic Conjecture which is a direct correspondence of the Yau Geometry conjecture. We have proved this conjecture for . This paper gives hope to prove the new conjecture in general. As an application, we give a sharp estimate of the Dickman‐de Bruijn function for .     

Nanotribological behavior of ZnO films prepared by atomic layer deposition

We used atomic layer deposition to form ZnO thin-film coatings on Si substrates and then evaluate the effect of pile-up using the nanoscratch technique under a ramped mode. The wear volume decreased with increasing annealing temperature from room temperature to 400 °C for a given load. Elastic-to-plastic deformation occurred during sliding scratch processing between the groove and film for loading penetration of 30 nm. The onset of non-elastic behavior and greater contact pressure were evident for loading penetration of 150 nm; thus, full plastic deformation occurred as a result of a substrate effect. We suspect that elastic–plastic failure events were related to edge bulging between the groove and film, with elastic–plastic deformation attributable to adhesion discontinuities and/or cohesion failure of the ZnO films.     

Enhancing electron transfer at a cytochrome c-immobilized microelectrode and macroelectrode

The redox reaction of cytochrome c immobilized on the bare surfaces of microelectrodes and macroscopic electrodes (macroelectrodes) composed of different planes of highly oriented pyrolytic graphite has been investigated using cyclic voltammetry. The protein-immobilized microelectrodes were fabricated using a simple masking method. For both macroelectrodes and microelectrodes, the redox reaction of immobilized cytochrome c needs to be activated by increasing the electrochemical potential maximum of cyclic voltammetry to a high positive value. The redox currents of this protein-electrode system can be enhanced using two approaches. The oxidation and reduction currents of cytochrome c adsorbed on microelectrodes that are composed of the edge plane show an anomalous enhancement compared to those for macroelectrodes composed of the basal plane. The difference in the surface chemical properties of the two kinds of electrodes results in the current anomaly. The oxidation current of the macroelectrode can be selectively enhanced by decreasing the potential minimum.