Logarithmic corrections for dilute uniaxial ferromagnets at the critical dimension

The leading logarithmic corrections to the critical behavior of a dilute uniaxial (Ising) ferromagnet in the disordered phase are derived using renormalization group methods. The values of the exponents in the logarithmic terms differ from those given by previous authors.     

An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension

The famous 1960's construction of Golod and Shafarevich yields infinite dimensional nil, but not nilpotent, algebras. However, these algebras have exponential growth. Here, we construct an infinite dimensional nil, but not locally nilpotent, algebra which has polynomially bounded growth.

     

Nitroxyl free radical binding to Si(1 0 0): a combined scanning tunneling microscopy and computational modeling study

The ultra-high vacuum scanning tunneling microscope (UHV-STM) was used to investigate the addition of the 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) radical to the Si(1 0 0) surface. Room temperature studies performed on clean Si(1 0 0)-2 × 1 confirm the proposed binding of the unpaired valence electron associated with the singly occupied molecular orbital (SOMO) of the molecule with a Si dangling bond. A strong bias dependence in the topography of isolated molecules was observed in the range of −2.0 to +2.5 V. Semiempirical and density functional calculations of TEMPO bound to a three-dimer silicon cluster model yield occupied state density isosurfaces below the highest occupied (HOMO) and unoccupied state densities isosurfaces above the lowest unoccupied molecular orbital (LUMO) which trend in qualitative agreement with the bias dependent STM topography. Furthermore, the placement of TEMPO molecules on dangling bonds was controlled with atomic precision on the monohydride Si(1 0 0) surface via electron stimulated desorption of H, demonstrating the compatibility of nitroxyl free radical binding chemistries with nanopatterning techniques such as feedback controlled lithography.     

Boundary-Value Problem of Drainage in a Fresh Groundwater Fringe above Saline Groundwater

A multiparameter boundary-value problem of fresh infiltration water seepage in a drained fringe above quiescent saline water is solved in the direct statement and studied in detail.     

The Elimination of Grains and Grain Boundaries in Grain Growth

The topological changes that occur during coarsening of 2D and 3Dcellular structures, such as polycrystals, areinvestigated. Particular attention is given to the elimination ofgrain boundaries and grains with more than the minimum number oftopological elements. A thermodynamic criterion is introduced tofind out which topological transformations are favoured, based on theevaluation of the Gibbs free energy of the initial and finalconfigurations. In general, elimination of grains is possible only ifthe number of their neighbours is below a critical value, which maybe affected by geometry.     

Study on the dispersion characteristic of the plasma-loaded relativistic BWO

The dispersion characteristic of the plasma-loaded relativistic backward wave oscillator has been analyzed. The theoretical model has been established and the numerical calculations accord with the experimental results, which provides some useful suggestions on the designing of slow-wave structure of BWO.     

Statistical mechanics of warm and cold unfolding in proteins

We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins. Received: 19 March 1998 / Revised and Accepted: 25 May 1998     

“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

具有新光学性质的Zn-Zn2SiO4纳米同轴线阵列

采用气相沉积技术在Si衬底上生长了Zn-Zn₂SiO₄芯-壳结构纳米同轴线阵列。根部呈笋状的纳米同轴线,直径约100nm,长度可以超过10μm;同轴线芯直径约50nm、壳层厚约25nm。通过X射线衍射的表征以及能量色散谱的线扫描,确定纳米同轴线的芯为Zn,壳层为Zn₂SiO₄。我们提出了一种新的生长机制,同时也为生长均匀的纳米同轴线提供一种新的技术。观察阴极荧光谱发现,纳米同轴线有三个主要发光带:强度最大的中紫外300nm发光、较弱的可见光区560nm以及红外谱区865nm的发光。对纳米同轴线截面的300nm发光峰观测发现,中紫外发光来源于Zn₂SiO₄壳层。正是这种同轴线的结构,使得其具备特殊的光学性质。