Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Ab initio study on structure and phase transition of A- and B-type rare-earth sesquioxides Ln2O3 (Ln=La-Lu, Y, and Sc) based on density function theory

Ab initio energetic calculations based on the density functional theory (DFT) and projector augmented wave (PAW) pseudo-potentials method were performanced to determine the crystal structural parameters and phase transition data of the polymorphic rare-earth sesquioxides Ln₂O₃ (where Ln=La-Lu, Y, and Sc) with A-type (hexagonal) and B-type (monoclinic) configurations at ground state. The calculated results agree well with the limited experimental data and the critically assessed results. A set of systematic and self-consistent crystal structural parameters, energies and pressures of the phase transition were established for the whole series of the A- and B-type rare-earth sesquioxides Ln₂O₃. With the increase of the atomic number, the ionic radii of rare-earth elements Ln and the volumes of the sesquioxides Ln₂O₃ reflect the so-called “lanthanide contraction”. With the increase of the Ln³⁺-cation radius, the bulk modulus of Ln₂O₃ decreases and the polymorphic structures show a degenerative tendency.     

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH3 on Pt(1 0 0) coupled by diffusion

The Lombardo–Imbihl–Fink (LFI) ODE model of the NO+NH₃ reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH₃ and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH₃ and H.     

相移掩模的制作

本文阐述相移掩模技术研究中，常用的几种主要相移掩模制作方法，重点介绍了无络ＰＳＭ、Ｌｅｖｅｎｓｏｎ交替型ＰＳＭ、边级ＰＳＭ、亚分辨辅助ＰＳＭ以及激光直写制作ＰＳＭ的方法。     

化学位移各向导性对半整数自旋四极核的2D NMR章动的影响

考察了化学位移各向异性对半整数自旋四极核2D NMR章动的影响.用数值方法对2D NMR章动实验的演化期的Hamiltonian矩阵进行对角化,然后用帐篷法进行粉末平均,获得了自旋为I=3/2、5/2、7/2和9/2的四极核在不同化学位移各向异性下的2D NMR章动谱.实验结果与理论计算符合较好.     

玻色—爱因斯坦凝聚和兰姆位移

扼要地介绍了ＢＥＣ研究的近况和研究方向，同时报道了我们在ＢＥＣ的光散射和兰姆位移方面的研究工作     

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     

Anomalies of attenuation and phase velocity of surface acoustic waves in YBa2Cu3O7‒δ thin films in the vicinity of Tc

We present measurements of the attenuation and phase velocity of surface acoustic waves in thin YBa₂Cu₃O films as a function of temperature, in magnetic fields up to 3.6 T applied parallel to the c-axis of the films. We have observed anomalies in both, the attenuation and the phase velocity in the vicinity of the superconducting critical temperature which do not depend on the magnetic field. Possible origins of these anomalies, observed, to our knowledge, for the first time in YBa₂Cu₃O thin films, are discussed and compared to bulk acoustic wave experiments. We present a kind of feedback technique for surface acoustic waves which improves the sensitivity of this type of measurement. The actual sensitivity limits are mentioned. Received: 7 August 1997 / Revised: 7 November 1997 / Accepted: 17 November 1997     

Modeling film flows down inclined planes

A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations. Received: 16 April 1998 / Revised: 29 June 1998 / Accepted: 2 July 1998     

Mn-site doping induced CMR properties in calcium rich manganites Pr1‒xCaxMnO3(0.6 ≤ x ≤ 0.7)

Doping of Mn-site by chromium, cobalt and nickel has been investigated in the calcium rich manganites and . Whatever the nature of the doping element, a rapid disappearance of the charge ordered (CO) state is observed, decreasing as the doping rate increases. But the most important result concerns the Cr-doped compounds for which a re-entrant insulator to metal transition at 90-120 K is observed for x =0.10-0.12, in a zero magnetic field. The possibility to induce colossal magnetoresistance (CMR) properties for high (IV) contents ((IV)/) for x =0.07-0.12 is shown for the first time, the resistance ratios reaching at 30 K. This study also shows differently that the small size of the A-site cation (Pr, Ca) is not a redhibitory obstacle to the appearance of CMR properties in manganites, in contrast with previously established phase diagrams. Received: 18 June 1997 / Revised: 4 August 1997 / Accepted: 10 November 1997