An ultrasonic measurement model using a multi-Gaussian beam model for a rectangular transducer

To date, ultrasonic measurement models have primarily treated systems where circular transducers are used. Recently, however, a highly efficient ultrasonic beam model for a rectangular transducer has also become available where the transducer is represented as a superposition of a relatively few Gaussian beams. Thus, using the multi-Gaussian beams, we developed ultrasonic measurement models for systems where a rectangular transducer is employed. In this paper, we describe the developed models including the beam model, the efficiency factor for a rectangular transducer and far-field scattering models for some standard scatterers. Furthermore, the accuracy of the proposed model is verified by the comparison of the model-based predictions to the experimental measurements.     

The Influence of Hydrogen Adsorption on Magnetic Properties of Ni/Cu(001) Surface

Ni/Cu(001) is known as a unique system showing the spin-reorientation transition from an in-plane to out-of-plane magnetization direction when the Ni-overlayer thickness is increased. We investigate different relaxed multilayer structures with a hydrogen adlayer using the full-potential linearized augmented plane-wave method. The relaxed geometries, determined by total energy and atomic force calculations, show that H-monolayer strongly influences the interlayer distance between the Ni-surface and sub-surface layers yielding the outward relaxation of Ni-layer at H/Ni interface. Furthermore, large decrease of local magnetic moments at the top surface area is found for the surface covered by H. The magneto-crystalline anisotropy energies are calculated for fully relaxed H/Ni-films. The spin-reorientation transition critical thickness of 4 ML is found in good quantitative agreement with the experiment.     

Homotopy invariance of Novikov-Shubin invariants and Betti numbers

We give short proofs of the Gromov-Shubin theorem on the homotopy invariance of the Novikov-Shubin invariants and of the Dodziuk theorem on the homotopy invariance of the Betti numbers of the universal covering of a closed manifold in this paper. We show that the homotopy invariance of these invariants is no more difficult to prove than the homotopy invariance of ordinary homology theory.

     

On dualizing a multivariable Poisson summation formula

It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function ø of one variable into a function and its cosine transform in a generalized sense. The present work presents conditions on ø for which the transform relation holds in the classical sense, and extends this result to a class of generalizations of the Poisson formula in any number of dimensions.     

On the blowing-up behavior of solutions for a parabolic boundary value problem

This paper discusses the existence and the blowing-up behaviour of the solution for an initial boundary value problem which arises from the ignition of mixtures of gases. It is shown under the Dirichlet or the third type of boundary condition that for certain a class of initial functions local solutions exist and grow unbounded in finite time, while for another class of initial functions there exist global solutions which converge to a steady state solution of the problem. These results lead to an interesting bifurcation phenomenon on the existence, stability and blowing-up property of the solution in terms of either the strength of the nonlinear function or the size of the diffusion region. Estimates for the stability and instability regions as well as bounds for the finite escape time are explicitly given.     

ChemInform Abstract: U and P4 Reaction Products: A Quantum Chemical and Matrix Isolation Spectroscopic Investigation.

Reactions of laser‐ablated U atoms with P₄ molecules in excess Ar or Ne during condensation at 5 K are monitored by FTIR spectroscopy.     

ChemInform Abstract: Matrix Infrared Spectra and Electronic Structure Calculations of the First Actinide Borylene: FB=ThF2.

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