Local radial Phragmén-Lindelöf estimates for plurisubharmonic functions on analytic varieties

We give a sufficient condition for a local radial Phragmén-Lindelöf principle on analytic varieties. This condition is expressed in terms of existence of hyperbolic directions.

     

Nonclassical multidimensional singular integral operators on R + n+1

Banach algebras of certain bounded operators acting on the half-spaceL _p (R ₊ ⁿ⁺¹ ,x ₀ ) (1<p<, –1<<p–1) are defined which contain for example Wiener-Hopf operators, defined by multidimensional singular convolution integral operators, as well as certain singular integral operators with fixed singularities. Moreover the symbol may be a positive homogeneous function only piecewise continuous on the unit sphere. Actually these multidimensional singular integral operators may be not Calderón-Zygmund operators but are built up by those in lower dimensions. This paper is a continuation of a joint paper of the author together with R.V. Duduchava [10]. The purpose is to investigate invertibility or Fredholm properties of these operators, while the continuity is given by definition. This is done in [10] forp=2 and –1<<1, and in the present paper forL _p (R ₊ ⁿ⁺¹ ,x ₀ ) with 1<p< and –1<<p–1.     

Variational calculus with sums of elementary tensors of fixed rank

In this article we introduce a calculus of variations for sums of elementary tensors and apply it to functionals of practical interest. The survey provides all necessary ingredients for applying minimization methods in a general setting. The important cases of target functionals which are linear and quadratic with respect to the tensor product are discussed, and combinations of these functionals are presented in detail. As an example, we consider the solution of a linear system in structured tensor format. Moreover, we discuss the solution of an eigenvalue problem with sums of elementary tensors. This example can be viewed as a prototype of a constrained minimization problem. For the numerical treatment, we suggest a method which has the same order of complexity as the popular alternating least square algorithm and demonstrate the rate of convergence in numerical tests.     

Multielement analysis of biological reference materials by total-reflection X-ray fluorescence and inductively coupled plasma mass spectrometry in the semiquant mode

Summary Total-reflection X-ray fluorescence (TXRF) and inductively coupled plasma mass spectrometry (ICP-MS) were used for the analysis of two biological reference materials. The quantifications were carried out after addition of one single standard element which serves as an internal standard in both cases. The results of TXRF analysis were good to satisfactory. The method is therefore suitable for fast multielement analysis, because it needs no special calibration specimens. The results of ICP-MS analysis are at least in the order of magnitude of the certified values. In some cases recoveries fit very well. For quantitative analysis, however, the use of the standard addition method or the calibration with external standards is required.     

Aerodynamic forces on a tall building in a turbulent boundary layer

The model studies were designed to obtain information concerning wind loads on a tall building by placing the model in a turbulent shear flow simulating expected atmospheric boundary-layer winds. Since current design codes are inadequate for predicting all possible motions of tall buildings, it is important that better knowledge of mean and fluctuating loadings and their distributions becomes available. Experiments were conducted to determine the mean and fluctuating forces and twisting moments at several levels over the surface of a model. By determining the effects at several levels simultaneously, it was possible to correlate forces and moments at five levels with one common level. A single model was tested at varying orientations. Tests were also conducted with an identical model placed upstream so that its wake influenced the flow around the instrumented model. Results are presented in terms of distributions of force and moment coefficients and correlations at different levels. The spectral character of the force and moment components is illustrated for one case. Paper was presented at 1977 SESA Spring Meeting held in Dallas, TX on May 15–20.