Report on highly automated works in Japan — management of labour in line with technology development

In recent years drastic shifts in the paradigms of politics, economics and technologies have occurred throughout the world. The shifts in these three fields are all related. It is our responsibility to investigate these shifts from the aspects of society and mankind for the prosperity of future generations. For this, societies should share with each other their wisdom and knowledge in an effort to plan for the future.Presented at conference on Ecology of Science and Technology, Japan Science Foundation, Tokyo, 1992.     

Decreasing of the initial shear modulus with increasing axial strain explained by means of a plastic-hypoelastic model

Summary The purpose of this work is to examine in detail the possibility to explain the decreasing of the initial shear modulus with increasing axial strain, observed first by Feigen, by means of the plastic-hypoelastic stress-strain relation suggested by Lehmann and by the author of the present paper.Notations _ij components of the infinitesimal strain tensor dilatation - strain deviator - _ij components of the stress tensor - spherical part of the stress tensor - stress deviator - ²= _{ij ij} second invariant of the stress deviator - = ₃₃ axial strain - e= ₁₃ shear component of the strain tensor - =2 ₁₃ shear strain - = ₃₃ axial stress - s= ₁₃ shear stress - T _ij components of Cauchy's stress tensor - F _ij components of the deformation gradient - L _ij components of the velocity gradient (Eulerian coordinates) - components of the rate of deformation tensor - components of the spin tensor - components of the rate of deformations deviator - components of Cauchy's stress deviator - T=T ₃₃ axial Cauchy's stress With 7 Figures     

Initiation of air core in a swirl nozzle using time-independent power-law fluids

Summary Theoretical and experimental analyses have been carried out for determining the injection condition below which the formation of air core does not take place in the course of flow of a time-independent power-law fluid through a swirl nozzle. Analytical solution lends one distinct value of generalized Reynolds number at the inlet to a nozzle below which the air core is not formed. Experiments reveal that there exist two limiting values of such generalized Reynolds number regarding the formation of air core in a nozzle. One value being the upper limit below which steady flow occurs without air core, the other one is the lower limit above which steady flow with fully developed air core persists. In between these two limiting values, there prevails a transition zone through which fully developed air core is set up within the nozzle. For all the nozzles, theoretical results are in fair agreement with the experimental values of upper limit of generalized Reynolds numbers with respect to steady flow without air core. Amongst all the pertinent independent geometrical parameters of a nozzle, the orifice-to-swirl chamber-diameter ratio has the remarkable influence on generalized Reynolds number describing the initiation of air core.Nomenclature D ₁ Swirl chamber diameter - D ₂ Orifice diameter - D _s Diameter of tangential entry ports - E A non-dimensional parameter defined by Eq. (9) - E _R A non-dimensional parameter defined by Eq. (25) - K Flow consistency index - L ₁ Length of the swirl chamber - n Flow behaviour index - P Static pressure inside the nozzle - P _b Back-pressure of the nozzle - Q Volume flow rate - R Radius vector or longitudinal coordinate with respect to spherical coordinate system (Fig. 3) - R ₁ Radius of the swirl chamber - R ₂ Radius of the orifice - Generalized Reynolds number at the inlet to the nozzle - Limiting value of generalized Reynolds number describing initiation of air core - R _z Radius at any section - r Radial distance from the nozzle axis - r _a Air core radius - u Longitudinal component of velocity with respect to spherical coordinate system (Fig. 3) - V _r Radial velocity component - V _z Axial velocity component - V Tangential velocity component - Tangential velocity at inlet to the nozzle - v Component of velocity in the axial plane perpendicular toR (Fig. 3) - w Component of velocity perpendicular to axial plane with respect to the spherical coordinate system (Fig. 3) - z Distance along the nozzle axis from its inlet plane - Half of the spin chamber angle - Boundary layer thickness measured perpendicularly from the nozzle wall - ₂ Boundary layer thickness at the orifice - Angle, which a radius vector makes with the nozzle axis, in spherical coordinate system (Fig. 3) - Density of the fluid - Running coordinate in the azimuthal direction with respect to the cylindrical polar coordinate system as shown in Fig. 3 - Circulation constant With 8 Figures     

Zur Konvergenz der Ableitungen von Interpolationspolynomen

Letp _n denote the polynomial of degreen or less that interpolates a given smooth functionf at the ?eby?ev nodest _j ⁿ =cos(jπ/n), 0≤j≤n, and let ‖·‖ be the maximum norm inC[?1, 1]. It is proved that fork-th derivatives (2≤k≤n) estimates of the following type hold $$\parallel f^{(k)} - p_n^{(k)} \parallel \leqslant c_k n^{k - 1} \inf \{ \parallel f^{(k)} - q\parallel :q \in \Pi _{n - k} \} .$$ In this relationc _k only depends onk andΠ _n?k denotes the space of polynomials up to degreen?k.     

On componentwise error estimates for inverse matrices

LetA be an×n-matrix with the property I–A<1. LetY be an approximation of the inverse ofA. This paper shows how to get a componentwise error estimate forY, that does not require too much numerical effort but generally presents better results than global error estimates do. Although proved by means of interval mathematics, the given error estimate can also be calculated in absence of any implementation of interval arithmetic.

---

Über komponentenweise Fehlerabschätzungen für inverse Matrizen

Zusammenfassung SeiA einen×n-Matrix mit der Eigenschaft I–A<1. SeiY eine Approximation der Inversen vonA. In dieser Arbeit wird gezeigt, wie man eine komponentenweise Fehlerabschätzung fürY erhalten kann, deren Berechnung nicht sehr aufwendig ist, die aber im allgemeinen schärfer ist als globale Fehlerabschätzungen. Obwohl mit intervallmathematischen Mitteln bewiesen, kann die angegebene Fehlerabschätzung auch berechnet werden, wenn keine Intervallarithmetik implementiert ist.

---

---

This research was supported in part by Sonderforschungsbereich 72-Approximation und Optimierung, University of Bonn.     

Explicit,optimal stability functionals and their application to cyclic discretization methods

The present paper contains a stability concept for discretization methods of a certain, very general classM, which is optimal (in the sense of yielding the best general, two-sided error bounds) without being more restrictive than any of the classical stability definitions. The optimal stability functional Ψ_h related to it depends on the linear part of the discretization operator, and has the important property that Ψ_h [δ] may be of orderq+1, i.e. Ψ_h [δ] = O(h ^q+1), even if the local error δ only has orderq, δ = O(h ^q). This result may be used for the construction of methods with maximum order. Its application to linear cyclic methods, for example, furnishes a new approach to the theory of linearM-cyclick-step methods of maximum order.     

Konvergenz von quadratischen Interpolations- und Flächenabgleichssplines

The purpose of this paper is to show that for continuous functions the related quadratic splines converge without any assumption on the spline grid. The points of the interpolatory grid can be chosen between the corresponding points of the spline grid with a division ratio from \(\frac{{\sqrt 2 }}{2}\) to \(1 - \frac{{\sqrt 2 }}{2}\) . In the case of continuously differentiable functions the division ratio can even be taken between 0 and 1; in addition, the order of convergence is increased. For twice differentiable functions the full order of convergence is obtained. Analogous results about the convergence of histo splines are proved.     

Sampling from binomial and poisson distributions: A method with bounded computation times

An accurate acceptance-rejection algorithm is devised and tested. The procedure requires an average of less than 3 uniform deviates whenever the standard deviation of the distribution is at least 4, and this number decreases monotonically to 2.63 as . Variable parameters are permitted, and no subroutines for sampling from other statistical distributions are needed.This research was supported by the Austrian Research Council (Fonds zur Förderung der wissenschaftlichen Forschung).     

Optimal interval enclosing of certain sets of matrices,with application to monotone enclosing of square roots

In this paper, two kinds of partial ordering for symmetric matrices are related to each other, namely, the natural partial ordering ≤ generated by the coneK of elementwise nonnegative matrices, and the definite partial ordering \( \leqslant \cdot\) generated by the coneK _D of nonnegative definite matrices. The main result of this paper shows how a matrix interval in the sense of the definite partial ordering can be enclosed between optimal bounds with respect to the natural partial ordering. By means of this result, it is possible to compute a numerically practicable inclusion based on the natural partial ordering from a given inclusion of some matrix with the definite partial ordering. In this way, an always and moreover quadratically convergent method of elementwise enclosing the square root of a positive definite, symmetric matrix can be constructed.