Solving Systems of Non-Linear Equations by Broyden's Method with Projected Updates

We introduce a modification of Broyden's method for finding a zero of n nonlinear equations in n unknowns when analytic derivatives are not available. The method retains the local Q-superlinear convergence of Broyden's method and has the additional property that if any or all of the equations are linear, it locates a zero of these equations in n+1 or fewer iterations. Limited computational experience suggests that our modification often improves upon Eroyden's method.

Fe II lifetimes and transition probabilities

Fe II radiative lifetimes were measured applying the time-resolved nonlinear laser-induced fluoresence technique. We investigated 21 levels of up to 47000 1/cm. The uncertainties are typically 2-3%. The lifetimes provide an improved absolute scale to our branching fractions which were measured with a Fourier transform spectrometer and a high-resolution grating spectrometer and which have been published earlier. We report absolute transition probabilities of 140 Fe II lines in the wavelength range 220-780 nm. The overall uncertainties are estimated to be 6% for the strong and up to 26% for the weak transitions. The results are compared with recent experimental data from the literature. Our large set of accurate data can be used for a reliability check of theoretical data calculated for iron abundances in astrophysical plasmas

Is There a Union Wage Premium in Germany and Which Workers Benefit Most?

Using representative data from the German Socio-Economic Panel (SOEP), this paper finds a statistically significant union wage premium in Germany of almost three percent, which is not simply a collective bargaining premium. Given that the union membership fee is typically about one percent of workers’ gross wages, this finding suggests that it pays off to be a union member. Our results show that the wage premium differs substantially between various occupations and educational groups, but not between men and women. We do not find that union wage premia are higher for those occupations and workers which constitute the core of union membership. Rather, unions seem to care about disadvantaged workers and pursue a wider social agenda

Changes in union membership over time : a panel analysis for West Germany

Despite the apparent stability of the wage bargaining institutions in West Germany, aggregate union membership has been declining dramatically since the early 90's. However, aggregate gross membership numbers do not distinguish by employment status and it is impossible to disaggregate these sufficiently. This paper uses four waves of the German Socioeconomic Panel in 1985, 1989, 1993, and 1998 to perform a panel analysis of net union membership among employees. We estimate a correlated random effects probit model suggested in Chamberlain (1984) to take proper account of individual specfic effects. Our results suggest that at the individual level the propensity to be a union member has not changed considerably over time. Thus, the aggregate decline in membership is due to composition effects. We also use the estimates to predict net union density at the industry level based on the IAB employment subsample for the time period 1985 to 1997. JEL - Klassifikation: J

A METHOD TO DETERMINE BALL IMPACT LOCATION AND ITS MOVEMENT ACROSS THE STRINGS OF A TENNIS RACKET

INTRODUCTION: The impact location of a ball on the string plane area of a given tennis racket and its movement across the strings influences ball speed, direction of flight, and the resulting spin of the ball. The accuracy and resolution of cinematographic recordings are limited because the racket head area is small in comparison to the necessary object space for filming. Because the interaction of the tennis racket with the ball is of fundamental importance for the game, an instrumented tennis racket was developed to electronically determine the point of ball impact on the strings. METHODS: A “Kuebler Inertial Light" tennis racket was used for this study. 32 very thin steel wires were woven around 14 longitudinal and 18 transverse string sections of the racket head. This resulted in a 14 by 18 wire matrix, covering a large area of the racket head. Each steel wire was electrically insulated and connected to a charge amplifier by a thin, shielded cable. The thin cable bundle from the 32 sensors ran along the racket handle to a small electronic unit, which was attached to a belt and carried by the subjects. Total racket weight was increased slightly by the wires, but was still well within the range of weights found in commercially available tennis rackets. Through its friction with the ground and during its flight through the air, the tennis ball was electrically charged before it made contact with the racket head. At ball contact, an electrostatic charge was detected by the steel wires and electronically processed by their charge amplifiers. Using a data acquisition system with a high sampling frequency, each wire was sampled with 5 kHz. In a pre-trigger mode, data were collected for a total of 12 ms, beginning 4 ms before initial charge detection by the sensors. Following data collection, further mathematical processing was performed by multiplying the charge values of each of the longitudinal sensors with all transverse sensors, resulting in a 14 by 18 matrix of numbers. Geometric averaging of all matrix values determined the point of contact on the string area. RESULTS AND CONCLUSIONS: According to the judgment of experienced tennis players, the handling of the instrumented racket was very similar to a regular racket for forehand and backhand strokes, as well as for the serve. Only for topspin and slice strokes was a slightly increased spin production on the ball recognized. Subjects felt comfortable with the racket, some of them achieving ball speeds over 190 km/h for their serves. The matrix sensor arrangement and the time resolution of 0.2 ms guaranteed an accurate determination of the contact location of the ball and its movement across the string area. From these data, ball movements on the racket head can be shown for typical examples of forehand, backhand, topspin and slice strokes, as well as for serves

Quantum engineering of squeezed states for quantum communication and metrology

We report the experimental realization of squeezed quantum states of light, tailored for new applications in quantum communication and metrology. Squeezed states in a broad Fourier frequency band down to 1 Hz has been observed for the first time. Nonclassical properties of light in such a low frequency band is required for high efficiency quantum information storage in electromagnetically induced transparency (EIT) media. The states observed also cover the frequency band of ultra-high precision laser interferometers for gravitational wave detection and can be used to reach the regime of quantum non-demolition interferometry. And furthermore, they cover the frequencies of motions of heavily macroscopic objects and might therefore support the attempts to observe entanglement in our macroscopic world.Comment: 12 pages, 3 figure