The effect of music participation on mathematical achievement and overall academic achievement of high school students

A study was conducted on high school students, comparing those with some music credits to those with none. No statistically significant difference was found in their mean math grade point averages (GPA) or their mean cumulative GPAs. Students were then separated into two groups based on the number of music credits. Students who had earned at least two music credits per grade level were placed into Group A. This category included ninth graders with two or more music credits, tenth graders with four or more music credits, eleventh graders with six or more music credits, and twelfth graders with eight or more music credits. The remaining students were placed into Group B. Group A students performed better than group B students. However, the differences were not statistically significant. Scatter plots indicated a slight upward trend in GPAs as the number of music credits increased. Lower GPAs were nonexistent as the music credits increased.     

The rate at which energy decays in a damped String

The energy in a string subject to positive viscous damping is known to decay exponentially in time. Under the assumption that the damping is of bounded variation, we identify the best rate of decay with the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup. We analyze the spectrum of this nonselfadjoint operator in some detail. Our bounds on its real eigenvalues and asymptotic form of its large eigenvalues translate into criteria for over/underdamping and a proof that the decay rate achieves its (negative) minimum over those dampings whose total variation does not exceed a prescribed value.     

A Test of Multivariate Independence Based on a Single Factor Model

A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation γ between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of γ is appreciably more powerful than that based on r₁, the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r₁.     

Final-state intensities in photoelectron spectra of 4f electrons as predicted by relativistic calculations

Relativistic calculations have been performed for the intensities of the various photoelectron signals expected in ionisation of a partly filled 4f subshell in lanthanoid ions. The results account for discepancies found between the predictions of non-relativistic theory and the 4f photoelectron spectra of ytterbium (III)compounds.     

Measuring the two-dimensional structure of a wavy water surface optically: A surface gradient detector

A new method of measuring the slopes of a water surface covered with short waves is developed. A camera is placed far above the water surface looking downward so that it receives only approximately vertical rays of light emerging from the water surface from a source below. A large lens is positioned horizontally underwater. A plane light source in the form of a translucent colored screen is placed horizontally in the focal plane below this lens. Corresponding to each value of water surface slope, regardless of observer position, there is one and only one point of origin on the color screen from which light rays can enter the camera. When the color screen has a suitable two-dimensional color pattern, we are able to detect the gradient of the surface elevation throughout the field of view of the camera. This refraction slope detector has been used to find statistical properties of short wind waves in a wind-wave channel where a broad angular beam width of capillary ripples and short gravity waves contribute to the surface slopes. In these experiments waves were generated by winds ranging from 5 m/s to 10 m/s at a fetch of 24 m. The wavenumber spectra of short wave slopes have two distinguishing features: a dip at the capillary-gravity transition and steep slopes in the capillary range. Surface shapes resembling the shape of solitary capillary-gravity waves have been found from profiles of wave elevation deduced by integration of the elevation gradient.We are especially grateful for the advice of Dr. M. Gharib on the use of the HSI color system. John Lyons provided expert help in the laboratory and materials for and advice on photography. We thank the staff of the SIO Hydraulics Laboratory for making the wind-wave channel available for our use, and the staff of UCSD library for enabling us to use the Barneyscanner photometer-digitizer. We thank an anonymous reviewer who pointed out a numerical error and improved the clarity of the text.     

Modelling hydrogen in silicate materials

The expectation that the hydroxyl analogue state of positive muons implanted in quartz should be stabilized by a suitable charge compensation centre is supported by preliminary data. The diamagnetic fraction correlates with aluminium content over the narrow range investigated. This revised version was published online in August 2006 with corrections to the Cover Date.