The Itô-Clifford integral III. The Markov property of solutions to stochastic differential equations

It is shown that the solution to the Itô-Clifford stochastic differential equationdX _t =F(X _t ,t)dΨ _t +dΨ _t G(X _t ,t)+H(X _t ,t)dt, whereF, G, H are suitable Lipschitz functions andΨ _t is the fermion martingale, satisfies a Markov property.     

Resonance structure in 15N(p,n0)15O in the region Ep = 8.5–19.0 MeV

Excitation functions at seven angles, covering the energy range E_p = 8.5–19.0 MeV, have been measured for ¹⁵N(p, n_o)¹⁵O using time-of-flight methods. Angular distributions were also measured at five energies. Activation methods were used to determine the total cross section below the excited-state threshold. Ten resonances were observed, four of which have also been found in ¹⁵N(p, γ)¹⁶O data. The energies, widths and nucleon widths have been extracted and are used, together with proton capture data, to derive radiative widths for certain levels.     

Novel approach to evaluate the interaction of pulsed ultrasound with embryonic development

An in vitro whole-embryo culture system was used which allowed ultrasound to interact directly with rat embryos, at 9.5 days of gestation, under conditions of controlled temperature. Neural plate damage, expressed during a critical period of forebrain development, was evaluated 48 h post-insonation. Ultrasound-induced effects were thus identified in the absence of significant temperature changes or complications from the influence of maternal physiology. Exposures to 3.2 microseconds pulses of 3.14 MHz ultrasound at a PRF of 2 kHz and 1.2 W cm-2 intensity (ISPTA) for durations of 5, 15 or 30 min produced no major morphological abnormalities at a temperature of 38.5 degrees C. Embryonic response to stress was evidenced by changes in protein synthesis, and delayed development was indicated by a reduction in somite number. These effects were enhanced when the insonation temperature was elevated by 1.5 degrees C.     

Productive and ineffective efforts: how student effort in high school mathematics relates to college calculus success

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the commonly expected benefits, the latter is associated with negative consequences. Time spent reading the course text in US high schools was negatively related to college calculus performance. Daily study time, however, was found to be either a productive or an ineffective effort, depending on the level of high school mathematics course and the student's performance in it.     

Greatest common divisors from generalized sylvester resultant matrices

Sylvester's classical resultant matrix for determining the degree of the greatest common divisor of two polynomials has recently been generalized to deal with m+1 polynomialsm>1. A slightly stronger version is given in this paper for the case when the polynomials do not all have the same degree. The proof relies .on using an appropriate companion matrix, and thereby provides a link with previous work using this approach. It is then shown how the coefficients in a greatest common divisor can be obtained by reducing this extended resultant matrix to row echelon form, this again being an extension of a previous result for the casem=1. Finally, it is shown how the results can be modified when the polynomials are expressed relative to an arbitrary orthogonal basis.     

The Histogram and Boxplot for the Display of Lifetime Data

Abstract

The importance of histograms and boxplots as exploratory data analysis (EDA) tools has been well established. Yet, adopting them for lifetime data is not straightforward. The first problem, particularly in histograms, is how to deal with censored observations. The second problem is that the underlying distribution of lifetime data is often highly positively skewed. Therefore, in the classical boxplot, large observations can be wrongly diagnosed as outliers. This article extends the definition of the histogram to accommodate for right-censored observations. We apply the “redistribution to the right” method so that the weight of each uncensored observation is actually the jump of the Kaplan—Meier estimation at this point. We also propose modified boxplots to resolve both problems of right censoring and skewness. In our procedure, the fences differ from those of the classical boxplot. Simulation results are presented for an evaluation of our procedure and an example is presented for illustration.     

First measurement of the W-boson mass in run II of the Tevatron

We present a measurement of the W-boson mass using 200 pb{-1} of data collected in pp[over ] collisions at sqrt[s]=1.96 TeV by the CDF II detector at run II of the Fermilab Tevatron. With a sample of 63 964 W-->enu candidates and 51 128 W-->munu candidates, we measure M_{W}=80 413+/-34{stat}+/-34{syst}=80,413+/-48 MeV/c;{2}. This is the most precise single measurement of the W-boson mass to date.