Iteratively Regularized Methods for Inverse Problems

We are examining iteratively regularized methods for solving nonlinear inverse problems. Of particular interest for these types of methods are application problems which are unstable. For these application problems, special methods of numerical analysis are necessary, since classical algorithms tend to be divergent

Students' understanding of the concepts involved in one-sample hypothesis testing

Hypothesis testing is a prevalent method of inference used to test a claim about a population parameter based on sample data, and it is a central concept in many introductory statistics courses. At the same time, the use of hypothesis testing to interpret experimental data has raised concerns due to common misunderstandings by both scientists and students. With statistics education reform on the rise, as well as an increasing number of students enrolling in introductory statistics courses each year, there is a need for research to investigate students' understanding of hypothesis testing. In this study we used APOS Theory to investigate twelve introductory statistics students' reasoning about one-sample population hypothesis testing while working two real-world problems. Data were analyzed and compared against a preliminary genetic decomposition, which is a conjecture for how an individual might construct an understanding of a concept. This report presents examples of Actions, Processes, and Objects in the context of one-sample hypothesis testing as exhibited through students' reasoning. Our results suggest that the concepts involved in hypothesis testing are related through the construction of higher-order, coordinated Processes operating on Objects. As a result of our data analysis, we propose re�finements to our genetic decomposition and o�ffer suggestions for instruction of one-sample population hypothesis testing. We conclude with appendices containing a comprehensive revised genetic decomposition along with a set of guided questions that are designed to help students make the constructions called for by the genetic decomposition.</p

Complex Structure in Class 0 Protostellar Envelopes

We use archived IRAC images from the Spitzer Space Telescope to show that many Class 0 protostars exhibit complex, irregular, and non-axisymmetric structure within their dusty envelopes. Our 8 $\mu$m extinction maps probe some of the densest regions in these protostellar envelopes. Many of the systems are observed to have highly irregular and non-axisymmetric morphologies on scales >= 1000 AU, with a quarter of the sample exhibiting filamentary or flattened dense structures. Complex envelope structure is observed in regions spatially distinct from outflow cavities, and the densest structures often show no systematic alignment perpendicular to the cavities. These results indicate that mass ejection is not responsible for much of the irregular morphologies we detect; rather, we suggest that the observed envelope complexity is mostly the result of collapse from protostellar cores with initially non-equilibrium structures. The striking non-axisymmetry in many envelopes could provide favorable conditions for the formation of binary systems. We also note that protostars in the sample appear to be formed preferentially near the edges of clouds or bends in filaments, suggesting formation by gravitational focusing.Comment: 20 pages, 11 figures, 3 Tables, accepted to ApJ. Paper with full resolution figures available at http://www.astro.lsa.umich.edu/~jjtobin/Envelopes.pd

Search for the Flavor-Changing Neutral-Current Decays D+→π+μ+μ−D^+\to \pi^+ \mu^+ \mu^- and D+→π+e+e−D^+\to \pi^+ e^+ e^-

We report the results of a search for the flavor-changing neutral-current decays $D^+\rightarrow \pi^+ \mu^+ \mu^-$ and $D^+\rightarrow \pi^+ e^+ e^-$ in data from Fermilab charm hadroproduction experiment E791. No signal above background is found, and we obtain upper limits on branching fractions, $B(D^+\rightarrow \pi^+ \mu^+ \mu^-) < 1.8 \times 10^{-5}$ and $B(D^+\rightarrow \pi^+ e^+ e^-) < 6.6 \times 10^{-5}$, at the 90\% confidence level.Comment: nine pages with figures; compressed, uuencoded postscrip

Measurement of the Ds Lifetime

We report the results of a precise measurement of the Ds meson lifetime based on 1662 +/- 56 fully reconstructed Ds -> phi pi decays, from the charm hadroproduction experiment E791 at Fermilab. Using an unbinned maximum likelihood fit, we measure the Ds lifetime to be 0.518 +/- 0.014 +/- 0.007 ps. The ratio of the measured Ds lifetime to the world average D0 lifetime is 1.25 +/- 0.04. This result differs from unity by six standard deviations, indicating significantly different lifetimes for the Ds and the D0.Comment: 12 pages, 3 figures, 2 table. LaTe

Direct measurement of the pion valence quark momentum distribution, the pion light-cone wave function squared

We present the first direct measurements of the pion valence quark momentum distribution which is related to the square of the pion light-cone wave function. The measurements were carried out using data on diffractive dissociation of 500 GeV/c $\pi^-$ into di-jets from a platinum target at Fermilab experiment E791. The results show that the $|q\bar {q}>$ light-cone asymptotic wave function, which was developed using perturbative QCD methods, describes the data well for $Q^2 \sim 10 ~{\rm (GeV/c)^2}$ or more. We also measured the transverse momentum distribution of the diffractive di-jets.Comment: 13 pages, 4 figure

Study of the Ds+→π−π+π+D^+_s \to \pi^- \pi^+ \pi^+ decay and measurement of f0f_0 masses and widths

From a sample of 848 $\pm$ 44 $D_s^+ \to \pi^- \pi^+ \pi^+$ decays, we find $\Gamma(D_s^+ \to \pi^- \pi^+ \pi^+) / \Gamma(D_s^+ \to \phi \pi^+) = 0.245 \pm 0.028^{+0.019}_{-0.012}$. Using a Dalitz plot analysis of this three body decay, we find significant contributions from the channels $\rho^0(770)\pi^+$, $\rho^0(1450)\pi^+$, $f_0(980)\pi^+$, $f_2(1270)\pi^+$, and $f_0(1370)\pi^+$. We present also the values obtained for masses and widths of the resonances $f_0(980)$ and $f_0(1370)$.Comment: 10 pages, 3 eps figure

Experimental evidence for a light and broad scalar resonance in D+→π−π+π+D^+\to \pi^-\pi^+\pi^+ decay

From a sample of $1172 \pm 61$ $D^+ \to \pi^- \pi^+ \pi^+$ decay, we find $\Gamma (D^+ \to \pi^- \pi^+ \pi^+) / \Gamma (D^+ \to K^- \pi^+ \pi^+) = 0.0311 \pm 0.0018 ^{+0.0016}_{-0.0026}$. Using a coherent amplitude analysis to fit the Dalitz plot of this decays, we find strong evidence that a scalar resonance of mass $478^{+24}_{-23} \pm 17$ MeV/$c^2$ and width $324^{+42}_{-40} \pm 21$ MeV/$c^2$ accounts for approximately half of all decays.Comment: 10 pages, 3 eps figure