Thue-Morse at Multiples of an Integer

Let (t_n) be the classical Thue-Morse sequence defined by t_n = s_2(n) (mod 2), where s_2 is the sum of the bits in the binary representation of n. It is well known that for any integer k>=1 the frequency of the letter "1" in the subsequence t_0, t_k, t_{2k}, ... is asymptotically 1/2. Here we prove that for any k there is a n<=k+4 such that t_{kn}=1. Moreover, we show that n can be chosen to have Hamming weight <=3. This is best in a twofold sense. First, there are infinitely many k such that t_{kn}=1 implies that n has Hamming weight >=3. Second, we characterize all k where the minimal n equals k, k+1, k+2, k+3, or k+4. Finally, we present some results and conjectures for the generalized problem, where s_2 is replaced by s_b for an arbitrary base b>=2.Comment: 14 page

The Use Of Contempt Of Court To Enforce Florida Divorce Decrees

Florida\u27s courts often use contempt sanctions as a highly effective means of enforcing final divorce decrees. Accordingly, when a party fails to comply with a provision of the divorce order, the recalcitrant party may be threatened with imprisonment

The Roadmap Seminar: Preparing Students for Success in Learning Communities

With institutions of many types embracing the rich possibilities offered by course-based learning communities, it is important for programs to consider how they might best prepare students for success in those courses. Key to this work is identifying the particular skills needed and creating opportunities to introduce students to those skills before their learning community experiences. At Queens University of Charlotte, we have tackled this important issue by designing a transition course, the Roadmap Seminar, with components that introduce students to the three skills central to our learning communities: integrative thinking, teamwork, and metacognition. Using mid-semester surveys of students and faculty, learning outcomes assessment, student course performance, and end of semester evaluations, our initial results of this approach are positive. Student work has shown the conscious development of integrative thinking and heightened awareness of how they function as part of a team. This framework provides an opportunity for other institutions to consider how they can prepare students with the specific skills that will make their learning communities truly high impact experiences

On Estimating the High-Energy Cutoff in the X-ray Spectra of Black Holes via Reflection Spectroscopy

The fundamental parameters describing the coronal spectrum of an accreting black hole are the slope $\Gamma$ of the power-law continuum and the energy $E_{cut}$ at which it rolls over. Remarkably, this parameter can be accurately measured for values as high as 1 MeV by modeling the spectrum of X-rays reflected from a black hole accretion disk at energies below 100 keV. This is possible because the details in the reflection spectrum, rich in fluorescent lines and other atomic features, are very sensitive to the spectral shape of the hardest coronal radiation illuminating the disk. We show that fitting simultaneous NuSTAR (3-79 keV) and low-energy (e.g., Suzaku) data with the most recent version of our reflection model RELXILL, one can obtain reasonable constraints on $E_{cut}$ at energies from tens of keV up to 1 MeV, for a source as faint as 1 mCrab in a 100 ks observation.Comment: Accepted for publication in ApJL, 6 pages, 5 figure

X-ray Reflection Spectroscopy of the Black Hole GX 339-4: Exploring the Hard State with Unprecedented Sensitivity

We analyze {\it simultaneously} six composite {\it RXTE} spectra of GX 339--4 in the hard state comprising 77 million counts collected over 196 ks. The source spectra are ordered by luminosity and spanthe range 1.6\% to 17\% of the Eddington luminosity. Crucially, using our new tool {\tt pcacorr}, we re-calibrate the data to a precision of 0.1\%, an order of magnitude improvement over all earlier work. Using our advanced reflection model {\tt relxill}, we target the strong features in the component of emission reflected from the disk, namely, the relativistically-broadened Fe K emission line, the Fe K edge and the Compton hump. We report results for two joint fits to the six spectra: For the first fit, we fix the spin parameter to its maximal value ($a_*=0.998$) and allow the inner disk radius $R_{\rm in}$ to vary. Results include (i) precise measurements of $R_{\rm in}$, with evidence that the disk becomes slightly truncated at a few percent of Eddington; and (ii) an order-of-magnitude swing with luminosity in the high energy cutoff, which reaches $>890$ keV at our lowest luminosity. For the second fit, we make the standard assumption in estimating spin that the inner edge of the accretion disk is located at the innermost stable circular orbit ($R_\mathrm{in} = R_\mathrm{ISCO}$) and find $a_* = 0.95^{+0.03}_{-0.05}$ (90\% confidence, statistical). For both fits, and at the same level of statistical confidence, we estimate that the disk inclination is $i = 48\pm 1$ deg and that the Fe abundance is super-solar, $A_\mathrm{Fe} = 5\pm1$.Comment: Accepted for publication in ApJ, 20 pages, 13 figure

Impact of surface roughness on diffusion of confined fluids

Using event-driven molecular dynamics simulations, we quantify how the self diffusivity of confined hard-sphere fluids depends on the nature of the confining boundaries. We explore systems with featureless confining boundaries that treat particle-boundary collisions in different ways and also various types of physically (i.e., geometrically) rough boundaries. We show that, for moderately dense fluids, the ratio of the self diffusivity of a rough wall system to that of an appropriate smooth-wall reference system is a linear function of the reciprocal wall separation, with the slope depending on the nature of the roughness. We also discuss some simple practical ways to use this information to predict confined hard-sphere fluid behavior in different rough-wall systems

Active Transport of Peptides Across the Intact Human Tympanic Membrane.

We previously identified peptides that are actively transported across the intact tympanic membrane (TM) of rats with infected middle ears. To assess the possibility that this transport would also occur across the human TM, we first developed and validated an assay to evaluate transport in vitro using fragments of the TM. Using this assay, we demonstrated the ability of phage bearing a TM-transiting peptide to cross freshly dissected TM fragments from infected rats or from uninfected rats, guinea pigs and rabbits. We then evaluated transport across fragments of the human TM that were discarded during otologic surgery. Human trans-TM transport was similar to that seen in the animal species. Finally, we found that free peptide, unconnected to phage, was transported across the TM at a rate comparable to that seen for peptide-bearing phage. These studies provide evidence supporting the concept of peptide-mediated drug delivery across the intact TM and into the middle ears of patients