Counting descents, rises, and levels, with prescribed first element, in words

Recently, Kitaev and Remmel [Classifying descents according to parity, Annals of Combinatorics, to appear 2007] refined the well-known permutation statistic ``descent'' by fixing parity of one of the descent's numbers. Results in that paper were extended and generalized in several ways. In this paper, we shall fix a set partition of the natural numbers $N$, $(N_1, ..., N_t)$, and we study the distribution of descents, levels, and rises according to whether the first letter of the descent, rise, or level lies in $N_i$ over the set of words over the alphabet $[k]$. In particular, we refine and generalize some of the results in [Counting occurrences of some subword patterns, Discrete Mathematics and Theoretical Computer Science 6 (2003), 001-012.].Comment: 20 pages, sections 3 and 4 are adde

Mean Row Values in (u,v)(u,v)-Calkin-Wilf Trees

We fix integers $u,v \geq 1$, and consider an infinite binary tree $\mathcal{T}^{(u,v)}(z)$ with a root node whose value is a positive rational number $z$. For every vertex $a/b$, we label the left child as $a/(ua+b)$ and right child as $(a+vb)/b$. The resulting tree is known as the $(u,v)$-Calkin-Wilf tree. As $z$ runs over $[1/u,v]\cap \mathbb{Q}$, the vertex sets of $\mathcal{T}^{(u,v)}(z)$ form a partition of $\mathbb{Q}^+$. When $u=v=1$, the mean row value converges to $3/2$ as the row depth increases. Our goal is to extend this result for any $u,v\geq 1$. We show that, when $z\in [1/u,v]\cap \mathbb{Q}$, the mean row value in $\mathcal{T}^{(u,v)}(z)$ converges to a value close to $v+\log 2/u$ uniformly on $z$

Estimating the avoidable burden of certain modifiable risk factors in osteoporotic hip fracture using Generalized Impact Fraction (GIF) model in Iran

Backgrounds: The number of hip fractures, the most common complication of osteoporosis, has increased rapidly over the past decades. The goal of this study is to estimate the avoidable burden of certain modifiable risk factor of the condition using the Generalized Impact Fraction (GIF) model, which has been suggested and used by epidemiologists to overcome the drawbacks associated with the use of Attributable Fraction index. In addition to preventing a risk factor or the avoidable fraction of burden, this index can also calculate the change in the burden, when a risk factor is altered.Methods: International databases were searched through PubMed, CINAHLD, Embase using OVID and Google scholar. National resources were searched through IranDoc, IranMedex, SID and Journal sites. Other resources include abstract books and articles sent to the IOF congress. The following search strategy was used: (" Osteoporotic fracture" OR " Fragility Hip fracture" OR " Calcium" OR " vitamin D" OR " BMI" OR " lean body weight" OR " Physical activity" OR " exercise" OR " Smoke" ) AND (" prevalence" OR " incidence" OR " relative risk" ) and limited to " humans." Results: With regards to different scenarios already explained in modifying the studied risk factors, the greatest impact in reducing the prevalence of risk factors on osteoporotic hip fractures, was seen in low serum vitamin D levels, low physical activity and low intake of calcium and vitamin D, respectively. According to the fact that interventions for low serum vitamin D and low intake of calcium and vitamin D, are related to each other, it can be concluded that implementing interventions to change these two risk factors, in the easy, moderate and difficult scenarios, would result in approximately a 5%, 11% and 17% decrease in the burden of osteoporotic hip fractures, respectively. The addition of interventions addressing low physical activity in the easy, moderate and difficult scenarios, an 8%, 21% and 35% reduction in the burden of osteoporotic hip fractures would be reported, respectively.Conclusion: Improving serum vitamin D levels, recommending the consumption of calcium and vitamin D supplementations and advocating physical activity are the most effective interventions to reduce the risk of osteoporotic hip fractures. © 2013 Shahnazari et al; licensee BioMed Central Ltd

Progress Towards Modeling the Ablation Response of NuSil-Coated PICA

The Mars Science Laboratory (MSL) Entry, Descent and Landing Instrumentation (MEDLI) collected in-flight data largely used by the ablation community to verify and validate physics-based models for the response of the Phenolic Impregnated Carbon Ablator (PICA) material [1-4]. MEDLI data were recently used to guide the development of NASAs high-fidelity material response models for PICA, implemented in the Porous material Analysis Toolbox based on OpenFOAM (PATO) software [5-6]. A follow-up instrumentation suite, MEDLI2, is planned for the upcoming Mars 2020 mission [7] after the large scientific impact of MEDLI. Recent analyses performed as part of MEDLI2 development draw the attention to significant effects of a protective coating to the aerothermal response of PICA. NuSil, a silicone-based overcoat sprayed onto the MSL heatshield as contamination control, is currently neglected in PICA ablation models. To mitigate the spread of phenolic dust from PICA, NuSil was applied to the entire MSL heatshield, including the MEDLI plugs. NuSil is a space grade designation of the siloxane copolymer, primarily used to protect against atomic oxygen erosion in the Low Earth Orbit environment. Ground testing of PICA-NuSil (PICA-N) models all exhibited surface temperature jumps of the order of 200 K due to oxide scale formation and subsequent NuSil burn-off. It is therefore critical to include a model for the aerothermal response of the coating in ongoing code development and validation efforts

What sets the magnetic field strength and cycle period in solar-type stars?

Two fundamental properties of stellar magnetic fields have been determined by observations for solar-like stars with different Rossby numbers (Ro), namely, the magnetic field strength and the magnetic cycle period. The field strength exhibits two regimes: 1) for fast rotation it is independent of Ro, 2) for slow rotation it decays with Ro following a power law. For the magnetic cycle period two regimes of activity, the active and inactive branches, also have been identified. For both of them, the longer the rotation period, the longer the activity cycle. Using global dynamo simulations of solar like stars with Rossby numbers between ~0.4 and ~2, this paper explores the relevance of rotational shear layers in determining these observational properties. Our results, consistent with non-linear alpha^2-Omega dynamos, show that the total magnetic field strength is independent of the rotation period. Yet at surface levels, the origin of the magnetic field is determined by Ro. While for Ro<1 it is generated in the convection zone, for Ro>1 strong toroidal fields are generated at the tachocline and rapidly emerge towards the surface. In agreement with the observations, the magnetic cycle period increases with the rotational period. However, a bifurcation is observed for Ro~1, separating a regime where oscillatory dynamos operate mainly in the convection zone, from the regime where the tachocline has a predominant role. In the latter the cycles are believed to result from the periodic energy exchange between the dynamo and the magneto-shear instabilities developing in the tachocline and the radiative interior.Comment: 43 pages, 14 figures, accepted for publication in The Astrophysical Journa

Direct Numerical Simulation of a Temporally Evolving Incompressible Plane Wake: Effect of Initial Conditions on Evolution and Topology

Direct numerical simulations have been used to examine the effect of the initial disturbance field on the development of three-dimensionality and the transition to turbulence in the incompressible plane wake. The simulations were performed using a new numerical method for solving the time-dependent, three-dimensional, incompressible Navier-Stokes equations in flows with one infinite and two periodic directions. The method uses standard Fast Fourier Transforms and is applicable to cases where the vorticity field is compact in the infinite direction. Initial disturbances fields examined were combinations of two-dimensional waves and symmetric pairs of 60 deg oblique waves at the fundamental, subharmonic, and sub-subharmonic wavelengths. The results of these simulations indicate that the presence of 60 deg disturbances at the subharmonic streamwise wavelength results in the development of strong coherent three-dimensional structures. The resulting strong three-dimensional rate-of-strain triggers the growth of intense fine scale motions. Wakes initiated with 60 deg disturbances at the fundamental streamwise wavelength develop weak coherent streamwise structures, and do not develop significant fine scale motions, even at high Reynolds numbers. The wakes which develop strong three-dimensional structures exhibit growth rates on par with experimentally observed turbulent plane wakes. Wakes which develop only weak three-dimensional structures exhibit significantly lower late time growth rates. Preliminary studies of wakes initiated with an oblique fundamental and a two-dimensional subharmonic, which develop asymmetric coherent oblique structures at the subharmonic wavelength, indicate that significant fine scale motions only develop if the resulting oblique structures are above an angle of approximately 45 deg

Science Teachers’ Beliefs: Perceptions of Efficacy and the Nature of Scientific Knowledge and Knowing

As we write this chapter, teachers across the United States are preparing for their first days of school. Besides the excitement associated with teaching students who are newly energized after a long summer break, science teachers also come into the school year with a host of beliefs that may well shape the ways in which they teach and may ultimately have some bearing on their students’ overall experiences with science. Although there are countless beliefs that teachers hold with regard to science, in this chapter we focus specifically on two beliefs that have received the most research attention—teachers’ self-efficacy, which describes their beliefs about their capability to teach science, and their epistemic beliefs, which describe their beliefs about the nature of scientific knowledge and knowing. Science has been described by many as one of the most difficult school subjects (Drew, 2011; Dweck, 2006; National Academies of Science, 2011). For this reason, the National Academies of Science has noted that a strong sense of competence is critical for success in science and for persistence in science-related careers. For science teachers in particular, this same robust sense of competence is required both to understand science and to teach it well, as teachers who feel incompetent in science are more likely to avoid teaching it (Grindrod, Klindworth, Martin, & Tytler, 1991; Skamp, 1995). Given the importance of competence beliefs in learning and teaching science, we focus on one of the most well-studied constructs dealing with this belief—teachers’ self-efficacy for teaching science. Besides self-efficacy, scholars and practitioners alike have documented the regrettable lack of sophistication that students have with regard to their basic scientific literacy. For example, many students in middle school believe that science is composed entirely of absolute truths (BouJaoude, 1996), and that the development of scientific knowledge leaves little room for creativity and imagination (Griffiths & Barman, 1995; Lederman & O’Malley, 1990; Smith, Maclin, Houghton, & Hennessey, 2000). These troubling cases can be traced to teachers not understanding the complex nature of scientific knowledge well enough to communicate that level of sophistication to their students (Brickhouse, 1990; Duschl & Wright, 1989; Hashweh, 1996; Keys & Bryan, 2001). They can also be traced to institutional structures, such as an undue emphasis on testing, which can lead some science teachers to avoid teaching about the complexities of science (Brickhouse & Bodner, 1992; Munby, Cunningham, & Lock, 2000). The development of students’ deep understanding and appreciation for the complexity of science starts first with teachers. Teachers must have a deep level of understanding about the complexity of scientific knowledge. That is, they must understand that knowledge in science is connected to other fields of knowledge; that scientific knowledge is often revised with new evidence; that scientists often disagree; and that scientific knowledge must be justified with evidence from multiple sources and multiple experiments. Teachers must also possess the selfefficacy to lead their students through learning activities that model that complexity. Being able to teach in such a manner is certainly no easy task. It requires substantial skills in planning and organizing. It requires teachers to possess excellent classroom management skills, the ability to engage and motivate students, as well as the ability to connect these rich learning activities to the standards on which students will be tested. Given these issues that science teachers must grapple with, we chose to study science teachers’ self-efficacy and their epistemic beliefs about science.https://scholarworks.wm.edu/bookchapters/1002/thumbnail.jp

Preliminary Measurements of the Motion of Arcjet Current Channel Using Inductive Magnetic Probes

This paper covers the design and first measurements of non-perturbative, external inductive magnetic diagnostics for arcjet constrictors which can measure the motion of the arc current channel. These measurements of arc motion are motivated by previous simulations using the ARC Heater Simulator (ARCHeS), which predicted unsteady arc motion due to the magnetic kink instability. Measurements of the kink instability are relevant to characterizing motion of the enthalpy profile of the arcjet, the arcjet operational stability, and electrode damage due to associated arc detachment events. These first measurements indicate 4 mm oscillations at 0.5-2 kHz of the current profile