Design research in mathematics education : the case of an ict-rich learning arrangement for the concept of function

The concept of function is a central but difficult topic in secondary school mathematics curricula, which encompasses a transition from an operational to a structural view. The question in this paper is how to design and evaluate a technology-rich learning arrangement that may foster this transition. With domain-specific pedagogical knowledge on the learning of function as a starting point, and the notions of emergent modeling and instrumentation as design heuristics, such a learning arrangement was designed for grade 8 students and field tested. The results suggest that these design heuristics provide fruitful guidelines for the design of both a hypothetical learning trajectory and concrete tasks, and can be generalized to other design processes

Fluid Models of Many-server Queues with Abandonment

We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience times of each customer. Deterministic fluid models are established to provide first-order approximation for this model. The fluid model solution, which is proved to uniquely exists, serves as the fluid limit of the many-server queue, as the number of servers becomes large. Based on the fluid model solution, first-order approximations for various performance quantities are proposed

Decay of the metastable phase in d=1 and d=2 Ising models

We calculate perturbatively the tunneling decay rate $\Gamma$ of the metastable phase in the quantum d=1 Ising model in a skew magnetic field near the coexistence line $0<h_{x}<1, h_{z}\to -0$ at T=0. It is shown that $\Gamma$ oscillates in the magnetic field $h_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2 Ising model at $T<T_c$, we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We find also evidence for the discrete-lattice corrections in this metastable phase free energy.Comment: 4 pages, REVTe

Three-body non-additive forces between spin-polarized alkali atoms

Three-body non-additive forces in systems of three spin-polarized alkali atoms (Li, Na, K, Rb and Cs) are investigated using high-level ab initio calculations. The non-additive forces are found to be large, especially near the equilateral equilibrium geometries. For Li, they increase the three-atom potential well depth by a factor of 4 and reduce the equilibrium interatomic distance by 0.9 A. The non-additive forces originate principally from chemical bonding arising from sp mixing effects.Comment: 4 pages, 3 figures (in 5 files

Non Linear Current Response of a Many-Level Tunneling System: Higher Harmonics Generation

The fully nonlinear response of a many-level tunneling system to a strong alternating field of high frequency $\omega$ is studied in terms of the Schwinger-Keldysh nonequilibrium Green functions. The nonlinear time dependent tunneling current $I(t)$ is calculated exactly and its resonance structure is elucidated. In particular, it is shown that under certain reasonable conditions on the physical parameters, the Fourier component $I_{n}$ is sharply peaked at $n=\frac {\Delta E} {\hbar \omega}$, where $\Delta E$ is the spacing between two levels. This frequency multiplication results from the highly nonlinear process of $n$ photon absorption (or emission) by the tunneling system. It is also conjectured that this effect (which so far is studied mainly in the context of nonlinear optics) might be experimentally feasible.Comment: 28 pages, LaTex, 7 figures are available upon request from [email protected], submitted to Phys.Rev.

GenTAC registry report: Gender differences among individuals with genetically triggered thoracic aortic aneurysm and dissection

Previous data suggest women are at increased risk of death from aortic dissection. Therefore, we analyzed data from the GenTAC registry, the NIH‐sponsored program that collects information about individuals with genetically triggered thoracic aortic aneurysms and cardiovascular conditions. We performed cross‐sectional analyses in adults with Marfan syndrome (MFS), familial thoracic aortic aneurysm or dissection (FTAAD), bicuspid aortic valve (BAV) with thoracic aortic aneurysm or dissection, and subjects under 50 years of age with thoracic aortic aneurysm or dissection (TAAD <50 years). Women comprised 32% of 1,449 subjects and were 21% of subjects with BAV, 34% with FTAAD, 22% with TAAD <50 years, and 47% with MFS. Thoracic aortic dissections occurred with equal gender frequency yet women with BAV had more extensive dissections. Aortic size was smaller in women but was similar after controlling for BSA. Age at operation for aortic valve dysfunction, aneurysm or dissection did not differ by gender. Multivariate analysis (adjusting for age, BSA, hypertension, study site, diabetes, and subgroup diagnoses) showed that women had fewer total aortic surgeries (OR = 0.65, P  < 0.01) and were less likely to receive angiotensin converting enzyme inhibitors (ACEi; OR = 0.68, P  < 0.05). As in BAV, other genetically triggered aortic diseases such as FTAAD and TAAD <50 are more common in males. In women, decreased prevalence of aortic operations and less treatment with ACEi may be due to their smaller absolute aortic diameters. Longitudinal studies are needed to determine if women are at higher risk for adverse events. © 2013 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97193/1/35836_ftp.pd

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc