Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking

The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.     

Analysis of ALD-processed thin films by ion-beam techniques

This review introduces the possibilities of ion-beam techniques for the analysis of thin films and thin-film structures processed by atomic layer deposition (ALD). The characteristic features of ALD are also presented. The analytical techniques discussed include RBS, NRA and ERDA with its variants, viz. the TOF-ERDA and HI-ERDA. The thin film examples are taken from flat-panel display technology (TFEL structures) and the semiconductor industry (high-k insulators).Dedicated to the memory of Wilhelm Fresenius     

Chlovalicin B,a Chlorinated Sesquiterpene Isolated from the Marine Mushroom Digitatispora marina

As part of our search for bioactive metabolites from understudied marine microorganisms, the new chlorinated metabolite chlovalicin B (1) was isolated from liquid cultures of the marine basidiomycete Digitatispora marina, which was collected and isolated from driftwood found at Vannøya, Norway. The structure of the novel compound was elucidated by spectroscopic methods including 1D and 2D NMR and analysis of HRMS data, revealing that 1 shares its molecular scaffold with a previously isolated compound, chlovalicin. This represents the first compound isolated from the Digitatispora genus, and the first reported fumagillin/ovalicin-like compound isolated from Basidiomycota. Compound 1 was evaluated for antibacterial activities against a panel of five bacteria, its ability to inhibit bacterial biofilm formation, for antifungal activity against Candida albicans, and for cytotoxic activities against malignant and non-malignant human cell lines. Compound 1 displayed weak cytotoxic activity against the human melanoma cell line A2058 (~50% survival at 50 µM). No activity was detected against biofilm formation or C. albicans at 50 µM, or against bacterial growth at 100 µM nor against the production of cytokines by the human acute monocytic leukemia cell line THP-1 at 50 µM.     

Optimal payout policy in presence of downside risk

We analyze the determination of a value maximizing dividend payout policy for a broad class of cash reserve processes modeled as spectrally negative jump diffusions. We extend previous results based on continuous diffusion models and characterize the value of the optimal dividend distribution strategy explicitly. We also characterize explicitly the values as well as the optimal dividend thresholds for a class of associated optimal liquidation and sequential lump sum dividend control problems. Our results indicate that both the value as well as the marginal value of the optimal policies are increasing functions of policy flexibility in the discontinuous setting as well.      

Two Novel Lyso-Ornithine Lipids Isolated from an Arctic Marine Lacinutrix sp. Bacterium

The Lacinutrix genus was discovered in 2005 and includes 12 Gram-negative bacterial species. To the best of our knowledge, the secondary metabolite production potential of this genus has not been explored before, and examination of Lacinutrix species may reveal novel chemistry. As part of a screening project of Arctic marine bacteria, the Lacinutrix sp. strain M09B143 was cultivated, extracted, fractionated and tested for antibacterial and cytotoxic activities. One fraction had antibacterial activity and was subjected to mass spectrometry analysis, which revealed two compounds with elemental composition that did not match any known compounds in databases. This resulted in the identification and isolation of two novel isobranched lyso-ornithine lipids, whose structures were elucidated by mass spectrometry and NMR spectroscopy. Lyso-ornithine lipids consist of a 3-hydroxy fatty acid linked to the alpha amino group of an ornithine amino acid through an amide bond. The fatty acid chains were determined to be iso-C15:0 (1) and iso-C16:0 (2). Compound 1 was active against the Gram-positive S. agalactiae, while 2 showed cytotoxic activity against A2058 human melanoma cells.     

In situ quadrupole mass spectrometry study of atomic-layer deposition of ZrO2 using Cp2Zr(CH3)2 and water

Reactions during the atomic layer deposition (ALD) process of ZrO(2) from Cp(2)Zr(CH(3))(2) and deuterated water as precursors were studied with a quadrupole mass spectrometer (QMS) at 210-440 degrees C. The detected reaction byproducts were CpD (m/z = 67) and CH(3)D (m/z = 17). Almost all (90%) of the CH(3) ligands were released during the Cp(2)Zr(CH(3))(2) precursor pulse because of exchange reactions with the OD-terminated surface, and the rest, during the D(2)O pulse. About 40% of the CpD was released during the metal precursor pulse, and 60%, during the D(2)O pulse. ALD-type self-limiting growth was confirmed from 210 to 400 degrees C. However, below 300 degrees C the growth rate was low. Precursor decomposition affected the film growth mechanism at temperatures exceeding 400 degrees C.     

Iranian students’ measurement estimation performance involving linear and area attributes of real-world objects

This article reports on an exploratory investigation of the measurement estimation performance of ten Iranian high school students on a set of real-world length and area measurement tasks. The results of a qualitative analysis of the data indicate that the students employed a variety of either mental or physically present Individual Frames of Reference as the non-tool units of measure in various estimation tasks. The analysis also found that a range of types of frames of reference was used across students in response to particular tasks and to the physical environments in which the tasks were situated. These results suggest that there is a complex interaction among a student’s individual preference for a particular type of Individual Frame of Reference, the nature of the estimation activity, and the physical context in which the activity takes place. These findings, which contribute to an understanding of the nature of the measurement unit that is employed during an estimation process, provide a different perspective from other studies that focus on categorizing estimation strategies, or processes.     

Design and analysis of a scaled model of a high-rise, high-speed elevator

A novel scaled model is developed to simulate the linear lateral dynamics of a hoist cable with variable length in a high-rise, high-speed elevator. The dimensionless groups used to formulate the scaling laws are derived through dimensional analysis. The model parameters are selected based on the scaling laws and are subject to the material, size, and hardware constraints. It is demonstrated that while it is impossible to obtain a fully scaled model unless the model is extremely tall, a reasonably sized model can be designed and the scaling laws that are not satisfied can be rendered to have a minimal effect on the scaling between the model and prototype. In conjunction with the model design, an analysis of model tension in a closed band loop is developed. A new movement profile that ensures a continuous jerk function during the entire period of motion is derived. The dynamic response of the prototype cable and that of the model band under consideration are compared numerically. Practical considerations that occur in the design of the model are addressed. The methodology can be used to investigate the vibration of a very long cable in other applications.     

Visual representations as objects of analysis: the number line as an example

Our paper examines the representational nature of number lines as they are used in instructional tasks. The examination is informed by a so-called mathedidactical analysis of the number line as a tool used in teaching students mathematics. This analysis led to the identification of a family of number line models, based on visual aspects of number lines each reflecting different forms and functions. In the article, number line tasks are unpacked to illustrate the visual representational components of particular number line models. We illuminate how these components of the models provide tools to locate whole numbers and integers, operate with them, and facilitate reasoning and understanding of underlying mathematical concepts.     

Dark energy as a mirage

Motivated by the observed cosmic matter distribution, we present the following conjecture: due to the formation of voids and opaque structures, the average matter density on the path of the light from the well-observed objects changes from Ω _M ≃ 1 in the homogeneous early universe to Ω _M ≃ 0 in the clumpy late universe, so that the average expansion rate increases along our line of sight from EdS expansion Ht ≃ 2/3 at high redshifts to free expansion Ht ≃ 1 at low redshifts. To calculate the modified observable distance–redshift relations, we introduce a generalized Dyer–Roeder method that allows for two crucial physical properties of the universe: inhomogeneities in the expansion rate and the growth of the nonlinear structures. By treating the transition redshift to the void-dominated era as a free parameter, we find a phenomenological fit to the observations from the CMB anisotropy, the position of the baryon oscillation peak, the magnitude–redshift relations of type Ia supernovae, the local Hubble flow and the nucleosynthesis, resulting in a concordant model of the universe with 90% dark matter, 10% baryons, no dark energy, 15 Gyr as the age of the universe and a natural value for the transition redshift z ₀ = 0.35. Unlike a large local void, the model respects the cosmological principle, further offering an explanation for the late onset of the perceived acceleration as a consequence of the forming nonlinear structures. Additional tests, such as quantitative predictions for angular deviations due to an anisotropic void distribution and a theoretical derivation of the model, can vindicate or falsify the interpretation that light propagation in voids is responsible for the perceived acceleration.