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"Political Geometry: Rethinking Redistricting in the US with Math, Law, and Everything In Between" is a comprehensive book that explores the issue of gerrymandering in the United States. It discusses different types of gerrymandering, such as partisan and racial gerrymandering, and the legal challenges associated with it. The book also examines the role of mathematics in redistricting and offers various perspectives from experts in the field. It emphasizes the importance of understanding the potential and limitations of ensemble analysis, a powerful tool for identifying gerrymandering, in order to effectively combat this issue. [Extracted from the article]

This study analyzed the Trends in International Mathematics and Science Study 2011 data on fourth-grade U.S. students' mathematics performance to answer four research questions: (a) How did U.S. students' geometry performance compare with their performance on the other mathematics subscales? (b) What were the patterns of student achievement among the mathematics subscales? (c) Was there a group of students who demonstrated specific difficulties in geometry only? and (d) Which demographic variables contributed to students' classification in the group with geometry difficulties? We found that (a) U.S. students' performance was poorer on the Geometry subscale than on other mathematics subscales; (b) using latent profile modeling, we identified a group of students with the lowest scores across all three mathematics subscales who showed a significant discrepancy between Geometry and the other subscales that did not exist within the high-achieving and average-achieving groups; and (c) gender, age, home language, race, and preference for mathematics and science significantly influenced the probability of being classified in the group with the lowest performance and the largest gap between Geometry and other mathematics subscales. Implications for educational theory and practice are discussed. [ABSTRACT FROM AUTHOR]

Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by ''fair districting'' intertwines mathematical, political, and legal reasoning; but only in recent years has the academic mathematical community gotten directly involved in the process. Here I report on recent progress in this area, how newly developed mathematical tools have affected real political decisions, and what remains to be done. This survey represents the content of a lecture presented by the author in the Current Events Bulletin session of the Joint Mathematics Meetings in January 2020. [ABSTRACT FROM AUTHOR]

Track geometry is highly important for ensuring railroad safety. Predicting track geometry degradation can support preventive maintenance by identifying and prioritizing track segments that are more prone to potential track geometry defects. This paper develops a novel machine learning approach that can simultaneously geospatially align track geometry data from multiple inspections accounting for positional errors, and also predict foot-by-foot track geometry change over time. The proposed position correction method considers multiple geometry parameters to provide highly accurate positional information for geometry measurements, which is a prerequisite for foot-by-foot track geometry prediction. A hybrid CNN (convolutional neural network)-LSTM (long short-term memory neural network) machine learning model is developed to account for spatial–temporal dependence with respect to foot-by-foot track geometry change. Specifically, CNN is used to incorporate spatial dependence of track geometry on adjacent segments. LSTM is applied to learn dynamic changes in track geometry data over time to consider the temporal dependence. The hybrid CNN-LSTM model is validated using track inspection data provided by one major freight railroad in the United States. The results show that our positional error correction method can reduce the relative positional error to less than 1 foot with a 99% confidence interval. Our proposed CNN-LSTM model outperforms four other models, including a naïve model (using the last observation), multi-layer perceptron (MLP), plain CNN, and plain LSTM, for both short-term and long-term prediction periods. The proposed hybrid machine learning methodology can be adapted to various other freight and passenger rail lines. The predictive track geometry change information can be used by the industry to plan and prioritize resources for preventative maintenance, yielding benefits in safety and operational efficiency. [ABSTRACT FROM AUTHOR]

Charlotte Angas Scott (1858–1932) was an internationally renowned geometer, the first British woman to earn a doctorate in mathematics, and the chair of the Bryn Mawr mathematics department for forty years. There she helped shape the burgeoning mathematics community in the United States. Scott often motivated her research as providing a "geometric treatment" of results that had previously been derived algebraically. The adjective "geometric" likely entailed many things for Scott, from her careful illustration of diagrams to her choice of references and citations. This article will focus on Scott's striking and consistent use of geometric to describe a reality of dynamic points, lines, planes, and spaces that could be manipulated analogously to physical objects. By providing geometric interpretations of algebraic derivations, Scott committed to an early-nineteenth-century aesthetic vision of a "whole" analytical geometry that she adapted to modern research areas. [ABSTRACT FROM AUTHOR]

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed. [ABSTRACT FROM AUTHOR]

There has been a recent media blitz on a cohort of mathematicians valiantly working to fix the democratic system in the United States by combatting gerrymandering with geometry. While statistics commonly features in the courtroom (forensics, DNA analysis, etc.), the gerrymandering news raises a natural question: in what other ways has pure mathematics, specifically geometry and topology, been involved in court cases and legal scholarship? In this survey article, we collect a few examples with topics ranging from the Pythagorean formula to the ham sandwich theorem, and we discuss some jurists' perspectives on geometric reasoning in the legal realm. One of our goals is to provide mathematics educators with engaging real-world instances of some abstract geometric concepts. [ABSTRACT FROM AUTHOR]

• A data-driven framework is proposed for estimating the risk of track geometry defects. • More influencing factors are considered, such as multiple substructure conditions. • Data resampling including undersampling and oversampling are implemented to solve the imbalanced data issue. Analyzing the relationship between track geometry defect occurrence and substructure condition can provide assistance for track inspection and spot maintenance, which contributes to better train operation quality. This paper develops a data-driven approach to estimate the occurrence of track geometry defects on concrete-tie tracks on one passenger railroad in the United States, using substructure data, rail seat abrasion data, infrastructure data, traffic data, track class information, and maintenance data. Feature extraction was implemented to generate input variables for the machine learning models. Recursive feature elimination (RFE) was applied to reduce data dimensionality by recursively considering smaller sets of features. Three data treatment methods, including no resampling, undersampling, and oversampling, were incorporated to address imbalanced data issues. The developed models included logistic regression, artificial neural network, and gradient boosting. The hyperparameters of the proposed models were optimized using Bayesian optimization. The performance of the proposed methods was finally evaluated based on the test dataset generated using random data partitioning. Based on data collected from one passenger railroad, the gradient boosting method with data oversampling shows the highest performance in estimating the occurrence of geometry defects. The F1-score of the model is 0.662, with G-Mean of 0.738. Feature importance identifies that surfacing, traffic, curvature, switch, and rail replacement are the top five factors influencing the predicted probability of track geometry defect occurrence. The proposed model can be used to prioritize maintenance activities on locations prone to track geometry defects and thus further improve infrastructure safety given budgetary constraints. [ABSTRACT FROM AUTHOR]

A significant concern about Metabolic Scaling Theory (MST) in real forests relates to consistent differences between the values of power law scaling exponents of tree primary size measures used to estimate mass and those predicted by MST. Here we consider why observed scaling exponents for diameter and height relationships deviate from MST predictions across three semi-arid conifer forests in relation to: (1) tree condition and physical form, (2) the level of inter-tree competition (e.g. open vs closed stand structure), (3) increasing tree age, and (4) differences in site productivity. Scaling exponent values derived from non-linear least-squares regression for trees in excellent condition (n = 381) were above the MST prediction at the 95% confidence level, while the exponent for trees in good condition were no different than MST (n = 926). Trees that were in fair or poor condition, characterized as diseased, leaning, or sparsely crowned had exponent values below MST predictions (n = 2,058), as did recently dead standing trees (n = 375). Exponent value of the mean-tree model that disregarded tree condition (n = 3,740) was consistent with other studies that reject MST scaling. Ostensibly, as stand density and competition increase trees exhibited greater morphological plasticity whereby the majority had characteristically fair or poor growth forms. Fitting by least-squares regression biases the mean-tree model scaling exponent toward values that are below MST idealized predictions. For 368 trees from Arizona with known establishment dates, increasing age had no significant impact on expected scaling. We further suggest height to diameter ratios below MST relate to vertical truncation caused by limitation in plant water availability. Even with environmentally imposed height limitation, proportionality between height and diameter scaling exponents were consistent with the predictions of MST. [ABSTRACT FROM AUTHOR]

Palinkas, C.M.; Barth, N.; Koch, E.W., and Shafer, D.J., 2016. The influence of breakwaters on nearshore sedimentation patterns in Chesapeake Bay, USA. This study describes nearshore Chesapeake Bay sedimentation at sites adjacent to and landward of 24 segmented breakwaters, varying in age (1-19 years) and physical setting. Grain-size and organic-content profiles are examined at the breakwater-protected sites to assess potential changes induced by breakwater installation as well as at the adjacent-exposed sites to establish historical trends. Sedimentation rates at all sites are calculated with 210Pb (half-life 22.3 years). At the breakwater-protected sites, these rates largely reflect preconstruction sedimentation because of the long half-life of 210Pb relative to breakwater ages. Determining the postconstruction sedimentation rate can be more difficult because the signature of breakwater influence in the sedimentological record can be obscured. For example, if the source of sediment is not affected dramatically by construction, down-core profiles may not have obvious changes. The depth of breakwater influence, however, can be interpreted by considering all the sedimentological evidence at a given location, and the postconstruction rates are calculated from this depth. In general, the sedimentological response to breakwater construction is fairly unique for each location but depends on such factors as breakwater age and geometry, shoreline sediment composition, and construction technique. [ABSTRACT FROM AUTHOR]

This paper aims to assess the Darrieus vertical axis wind turbine (VAWT) configurations, including the drawbacks of each variation that hindered the development into large scale rotor. A comprehensive timeline is given as a lineage chart. The variations are assessed on the performance, components and operational reliability. In addition, current development and future prospects of Darrieus VAWT are presented. The Darrieus VAWT patented in France in 1925 and in the US in 1931 had two configurations: (i) curved blades and (ii) straight blades configurations. Curved blades configuration (egg-beater or phi-rotor) has evolved from the conventional guy-wires support into fixed-on-tower and cantilevered versions. Straight blades configuration used to have variable-geometry (Musgrove-rotor), variable-pitch (Giromill), Diamond, Delta and V/Y rotor variations. They were stopped due to low economical value, i.e. high specific cost of energy (COE). Musgrove-rotor has evolved into fixed-pitch straight-bladed H-rotor (referred as H-rotor in this paper for simplicity). H-rotor, in turn, has evolved into several variations: Articulating, Tilted and Helical H-rotors. [ABSTRACT FROM AUTHOR]

In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in mathematics by analyzing their problem-posing abilities in geometric scenarios. The participants in this study were from one location in the USA and two locations in China. All participants were enrolled in advanced mathematical courses in the local high school. Differences in the problems posed by the three groups are discussed in terms of quality (novelty/elaboration) as well as quantity (fluency). The analysis of the data indicated that even mathematically advanced high school students had trouble posing good quality and/or novel mathematical problems. We discuss our findings in terms of the culture and curricula of the respective school systems and suggest implications for future directions in problem-posing research within mathematics education. [ABSTRACT FROM AUTHOR]

Abstract: Although there have been multiple studies on window thermal properties in energy-efficient fenestration design, the effects of building geometry factors have been studied much less. The study presented in this paper evaluated the role of geometry factors, such as window orientation, window to wall ratio, and room width to depth ratio, on building energy performance in a commercial office building. A series of energy simulations were performed for six climate zones in the United States using a model of a room in a typical office building created in Design Builder, an energy analysis program, to evaluate total annual energy consumption. The simulation results were analyzed to find the combination of parameters yielding the lowest energy consumption and to define potential energy savings for office buildings located in various climate zones. The study showed that geometry factors affect energy consumption significantly in hot climates (Zones 2 and 3) and cold climates (Zones 6 and 7) but only marginally in temperate climates (Zones 4 and 5). Energy savings were on average 3% and 6% reaching a maximum of 10% and 14% in hot climates (Zones 2 and 3) and 1% in temperate and cold climates (Zones 4–7). [Copyright &y& Elsevier]

Abstract: In this study, the thermal performance of various shapes and geometries of atriums in buildings is examined under various conditions. The goal of the study is to assess the impact of the atrium shape on the building total energy consumption and to identify the most energy-efficient atrium design. The study focuses on four different central atriums types with square and rectangular geometries which have same areas, use, schedule, controls, occupancy, and construction. The atriums exhibit different aspect ratios (length to width). Four cities in United States are selected to represent primary climatic regions of hot-dry, hot-humid, cold, and temperate. Besides, the atrium height, the atrium glazing type, and the glazing ratio are varied throughout the simulation process. Buildings models are constructed using the DOE-2.1E building energy simulation program. The results of this study indicate that in general, the total energy consumption of the narrow, elongated atrium or the rectangular atrium with high ratio of length to width is significantly greater than the square shaped atrium. [Copyright &y& Elsevier]

In visually sensitive areas, planners use a variety of techniques to mitigate the visible effects of harvesting, including creating designs that appear more natural and less blocky. However, little empirical evidence exists about the degree to which these shapes influence preferences. We aim to fill this gap by investigating the perceptual effects of three shape characteristics: geometric primitive (circle, square, triangle, and trapezoid), complexity, and aspect ratio. Fifty-two photo-realistic images were rendered of a forest scene with a single harvest on a hillside. Forty individuals rated each image. The results indicate that geometric primitive had the largest effect on preference for harvest design of the three variables tested followed very closely by complexity. Yet, the most intriguing finding was the interaction of these two variables. In general, an increase in complexity for square and circular shapes caused higher preference ratings, while for trapezoid and triangle, this was only true as complexity progressed from low to moderate levels. The relationship between preference rating and complexity was nonlinear; the largest improvement existed at the moderate level of complexity. Operationally, this demonstrates that rounded-edged circular shapes are the most preferable but that even with a moderate level of complexity, preferences increase dramatically. [ABSTRACT FROM AUTHOR]

Abstract: A coupling framework between a hydrologic model and a hydrodynamic model has been developed. The resultant coupled model, tRIBS-OFM, considers spatially-distributed, physically-based hydrologic processes over the land-surface and subsurface by using the TIN (Triangulated Irregular Network)–Based Real Time Integrated Basin Simulator (tRIBS); the hydrodynamic component is the overland flow model (OFM), which solves the two-dimensional Saint–Venant (shallow-water) equations using Roe’s approximate Riemann solver on an unstructured grid. The original OFM formulation targeted hydraulic applications and did not provide an accurate solution for partially-submerged mesh cells. Modifications of the hydrodynamic model are presented here that affect the calculation of flux, bottom slope, and friction slope terms of the Saint–Venant formulation by applying a new method of reconstruction of variables. The proposed method significantly enhances the accuracy of hydrologic applications by resolving the typical numerical artifacts associated with low precipitation and runoff production rates. Several comparisons with analytical solutions, observed data, and other numerical models have been carried out for different domain geometries and various flow conditions. Two applications to a synthetic domain and a real-world basin, the Peacheater Creek watershed (64km2) located near Christie, OK, USA, are also presented to demonstrate the scalability of the model’s application and its robust performance. Various physically-based metrics of watershed simulation are illustrated, such as the runoff production occurrences and rates, streamflow, flow depth, velocity, etc. The coupled model makes feasible a range of real-world problems that models based on the kinematic or inertia-free approximations cannot simulate accurately. These include microtopographic flow disturbances due to vegetation and obstacles, backwater effects, and converging–diverging flow characteristics. The coupled model thus provides more comprehensive simulation capabilities that are not affected by assumptions regarding the reproduced flow regime. [Copyright &y& Elsevier]

The article discusses the art of paper folding called origami introduced to mathematics class in the U.S. middle school. Modular origami or unit origami involves two or more pieces of folded paper in congruent shapes assembled into an origami model. It reports that modular origami is an ideal activity to connect with the areas of mathematics including geometry, measurement, and communication.

The article discusses the use of mysteries and detective stories with technical vocabulary for geometry lessons in mathematics class in the U.S. middle school. According to the International Reading Association (IRA), story plot lines provide geometry lessons in which many states require reading and understanding of mathematical language. Novels which mention mathematical language include "Flatland: A romance of Many Dimensions," "The Da Vinci Code," and "Crimes and Mathdemeanors."

Abstract: Geographic features have traditionally been visualized with fairly high amount of geometric detail, while relationships among these features in attribute space have been represented at a much coarser resolution. This limits our ability to understand complex high-dimensional relationships and structures existing in attribute space. In this paper, we present an alternative approach aimed at creating a high-resolution representation of geographic features with the help of a self-organizing map (SOM) consisting of a large number of neurons. In a proof-of-concept implementation, we spatialize 200,000+ U.S. Census block groups using a SOM consisting of 250,000 neurons. The geographic attributes considered in this study reflect a more holistic representation of geographic reality than in previous studies. The study includes 69 attributes regarding population statistics, land use/land cover, climate, geology, topography, and soils. This diversity of attributes is informed by our desire to build a comprehensive two-dimensional base map of n-dimensional geographic space. The paper discusses how standard GIS methods and neural network processing are combined towards the creation of an alternative map of the United States. [Copyright &y& Elsevier]

Terrain topology is the principal source of vertical excitation into the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle models over a wide range of terrain, but it is computationally impractical to simulate long distances of every terrain type. A method to characterize terrain topology is developed in this work so that terrain can be grouped into meaningful sets with similar physical characteristics. Specifically, measured terrain profiles are considered realizations of an underlying stochastic process; an autoregressive model provides the mathematical framework to describe this process. The autocorrelation of the spatial derivative of the terrain profile is examined to determine the form of the model. The required order for the model is determined from the partial autocorrelation of the spatial derivative of the terrain profile. The stability of the model is evaluated and enforced by transforming the autoregressive difference equation into an infinite impulse response filter representation. Finally, the method is applied to a set of U.S. highway profile data and an optimal model order is determined for this application. [ABSTRACT FROM AUTHOR]

Two new µ-carboxylato-bridged binuclear copper(II) complexes [Cu2(bpea)2 (µ-C2O4)](ClO4)2 · H2O (1) and [Cu2(bpma)2 (µ-ta)](ClO4)2 · H2O (2) (bpea = N,N-bis(2-pyridylmethyl)ethylamine; bpma = N,N-bis(2-pyridylmethyl)methylamine; ta = terephthalate dianion) have been synthesized and structurally determined by X-ray diffraction. Complex 1 is crystallized in a monoclinic space group C2/c with unit cell parameters a = 21.539(17) Å, b = 12.608(10) Å, c = 13.117(11) Å, β = 96.788(13)°. In 1, each Cu(II) is five-coordinate, square-pyramidal geometry with a CuN3O2 donor set. Complex 2 is crystallized in a monoclinic space group P21/n with unit cell parameters a = 11.346(3) Å, b = 15.418(4) Å, c = 11.958(3) Å, β = 116.519(4)°. In 2, each Cu(II) also is square-pyramidal CuN3O2 core, where three N- and one O-donors are equatorial and an oxygen of the bridging ligand occupies the axial site with a weak link. Elemental analyses, IR, UV and EPR spectra of the complexes were determined. [ABSTRACT FROM AUTHOR]

The article discusses the relevance of geometric shapes in the early mathematical learning of American children. The author notes that children started to learn mathematics in an early age and before they acquire formal education wherein they developed the basic concept and skills in geometry and numbers through playing games. It also offers information on the different types of educational toys that can help children understand the concept of mathematical along with the advantages and benefits it provide. In addition, the author notes that high competence of geometric skills helps them expands their knowledge on numbers which could serve as the basic foundation of their future in academics.

The article discusses the relevance of embedded shapes and design in natural and manufacture objects on the learning ability of children regarding geometric concepts in the U.S. The author states that children's daily interaction with shapes and design helps them gain understanding on the application of geometry in the real world wherein they can identify the unique attribution of different shapes. It also cites that different learning activities that can be introduced to students along with their advantages and disadvantages. In addition, the author notes that geometric shapes allows students to gain higher understanding on shapes and other geometric elements along with its essential elements.

Noise assessments have been conducted using full-shift dosimetry and short-term task-based measurements. Advantages of the task-based method include the opportunity to directly identify high-noise exposure tasks and to target control measures, as well as obtain estimates of task-based full-shift exposures; however, there is little empirical evidence comparing the two methods. National Institute for Occupational Safety and Health assessed noise exposures at three industrial facilities using dosimetry and task-based methods with the objective of comparing the two strategies and assessing the degree of agreement and causes of disagreement. Eight indices of task-based full-shift exposures were created from task-based sampling using three methods to assess time-at-task (direct observation by industrial hygienist, end-of-shift worker estimates and supervisor estimates) and three methods to assign noise levels to tasks [direct measurement, arithmetic mean (AM) and geometric mean (GM)]. We assessed aspects of agreement (precision, bias and absolute agreement) using Bland–Altman plots and concordance correlation coefficient (CCC). Overall, the task-based methods worked fairly well, with mean biases less than ±2.8 dBA and precision ranges of 3.3–4.4 dBA. By all measures, task-based full-shift estimates based on supervisor assessment of time-at-task agreed most poorly with the dosimetry data. The task-based full-shift estimates based on worker estimates of time-at-task generally agreed as well as those based on direct observation. For task noise level, task-based full-shift estimates based on directly measured task agreed the best with dosimetry data, while agreement for task-based indices based on task AM or GM was variable. Overall, the task-based full-shift estimates based on direct observation task and direct measured task noise level achieved the best agreement with the dosimetry data (CCC 0.84) with 95% of their differences being within 7.4 dBA and 56% of the differences <3 dBA. For this index, a high degree of accuracy was observed (accuracy coefficient = 0.96) with major cause of disagreement arising from a lack of precision (precision coefficient = 0.88). When the measurements were classified by job characteristics, significant improvements in the degree of agreement were observed in the low job mobility, low job complexity and low job variability categories. Our data suggest that a high degree of absolute agreement can be achieved between the task-based and dosimetry-based estimates of full-shift exposures. The task-based approach that uses worker reports combined with task AM or GM levels is similar to the more time-intensive direct observation method to estimate full-shift exposures. [ABSTRACT FROM PUBLISHER]

The article explores on the important role nets play in conceptualizing mathematical activity of the elementary level in the U.S. Creating nets for a cube is the basic classroom activity for geometry students. Nets assist students create the connection between division of two-dimensional figures and three-dimensional objects. The elementary school children discover several different nets for a cube and its basic characteristics. It highlights comprehensive discussion why several different shape nets have the same area and parameter.

We document the development and application of a one-dimensional flow model of the Chesapeake and Delaware Canal based on the dynamic form of the St. Venant equations. Model geometry is based on hydrographic surveys obtained by the U.S. Army Corps of Engineers (USACE) in 2006. The model is forced with time-varying tidal boundary conditions at the east and west ends of the Canal, and predicts velocity and discharge at selected locations within the canal. The model was calibrated using current meter data obtained between October 1992 and October 1993, when USACE operated recording current meters in and adjacent to the canal. Following selection of these parameters, the model was run to simulate other periods between October 1992 and October 1993. Comparison of model and prototype current speeds for these simulations demonstrates the ability of the model to reproduce observed flows accurately under a range of tidal forcing conditions. The model was used to describe the average net flow in the canal which is normally from the Chesapeake to the Delaware but which reversed during the Northeaster of December 1992, a period of unusually high meteorologically driven tides of the Delaware Estuary. [ABSTRACT FROM AUTHOR]

Aim The peninsula effect is the prediction that the number of species declines from a peninsula's base to its tip. We evaluated evidence for and against the peninsula effect, and conducted a field study designed to test alternative hypotheses for that effect. Location The Florida peninsula, USA. Methods First, we critically reviewed the accumulated literature on peninsula effects; second, we sampled microcrustaceans in palustrine wetlands on the ridges of peninsular Florida. Site selection in our field study accounted for historical effects and partially controlled for habitat effects. Statistical analyses further accounted for habitat effects, leaving peninsular geometry as the remaining causative mechanism for residual variation in species richness regression analyses. Results Our literature review found mixed evidence (49% of cases) for a peninsula effect. However, most study designs did not control for alternative hypotheses, most comparisons of alternative hypotheses were qualitative, and most studies focused on vertebrate animals. Our field study found that freshwater microcrustaceans inhabiting isolated wetlands on Florida’s peninsular ridges do not exhibit a peninsula effect. Essentially, no variation in microcrustacean species richness could be attributed to peninsular geometry, but 82.5% of variation in species richness was attributed to habitat and sampling effort. Main conclusions Although our research results support the ‘red herring’ label for the peninsula effect, our literature review leads us to argue that more illumination (in the form of study design and quantitative analysis) is needed if mechanisms causing the peninsula effect hypothesis are to be resolved. Future studies of peninsula effects need to control for alternative causative hypotheses (geometry, habitat or history) in study design, and compare quantitatively the effects of hypothesized mechanisms on peninsular diversity patterns. Additionally, studies of taxa other than vertebrate animals need to be conducted for generality. Our study may serve as an example of such an approach. [ABSTRACT FROM AUTHOR]

Abstract: We use SPOT image pairs to determine horizontal offsets associated with the Mw 7.9 November 2002 Denali earthquake in the vicinity of Slate Creek, AK. Field measurements and aerial photographs are used to further characterize the geometry of the surface rupture. Aerial photographs show that shear localization occurs where the rupture trace is linear, and distributed off-fault deformation is common at fault bends and step-overs, or at geologic contacts between rock, glacial sediments, and ice. The displacement field is generated using a sub-pixel cross correlation technique between SPOT images taken before and after the earthquake. We identify the effects of glacier motion in order to isolate the tectonic displacements associated with the Denali earthquake. The resulting horizontal displacement field shows an along-strike variation in dextral shear, with a maximum of approximately 7.5 m in the east near 144° 52′W, which decreases to about 5 m to the west near 145° 45′W. If the November 2002 earthquake represents the long-term behavior of the Denali fault, it implies a westward decrease in the long-term dextral slip rate. A possible mechanism to accommodate the westward decreasing slip on the Denali fault is to transfer fault slip to adjacent east-trending contractional structures in the western region of the central Alaskan Range. [Copyright &y& Elsevier]

Objective: The author reviews the paper by Kroemer (1972) on the design of the split geometry keyboard and the subsequent 35 years of research on the topic. Background: It was first suggested in the 1920s that arm strain in the typist could be reduced by splitting the keyboard into two halves and inclining the two halves laterally. The first systematic research on the split keyboard was conducted by Kroemer in the 1960s and published in his 1972 article. Methods: The literature on split geometry keyboards was identified, and the progression of the research was reviewed. Results: The Kroemer article marked the beginning of a prolonged, worldwide research effort to determine whether and how the split keyboard design might improve comfort and prevent pain in keyboard users. Conclusions: In the early 1990s, split keyboard designs began to be broadly commercially available. Clear evidence of a health benefit of the split keyboards emerged in the late 1990s. By 2006, a split keyboard was the number one-selling keyboard, of all keyboards sold, in the U.S. retail market. Application: The history of research on this topic, the challenges to changing the conventional design, and the broader acceptance of the split design are a success story with lessons for all of us. [ABSTRACT FROM AUTHOR]

Associative reinforcement provides a powerful explanation of learned behavior. However, an unproven but long-held conjecture holds that spatial learning can occur incidentally rather than by reinforcement. Using a carefully controlled virtual-reality object- location memory task, we formally demonstrate that locations are concurrently learned relative to both local landmarks and local boundaries but that landmark-learning obeys associative reinforcement (showing "overshadowing" and "blocking" or "learned irrelevance"), whereas boundary-learning is incidental, showing neither overshadowing nor blocking nor learned irrelevance. Crucially, both types of learning occur at similar rates and do not reflect differences in levels of performance, cue salience, or instructions. These distinct types of learning likely reflect the distinct neural systems implicated in processing of landmarks and boundaries: the striatum and hippocampus, respectively [Doeller (F, King JA, Burgess N (2008) Proc Nat!AcadSci USA 105:5915-5920]. In turn, our results suggest the use of fundamentally different learning rules by these two systems, potentially explaining their differential roles in procedural and declarative memory more generally. Our results suggest a privileged role for surface geometry in determining spatial context and support the idea of a "geometric module," albeit for location rather than orientation. Finally, the demonstration that reinforcement learning applies selectively to formally equivalent aspects of task-performance supports broader consideration of two-system models in analyses of learning and decision making. [ABSTRACT FROM AUTHOR]

Abstract: The basic patterns and processes of steep channels remain poorly known relative to lower-gradient channels. In this analysis, characteristics of step-pool, plane-bed, and pool-riffle channels are examined using a data set of 335 channel reaches from the western United States, Nepal, New Zealand, and Panama. We analyzed differences among the three channel types with respect to hydraulics, channel geometry, boundary roughness, and bedforms. Step-pool channels have significantly steeper gradients, coarser substrate, higher values of shear stress and stream power for a given discharge, and larger ratios of bedform amplitude/wavelength (H/L). Pool-riffle channels have greater width/depth ratios and relative grain submergence (R/D 84) than the other channel types. Plane-bed channels tend to have intermediate values for most variables examined. Relative form submergence (R/H) is statistically similar for step-pool and pool-riffle channels. Despite the lesser relative grain submergence and greater bedform amplitude of step-pool channels, mean values of Darcy–Weisbach friction factor do not change in response to changes in relative grain submergence. These patterns suggest that adjustments along mountain streams effectively maximize resistance to flow and minimize downstream variability in resistance among the different channel types. [Copyright &y& Elsevier]

The article offers information about Project M³: Mentoring Mathematical Minds project under the Javits Program research grant of the U.S. Department of Education. The project aims to develop curriculum units for elementary students who excel in mathematics. Some of the topics included in the units are algebra, geometry and probability.

The purpose of the research was to compare measuring orthometric heights using differential leveling, static global positioning observations, and real-time kinematic (RTK) Global Positioning System (GPS) observations in the vicinity of the University of Conn. campus. Height observations were recorded at temporary and permanent monuments using differential leveling, static GPS, and RTK. Heights at permanent monuments with published elevations were observed using each method and served as control and to check the quality of all measurements. Three-dimensional reference ellipsoid coordinates derived from GPS observations and published orthometric heights were used to create local geoid models, which were then used to convert ellipsoid heights observed with the static GPS and RTK to orthometric heights. The resulting values were used to compare between the measuring methods. In general, static GPS performed better than RTK. Several polynomial surface models of different orders were fitted to the geoid heights, from a constant up to a quadratic. No meaningful distinctions could be drawn between the models indicating that, for a small geographical area, shifting the national geoid model, GEOID03, by a constant vertical amount performs as well as the more complicated approaches. Experience showed that multiple, independent RTK observations on the same day are not sufficient to ensure freedom from systematic errors. [ABSTRACT FROM AUTHOR]

The article focuses on several classroom activities that prompt students to investigate and discover mathematical formulas in determining the areas of shapes through the use of dot papers. It is said that students in the U.S. are rarely provided with chance to find out the formulas for themselves. Several mathematical problems on finding areas on dot paper are presented.

Abstract: Main objectives: This study was conducted to estimate the costs per crash for three police-coded crash severity groupings within 16 selected crash geometry types and within two speed limit categories (≤45 and ≥50mph). Methods: We merged previously developed costs per victim by abbreviated injury scale (AIS) score into U.S. crash data files that scored injuries in both the AIS and police-coded severity scales to estimate injury costs, then aggregated the estimates into costs per crash by maximum injury severity. Results: The most costly crashes were non-intersection fatal/disabling injury crashes on a road with a speed limit of 50 miles per hour or higher where multiple vehicles crashed head-on or a single vehicle struck a human (over $1.69 and $1.16 million per crash, respectively). The annual cost of police-reported run-off-road collisions, which include both rollovers and object impacts, represented 34% of total costs. Conclusions: This paper provides cost estimates useful for evaluating roadway countermeasures and for designing vehicles to minimize crash harm. It gives unit costs of crashes by type in the coding system used by the police. The costs are in an appropriate form for economic analysis of countermeasures addressing locally defined problems identified by analyzing police crash reports. [Copyright &y& Elsevier]

Current spatial database systems offer limited querying capabilities beyond binary topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane into separate zones that are obtained from projective properties of two reference objects: Then, by considering the empty/nonempty intersections of a primary object with these zones, the model is able to distinguish between 34 different projective relations. Then, the paper proposes original algorithms for computing the relations under the assumption that regions of the plane are stored as vector polygons in a spatial database. These algorithms run in optimal O(n log n) time. [ABSTRACT FROM AUTHOR]

The article discusses key ideas and insights in the context of three high school geometry proofs in the U.S. The author argues that one cause of students' troubles with proof is that they are not accustomed to making the important, but difficult, connections between their intuitive sense-making and the formal proofs they are supposed to produce. Teachers should provide opportunities for students to make these connections. It is important for teachers to create tasks and classroom activities that emphasize both intuitive and formal proofs. The author provided three tasks that will provide natural situations for student exploration.

One of the primary design requirements of automotive generation systems is maximizing power density subject to the constraint of minimizing the overall system cost. However, with the progress made in the reduction of automotive drive train noise, the torque ripple of the generator has been found to be a dominant noise source under idle conditions at high electrical loads. Thus, an added design constraint is the minimization of the torque ripple produced by the machine. In order to evaluate alternative machine designs (and select an optimal), numerical tools are typically applied. In this research, a focus is placed on the creation of numerical tools that can be used to effectively search for an optimal design. A primary tool is an evolutionary algorithm (EA) that has been integrated within a customized magnetic equivalent circuit (MEC) model of the machine. The selection of an EA that is most likely to converge to an optimal solution in the least amount of time is described along with its use in selecting an optimal rotor-pole geometry. [ABSTRACT FROM AUTHOR]

NASA conducts and funds research to advance the state of the art in aeronautics, including improvements in aircraft design leading to enhanced performance in areas such as noise, emissions, and safety. A particular initiative involves development of an all-electric aircraft requiring significant improvements in certain technologies. NASA has started a new project with one of the objectives being the development of enabling technologies for an all-electric aircraft. Electrical aeropropulsion requires the design of more compact and efficient electrical motors. In order to me crease the power density, the weight/size must be minimized and the air gap flux density must increase significantly the use of superconducting materials is an obvious choice. Existing HTS motors are proof-of-principle demonstrators and exhibit power densities lower than 1 HP/lb, which is too low to be considered in mobile systems. This paper deals with a preliminary electromagnetic design of a 200 HP high temperature superconducting motor optimized in terms of power density. The presented configuration is a synchronous motor with a nonconventional topology enhanced by HTS bulk material. The design targets the Cessna 172 propulsion requirements that are 200 HP at 2700 RPM. [ABSTRACT FROM AUTHOR]

This article describes the following phenomenon: Gifted high school students trained in solving Olympiad-style mathematics problems experienced conflict between their conceptions of effectiveness and elegance (the EEC). This phenomenon was observed while analyzing clinical task-based interviews that were conducted with three members of the Israeli team participating in the International Mathematics Olympiad. We illustrate how the conflict between the students' conceptions of effectiveness and elegance is reflected in their geometrical problem solving, and analyze didactical and epistemological roots of the phenomenon. [ABSTRACT FROM AUTHOR]

An analytical procedure for simulating roof snow drift loads is presented. The procedure is based upon the physics of drift formation and consists of two elements. The first element is the transport rate which quantifies the snow flux from the snow source area. The second element is the trapping efficiency which quantifies the percentage of transported snow from the source area which is captured at the drift. Knowing wind speed and snowfall information for a given winter, the procedure can be used to simulate the annual maximum drift for a given snow source area. The method is applied to over 40 years of weather data at each of over 50 NWS first-order sites across the United States. The calculated annual maxima are fit with an extreme value distribution to determine 50-year drift loads for both roof step and gable roof geometries. It is shown that current leeward roof step drift provisions in ASCE 7-02 as well as gable roof drift provisions proposed for ASCE 7-05 yield loads with something close to a 50 year mean recurrence interval. [ABSTRACT FROM AUTHOR]

A large-scale railgun is being considered by the U.S. Navy as a future long-range (>200 nm) naval weapon system. The notional concept includes a 15 kg projectile with a 2.5 km/s muzzle velocity. The choice of bore and rail geometry for such a weapon can influence, key aspects of the total system design. This study explored a range of bore and rail geometries and looked at their effects on key railgun system parameters such as parasitic mass, inductance gradient, linear current density, required pulse forming network (PFN) size, and barrel mass. Preliminary solid modeling and structural analysis of the integrated launch package was performed in order to quantify parasitic mass. Inductance gradient calculations were based on a current density distribution analysis. A PFN/launcher numerical simulation model was then used to determine linear current density and PFN size. Finally, barrel mass was estimated by structural analysis based on calculated rail repulsive forces. Trends and sensitivities of the different parameters to changes in the bore and rail geometries are presented and conclusions are given. [ABSTRACT FROM AUTHOR]

We describe and validate a simple PV simulation model capable of predicting average PV output as a function of array geometry (slope and azimuth) and location. This simulation tool is used in the Clean Power Estimator––a web-based PV economic evaluation program available in the US and several countries. Results show that the simplified model accurately captures array geometry, seasonal and daily PV output variations when benchmarked against a standard PV simulation program. This paper concludes that web-based Clean Power Estimator simulations have a sound physical basis. [Copyright &y& Elsevier]

Arid alluvial channels on piedmonts and valley floors often exhibit an oscillating pattern of narrow, deeply incised reaches and wide, shallow reaches with a characteristic wavelength. How do these oscillations develop and what controls their wavelengths? To address these questions we developed a two-dimensional numerical model that couples erosion and deposition in a channel bed with cross-sectional widening and narrowing. This model is inherently unstable over a range of spatial scales dependent on the channel width, depth, and slope. In the initial phase of model evolution, wider-than-average channel reaches become zones of distributary flow that aggrade, lose stream power, and further widen in a positive feedback. Simultaneously, narrower-than-average reaches incise, gain stream power, and further narrow. In the second stage of model evolution, this instability is balanced by the diffusive nature of longitudinal profile evolution, and solitary topographic waves propagate in the upstream direction with a characteristic wavelength and amplitude. The model predicts a specific quantitative relationship between the oscillation wavelength and channel width, depth, and slope that is verified by a database of channel geometries in southern Arizona. [ABSTRACT FROM AUTHOR]

Models for the evolution of faults formed by shearing along joint zones in Aztec sandstone, Valley of Fire, Nevada predict damage zones either localized within the fault core or symmetrically distributed about the core or a slip surface therein. We expand these models by presenting two examples of faults with asymmetric damage zones from the same field locality. Asymmetric damage is attributed to the inherited geometry of a parent joint with a peripheral joint breakdown fringe. One example is of a fault formed along a parent joint with continuous breakdown fringe. The other example is of a fault formed in part along a parent joint with abrupt breakdown fringe. When compared with the symmetric examples, the damage in the asymmetric cases is minimized due to the presence of an already through-going surface. [Copyright &y& Elsevier]

Most existing reservoir models are based on 2D outcrop studies; 3D aspects are inferred from correlation between wells, and so are inadequately constrained for reservoir simulations. To overcome these deficiencies, we have initiated a multidimensional characterization of reservoir analogues in the Cretaceous Ferron Sandstone in Utah. Detailed sedimentary facies maps of cliff faces define the geometry and distribution of reservoir flow units, barriers and baffles at the outcrop. High-resolution 2D and 3D ground-penetrating radar (GPR) images extend these reservoir characteristics into 3D to allow the development of realistic 3D reservoir models. Models use geometric information from mapping and the GPR data, combined with petrophysical data from surface and cliff-face outcrops, and laboratory analyses of outcrop and core samples. The site of the field work is Corbula Gulch, on the western flank of the San Rafael Swell, in east-central Utah. The outcrop consists of an 8-17 m thick sandstone body which contains various sedimentary structures, such as cross-bedding, inclined stratification and erosional surfaces, which range in scale from less than a metre to hundreds of metres. 3D depth migration of the common-offset GPR data produces data volumes within which the inclined surfaces and erosional surfaces are visible. Correlation between fluid permeability, clay content, instantaneous frequency and instantaneous amplitude of the GPR data provides estimates of the 3D distribution of fluid permeability and clay content. [ABSTRACT FROM AUTHOR]

Discusses the responses of the fourth and sixth grade students of Karen Yahr and Tom Lewis in the U.S., respectively, to the Shape Search Problem, an activity designed to encourage students to use their spatial skills when forming or taking apart shapes. Significance of the Shape Search Problem to students' depth of understanding of shape names; Comparison between Sunshine Math and Shape Search problems; Strategies used by the students in solving the problems.

This article describes design parameters and test results for a 1–10 GHz microstrip balun with a 240 Ω balanced port and a 50 Ω unbalanced port. The tapered geometry and rf performance are favorable for integrating a low noise amplifier with a nonplanar log periodic antenna developed at the University of California’s radio astronomy lab. The design can be modified for use in cryogenic low noise applications. When the balun is placed in a conducting enclosure, excitation of unwanted transmission modes can be minimized by careful field and impedance matching of balun ports and by inclusion of a resistive vane in proximity to the balun. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Presents a study that examined the benefits of a project designed to develop a learning experience that contextualizes measurement and geometry concepts among school children in the U.S. Components of a mathematical investigation; Details of the creation of the project; Overview of activities included in the project.