The Number Crunch game : a simple vehicle for building algebraic reasoning skills

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.

Recycling concrete: An undiscovered source of ultrafine particles

While concrete recycling is practiced worldwide, there are many unanswered questions in relation to ultrafine particle (UFP; Dp<100nm) emissions and exposure around recycling sites. In particular: (i) Does recycling produce UFPs and in what quantities? (ii) How do they disperse around the source? (iii) What impact does recycling have on ambient particle number concentrations (PNCs) and exposure? (iv) How effective are commonly used dust respirators to limit exposure? We measured size-resolved particles in the 5-560 nm range at five distances from a simulated concrete recycling source and found that: (i) the size distributions were multimodal, with up to ~93% of total PNC in the UFP size range; and (ii) dilution was a key particle transformation mechanism. UFPs showed a much slower decay rate, requiring ~62% more distance to reach 10% of their initial concentration compared with their larger counterparts. Compared with typical urban exposure during car journeys, exposure decay profiles showed up to ~5 times higher respiratory deposition within 10 m of the source. Dust respirators were found to remove half of total PNC; however the removal factor for UFPs was only ~57% of that observed in the 100-560 nm size range. These findings highlight a need for developing an understanding of the nature of the particles as well as for better control measures to limit UFP exposure.

A vibrational spectroscopic study of the silicate mineral analcime – Na2(Al4SiO4O12)·2H2O : a natural zeolite

We have studied the mineral analcime using a combination of scanning electron microscopy with energy dispersive spectroscopy and vibrational spectroscopy. The mineral analcime Na2(Al4SiO4O12)·2H2O is a crystalline sodium silicate. Chemical analysis shows the mineral contains a range of elements including Na, Al, Fe2+ and Si. The mineral is characterized by intense Raman bands observed at 1052, 1096 and 1125 cm−1. The infrared bands are broad; nevertheless bands may be resolved at 1006 and 1119 cm−1. These bands are assigned to SiO stretching vibrational modes. Intense Raman band at 484 cm−1 is attributed to OSiO bending modes. Raman bands observed at 2501, 3542, 3558 and 3600 cm−1 are assigned to the stretching vibrations of water. Low intensity infrared bands are noted at 3373, 3529 and 3608 cm−1. The observation of multiple water bands indicate that water is involved in the structure of analcime with differing hydrogen bond strengths. This concept is supported by the number of bands in the water bending region. Vibrational spectroscopy assists with the characterization of the mineral analcime.

Maternal feeding self-efficacy and fruit and vegetable intakes in infants. Results from the SAIDI study

Adequate consumption of fruits and vegetables (FV) is a characteristic of a healthy diet but remains a challenge in nutrition interventions. This cross-sectional study explored the multi-directional relationships between maternal feeding self-efficacy, parenting confidence, child feeding behaviour, exposure to new food and FV intake in a cohort of 277 infants. Mothers with healthy infants weighing ≥2500 g and ≥37 weeks gestation were recruited post-natally from 11 South Australian hospitals. Socio-demographic datawere collected at recruitment. At 6 months postnatal, infantswereweighed and measured, andmothers completed a questionnaire exploring their perceptions of child feeding behaviour and child exposure to newfoods. The questionnaire also included the Short Temperament Scale for Infants, Kessler 10 to measure maternal psychological distress and 5 items measuring maternal feeding self-efficacy. The number of occasions and variety of FV (number of subgroups within food groups) consumed by infants were estimated from a 24-hour dietary recall and 2 days food record. Structural equation modellingwas performed using Mplus version 6.11. Median (IQR) variety scores were 2 (1–3) for fruit and 3 (2–5) for vegetable intake. The most popular FV consumed were apple (n = 108, 45.0%) and pumpkin (n = 143, 56.3%). None of the variables studied predicted the variety of child fruit intake. Parenting confidence, exposure to new foods and child feeding behaviourwere indirectly related to child vegetable intake through maternal feeding self-efficacy while total number of children negatively predicted child vegetable variety (p < 0.05). This highlights the need for addressing antecedents of maternal feeding self-efficacy and the family eating environment as key strategies towards development of healthy eating in children.

Aspects of elementary number theory illustrated in the spreadsheet environment

Number theory has in recent decades assumed a great practical importance, due primarily to its application to cryptography. This chapter discusses how elementary concepts of number theory may be illuminated and made accessible to upper secondary school students via appropriate spreadsheet models. In such environments, students can observe patterns, gain structural insight, form and test conjectures, and solve problems. The chapter begins by reviewing literature on the use of spreadsheets in general and the use of spreadsheets in number theory in particular. Two sample applications are then discussed. The first, factoring factorials, is presented and instructions are given to construct a model in Excel 2007. The second application, the RSA cryptosystem, is included because of its importance to Science, Technology, Engineering, and Mathematics (STEM) students. Number theoretic concepts relevant to RSA are discussed, and an outline of RSA. is given, with example. The chapter ends with instructions on how to construct a simple spreadsheet illustrating RSA.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

The molecular structure of the phosphate mineral kidwellite NaFe93+(PO4)6(OH)11⋅3H2O – a vibrational spectroscopic study

The mineral kidwellite, a hydrated hydroxy phosphate of ferric iron and sodium of approximate formula NaFe93+(PO4)6(OH)11⋅3H2O, has been studied using a combination of electron microscopy with EDX and vibrational spectroscopic techniques. Raman spectroscopy identifies an intense band at 978 cm−1 and 1014 cm−1. These bands are attributed to the PO43− ν1 symmetric stretching mode. The ν3 antisymmetric stretching modes are observed by a large number of Raman bands. The series of Raman bands at 1034, 1050, 1063, 1082, 1129, 1144 and 1188 cm−1 are attributed to the ν3 antisymmetric stretching bands of the PO43− and HOPO32− units. The observation of these multiple Raman bands in the symmetric and antisymmetric stretching region gives credence to the concept that both phosphate and hydrogen phosphate units exist in the structure of kidwellite. The series of Raman bands at 557, 570, 588, 602, 631, 644 and 653 cm−1are assigned to the PO43− ν2 bending modes. The series of Raman bands at 405, 444, 453, 467, 490 and 500 cm−1 are attributed to the PO43− and HOPO32− ν4 bending modes. The spectrum is quite broad but Raman bands may be resolved at 3122, 3231, 3356, 3466 and 3580 cm−1. These bands are assigned to water stretching vibrational modes. The number and position of these bands suggests that water is in different molecular environments with differing hydrogen bond distances. Infrared bands at 3511 and 3359 cm−1 are ascribed to the OH stretching vibration of the OH units. Very broad bands at 3022 and 3299 cm−1 are attributed to the OH stretching vibrations of water. Vibrational spectroscopy offers insights into the molecular structure of the phosphate mineral kidwellite.

Spatially averaged model of complex-plasma discharge with self-consistent electron energy distribution

A global, or averaged, model for complex low-pressure argon discharge plasmas containing dust grains is presented. The model consists of particle and power balance equations taking into account power loss on the dust grains and the discharge wall. The electron energy distribution is determined by a Boltzmann equation. The effects of the dust and the external conditions, such as the input power and neutral gas pressure, on the electron energy distribution, the electron temperature, the electron and ion number densities, and the dust charge are investigated. It is found that the dust subsystem can strongly affect the stationary state of the discharge by dynamically modifying the electron energy distribution, the electron temperature, the creation and loss of the plasma particles, as well as the power deposition. In particular, the power loss to the dust grains can take up a significant portion of the input power, often even exceeding the loss to the wall.

A kinetic model for an argon plasma containing dust grains

A complex low-pressure argon discharge plasma containing dust grains is studied using a Boltzmann equation for the electrons and fluid equations for the ions. Local effects, such as the spatial distribution of the dust density and external electric field, are included, and their effect on the electron energy distribution, the electron and ion number densities, the electron temperature, and the dust charge are investigated. It is found that dust particles can strongly affect the plasma parameters by modifying the electron energy distribution, the electron temperature, the creation and loss of plasma particles, as well as the spatial distributions of the electrons and ions. In particular, for sufficiently high grain density and/or size, in a low-pressure argon glow discharge, the Druyvesteyn-like electron distribution in pristine plasmas can become nearly Maxwellian. Electron collection by the dust grains is the main cause for the change in the electron distribution function.

JK1 (FAM134B) gene and colorectal cancer : a pilot study on the gene copy number alterations and correlations with clinicopathological parameters

AIMS The aims of the study are to characterize changes in JK-1 (FAM134B) at the DNA level in colorectal adenocarcinoma and adenoma and exploring the possible correlations with clinical and pathological features. METHOD JK-1 gene DNA copy number changes were studied in 211 colorectal carcinomas, 32 colorectal adenoma and 20 colorectal non-cancer colorectal tissue samples by real-time quantitative polymerase chain reaction. The results were correlated with clinical and pathological parameters. RESULTS Colorectal adenomas were more likely to be amplified than deleted with regard to JK-1 (FAM134B) DNA copy number change. The copy number level of JK-1 (FAM134B) DNA in colorectal adenocarcinomas was significantly lower in comparison to colorectal adenomas. Changes in JK-1 (FAM134B) DNA copy number were associated with histological subtypes, and cancer stage. Lower copy numbers were associated with higher tumor stage, lymph node stage and overall pathological stage of cancer. Conversely, higher DNA copy numbers were detected more often in the mucinous adenocarcinoma. CONCLUSIONS This is the first study showing significant correlations of the JK-1 (FAM134B) gene copy number alterations with clinical and pathological features in a large cohort of pre-invasive and invasive colorectal malignancies. The changes in DNA copy number associated with progression of colorectal malignancies reflect that JK-1 (FAM134B) gene could play a role in controlling some steps in development of the invasive phenotypes.

Particle number emissions from a large fleet of diesel and CNG buses

Exhaust emissions were monitored in real-time at the kerb of a busy busway used by a mix of diesel and CNG-powered transport buses. Particle number concentration in the size range 3 nm to 3 µm was measured with a TSI condensation particle counter (CPC 3025). Particle mass (PM2.5) was measured with a TSI Dustrak 8520. The CO2 emissions were measured with a fast response CO2 analyser (Sable CA-10A). All emission concentrations were recorded in real time at 1 sec resolution, together with the precise passage times of buses. The instantaneous ratio of particle number (or mass) to CO2 concentration, denoted Z, was used as a measure of the particle number (or mass) emission factor of each passing bus.

Nano and ultrafine particle number concentrations in different environments : application towards air quality regulations

Particle number concentrations vary significantly with environment and, in this study, we attempt to assess the significance of these differences. Towards this aim, we reviewed 85 papers that have reported particle number concentrations levels at 126 sites covering different environments. We grouped the results into eight categories according to measurement location including: road tunnel, on-road, road-side, street canyon, urban, urban background, rural, and clean background. From these reports, the overall median number concentration for each of the eight site categories was calculated. The eight location categories may be classified into four distinct groups. The mean median particle number locations for these four types were found to be statistically different from each other. Rural and clean background sites had the lowest concentrations of about 3x103 cm-3. Urban and urban background sites showed concentrations that were three times higher (9x103 cm-3). The mean concentration for the street canyon, roadside and on-road measurement sites was 4.6x104 cm-3, while the highest concentrations were observed in the road tunnels (8.6x104 cm-3). This variation is important when assessing human exposure-response for which there is very little data available, making it difficult to develop health guidelines, a basis for national regulations. Our analyses shows that the current levels in environments affected by vehicle emissions are 3 to 28 times higher than in the natural environments. At present, there is no threshold level in response to exposure to ultrafine particles. Therefore, future control and management strategies should target a decrease of these particles in urban environments by more than one order of magnitude to bring them down to the natural background. At present there is a long way to go to achieve this.

Comparison of particle number concentrations between different environments

Particle number concentrations vary significantly with environment and, in this study, we attempt to assess the significance of these differences. Towards this aim, we reviewed 85 papers that have reported particle number concentrations levels at 126 sites covering different environments. We grouped the results into eight categories according to measurement location including: road tunnel, on-road, road-side, street canyon, urban, urban background, rural, and clean background. Median values were calculated for each category. This review was restricted to papers that presented concentrations numerically. The majority of the reports were based on either CPC or SMPS measurements, with a limited number of papers reporting results from both instruments at the same site. Hence there were several overlaps between the number of CPC and SMPS measuring sites. Most of the studies reported multiple measurements at a given study site, while some studies included results from more than one site. From these reports, the overall median value for each location category was calculated...

Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.