Sets, sequences, and mappings: the basic concepts of analysis

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Analysis conciliorum generalium et particularium ... /

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An essay on the application of mathematical analysis to the theories of electricity and magnetism /

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Four lectures on mathematics, delivered at Columbia University in 1911,

I. The defintion of solutions of linear partial differnetial equations by boundary conditions.--II. Contemporary researches in differential equations, integral equations, and integro-differential equations.--III. Analysis situs in connection with correspondences and differential equations.--IV. Elementary solutions of partial differential equations and Green's functions.

Synthesis dataset of physical and ecosystem properties from pan-arctic wetland sites using peat core analysis

Permafrost dynamics play an important role in high-latitude peatland carbon balance and are key to understanding the future response of soil carbon stocks. Permafrost aggradation can control the magnitude of the carbon feedback in peatlands through effects on peat properties. We compiled peatland plant macrofossil records for the northern permafrost zone (515 cores from 280 sites) and classified samples by vegetation type and environmental class (fen, bog, tundra and boreal permafrost, thawed permafrost). We examined differences in peat properties (bulk density, carbon (C), nitrogen (N) and organic matter content, C/N ratio) and C accumulation rates among vegetation types and environmental classes.

A Comparative Analysis of Two Slug Test Methods in Puget Lowland Glacio-Fluvial Sediments near Coupeville, WA

Two different slug test field methods are conducted in wells completed in a Puget Lowland aquifer and are examined for systematic error resulting from water column displacement techniques. Slug tests using the standard slug rod and the pneumatic method were repeated on the same wells and hydraulic conductivity estimates were calculated according to Bouwer & Rice and Hvorslev before using a non-parametric statistical test for analysis. Practical considerations of performing the tests in real life settings are also considered in the method comparison. Statistical analysis indicates that the slug rod method results in up to 90% larger hydraulic conductivity values than the pneumatic method, with at least a 95% certainty that the error is method related. This confirms the existence of a slug-rod bias in a real world scenario which has previously been demonstrated by others in synthetic aquifers. In addition to more accurate values, the pneumatic method requires less field labor, less decontamination, and provides the ability to control the magnitudes of the initial displacement, making it the superior slug test procedure.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Sexual dimorphism of the femoral neck during the adolescent growth spurt: a structural analysis

Before puberty, there are only small sex differences in body shape and composition. During adolescence, sexual dimorphism in bone, lean, and fat mass increases, giving rise to the greater size and strength of the male skeleton. The question remains as to whether there are sex differences in bone strength or simply differences in anthropometric dimensions. To test this, we applied hip structural analysis (HSA) to derive strength and geometric indices of the femoral neck using bone densitometry scans (DXA) from a 6-year longitudinal study in Canadian children. Seventy boys and sixty-eight girls were assessed annually for 6 consecutive years. At the femoral neck, cross-sectional area (CSA, an index of axial strength), subperiosteal width (SPW), and section modulus (Z, an index of bending strength) were determined, and data were analyzed using a hierarchical (random effects) modeling approach. Biological age (BA) was defined as years from age at peak height velocity (PHV). When BA, stature, and total-body lean mass (TB lean) were controlled, boys had significantly higher Z than girls at all maturity levels (P < 0.05). Controlling height and TB lean for CSA demonstrated a significant independent sex by BA interaction effect (P < 0.05). That is, CSA was greater in boys before PHV but higher in girls after PHV The coefficients contributing the greatest proportion to the prediction of CSA, SPW, and Z were height and lean mass. Because the significant sex difference in Z was relatively small and close to the error of measurement, we questioned its biological significance. The sex difference in bending strength was therefore explained by anthropometric differences. In contrast to recent hypotheses, we conclude that the CSA-lean ratio does not imply altered mechanosensitivity in girls because bending dominates loading at the neck, and the Z-lean ratio remained similar between the sexes throughout adolescence. That is, despite the greater CSA in girls, the bone is strategically placed to resist bending; hence, the bones of girls and boys adapt to mechanical challenges in a similar way. (C) 2004 Elsevier Inc. All rights reserved.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Learning mathematics in a classroom community of inquiry

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.

Multivariate genetic analysis of cognitive abilities in an adolescent twin sample

The sources of covariation among cognitive measures of Inspection Time, Choice Reaction Time, Delayed Response Speed and Accuracy, and IQ were examined in a classical twin design that included 245 monozygotic (MZ) and 298 dizygotic (DZ) twin pairs. Results indicated that a factor model comprising additive genetic and unique environmental effects was the most parsimonious. In this model, a general genetic cognitive factor emerged with factor loadings ranging from 0.28 to 0.64. Three other genetic factors explained the remaining genetic covariation between various speed and Delayed Response measures with IQ. However, a large proportion of the genetic variation in verbal (54%) and performance (25%) IQ was unrelated to these lower order cognitive measures. The independent genetic IQ variation may reflect information processes not captured by the elementary cognitive tasks, Inspection Time and Choice Reaction Time, nor our working memory task, Delayed Response. Unique environmental effects were mostly nonoverlapping, and partly represented test measurement error.

Functional promoter analysis using an approach based on an in vitro evolution strategy

In vitro evolution imitates the natural evolution of genes and has been very successfully applied to the modification of coding sequences, but it has not yet been applied to promoter sequences. We propose an alternative method for functional promoter analysis by applying an in vitro evolution scheme consisting of rounds of error-prone PCR, followed by DNA shuffling and selection of mutant promoter activities. We modified the activity in embryogenic sugarcane cells of the promoter region of the Goldfinger isolate of banana streak virus and obtained mutant promoter sequences that showed an average mutation rate of 2.5% after applying one round of error-prone PCR and DNA shuffling. Selection and sequencing of promoter sequences with decreased or unaltered activity allowed us to rapidly map the position of one cis-acting element that influenced promoter activity in embryogenic sugarcane cells and to discover neutral mutations that did not affect promoter Junction. The selective-shotgun approach of this promoter analysis method immediately after the promoter boundaries have been defined by 5' deletion analysis dramatically reduces the labor associated with traditional linker-scanning deletion analysis to reveal the position of functional promoter domains. Furthermore, this method allows the entire promoter to be investigated at once, rather than selected domains or nucleotides, increasing the, prospect of identifying interacting promoter regions.

Hydrodynamics and mass transfer coefficient in activated sludge aerated stirred column reactor: Experimental analysis and modeling

The aerated stirred reactor (ASR) has been widely used in biochemical and wastewater treatment processes. The information describing how the activated sludge properties and operation conditions affect the hydrodynamics and mass transfer coefficient is missing in the literature. The aim of this study was to investigate the influence of flow regime, superficial gas velocity (U-G), power consumption unit (P/V-L), sludge loading, and apparent viscosity (pap) of activated sludge fluid on the mixing time (t(m)), gas hold-up (epsilon), and volumetric mass transfer coefficient (kLa) in an activated sludge aerated stirred column reactor (ASCR). The activated sludge fluid performed a non-Newtonian rheological behavior. The sludge loading significantly affected the fluid hydrodynamics and mass transfer. With an increase in the UG and P/V-L, the epsilon and k(L)a increased, and the t(m), decreased. The E, kLa, and tm,were influenced dramatically as the flow regime changed from homogeneous to heterogeneous patterns. The proposed mathematical models predicted the experimental results well under experimental conditions, indicating that the U-G, P/V-L, and mu(ap) had significant impact on the t(m) epsilon, and k(L)a. These models were able to give the tm, F, and kLa values with an error around +/- 8%, and always less than +/- 10%. (c) 2005 Wiley Periodicals, Inc.

Fractal analysis of pyramidal cells in the visual cortex of the galago (Otolemur garnetti): Regional variation in dendritic branching patterns between visual areas

Previously it has been shown that the branching pattern of pyramidal cells varies markedly between different cortical areas in simian primates. These differences are thought to influence the functional complexity of the cells. In particular, there is a progressive increase in the fractal dimension of pyramidal cells with anterior progression through cortical areas in the occipitotemporal (OT) visual stream, including the primary visual area (V1), the second visual area (V2), the dorsolateral area (DL, corresponding to the fourth visual area) and inferotemporal cortex (IT). However, there are as yet no data on the fractal dimension of these neurons in prosimian primates. Here we focused on the nocturnal prosimian galago (Otolemur garnetti). The fractal dimension (D), and aspect ratio (a measure of branching symmetry), was determined for I I I layer III pyramidal cells in V1, V2, DL and IT. We found, as in simian primates, that the fractal dimension of neurons increased with anterior progression from V1 through V2, DL, and IT. Two important conclusions can be drawn from these results: (1) the trend for increasing branching complexity with anterior progression through OT areas was likely to be present in a common primate ancestor, and (2) specialization in neuron structure more likely facilitates object recognition than spectral processing.

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis

QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulae for obtaining MLEs via the expectation maximization (EM) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.