Throwing Some Light on the Vast Darkness that is Analysis: Niels Henrik Abel's Critical Revision and the Concept of Absolute Convergence

During the first half of the nineteenth century, mathematical analysis underwent a transition from a predominantly formula-centred practice to a more concept-centred one. Central to this development was the reorientation of analysis originating in A ugustin- L ouis C auchy's (1789–1857) treatment of infinite series in his Cours d'analyse . In this work, C auchy set out to rigorize analysis, thereby critically examining and reproving central analytical results. One of C auchy's first and most ardent followers was the Norwegian N iels H enrik A bel (1802–1829) who vowed to shed some light on the vast darkness in analysis.
This paper investigates some important aspects of A bel's contribution to the reorientation in analysis. In particular, it stresses the role for critical revision in the process of rigorization. By critically examining past practice, the new practice sought to explain the relative success of the previous—now outdated—approach. This is illustrated by discussing a number of issues related to A bel's new proof of the binomial theorem (1826) including his reactions to the exception that he encountered to one of the central theorems of C auchy's theory.
Following this discussion, the formation of new concepts as the result of critical revisions is illustrated by analysing the early history of the concept of absolute convergence. Thereby, it is shown how a new concept was distilled, investigated, put to use and eventually superseded.     

Determination of estrogens in sludge and sediments by liquid extraction and GC/MS/MS

Two methods have been developed that enable the determination of estrogens down to 2 ng/g in digested and activated sludge from domestic sewage treatment plants (STPs) and down to 0.2 ng/g in freshwater sediments. The method for sludge analysis consists of solvent extraction; a gel permeation chromatography (GPC) cleanup step, a 1 g silica gel column; and finally, detection by GC-ion trap MS/MS of the silylated estrogens with MSTFA. For sediments, the solvent extraction was successively followed by silica gel cleanup, solid phase enrichment (SPE), and a HPLC cleanup before derivatization and GC/MS/MS detection. Mean recoveries of the estrogens mainly exceeded 70% in sludge and 90% in sediments. In activated and digested sewage sludge, estrone and 17beta-estradiol were detected up to 37 ng/g and 49 ng/g, respectively, and 17alpha-ethinylestradiol up to 17 ng/g. The occurrence of estrogens in digested sludge indicates that estrogens can be persistent during sludge digestion. In river sediments, estrone and 17beta-estradiol were detected up to 2 ng/g (estrone), and the contraceptive 17alpha-ethinylestradiol was found with a maximum of 0.9 ng/g. Mestranol, a prodrug for 17alpha-ethinylestradiol, was not detected either in sludge or in sediments.     

Psychopathy and suicide: A multisample investigation.

Evidence suggests that behavioral aspects of psychopathy are associated with suicidal behavior, whereas the affective and interpersonal aspects are not. The authors tested the robustness of this bifurcated association across 1,711 persons and 12 samples of adult and juvenile criminal offenders, forensic psychiatric patients, and civil psychiatric patients. The authors observed a small but significant partial correlation (.13) between the behavioral/impulsive lifestyle features of psychopathy and suicidality, but no effect for affective/interpersonal features. Several method and sample features (mental disorder; psychopathy and suicidality measurement format) significantly strengthened or weakened this association. The authors conclude that it is not possible to speak of "the" association between psychopathy and suicide, but that this relationship appears to be partially dependent on methodological (i.e., self-report vs. clinician-administered psychopathy measures) and sample composition (i.e., age; mental illness) factors. Recommendations for practice are provided, including that clinicians should not consider psychopathy a buffer against suicidal behavior. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Data‐Driven Modelling of Quality and Performance Indices in Sintermaking

In developing data‐driven models of complex real‐world systems, a common problem is how to select relevant inputs from a large set of measurements. If the observations of the outputs to be predicted by the model are scarce, which may be the case if the outputs are indices determined in toilsome laboratory tests, strict constraints have to be imposed on the number of model parameters. In neural network modelling, this limitation in practice also restricts the number of hidden nodes as well as the number of input variables, since the dimension of the weight vector strongly depends on these. This paper presents a systematic method for data‐driven modelling with feedforward layered neural networks, including a method for the selection of input variables. The method is illustrated on a problem from ironmaking industry, where sinter quality indices are predicted on the basis of raw material properties. Furthermore, an inversion technique of the resulting network models is proposed, where an optimization problem is solved to maximize the performance of the sintering operation by manipulating the inputs.     

A genetic factor explains most of the variation in the psychopathic personality.

The psychopathic personality can be conceptualized as three interrelated dimensions, (a) an interpersonal style of glibness, grandiosity, and manipulation; (b) an affective disposition of callousness, lack of empathy, and unemotionality; and (c) a behavioral/lifestyle dimension of impulsivity, need for stimulation, and irresponsibility, underpinning a higher order construct, psychopathic personality. The authors used a self-report questionnaire (The Youth Psychopathic Traits Inventory) to study the importance of genetic and environmental influences on psychopathic personality traits in a sample of 1,090 monozygotic and dizygotic twin pairs, aged 16-17 years. Results showed a strong genetic influence behind the higher order "psychopathic personality" factor, underpinned by the three psychopathic personality dimensions. Over and above the effects to the higher order factor, significant unique genetic influences were also found in the callous/unemotional and in the impulsive/irresponsible dimension, but not in the grandiose/manipulative dimension. The authors propose that this latent psychopathic personality factor is a meaningful target for future etiological research. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Control volume based modelling in one space dimension of oscillating, compressible flow in reciprocating machines

We present an approach for modelling unsteady, primarily one-dimensional, compressible flow. The conservation laws for mass, energy, and momentum are applied to a staggered mesh of control volumes and loss mechanisms are included directly as extra terms. Heat transfer, flow friction, and multidimensional effects are calculated using empirical correlations. Transformations of the conservation equations into new variables, artificial dissipation for dissipating acoustic phenomena, and an asymmetric interpolation method for minimising numerical diffusion and non physical temperature oscillations are presented. The capabilities of the approach are illustrated with an example solution and an experimental validation of a Stirling engine model.     

An Inductorless 300 MHz Wideband CMOS Power Amplifier

The power amplifier tends to be one of the most demanding parts to fully integrate when building an entire radio on a CMOS chip. In this paper the design of a fully integrated RF power amplifier without inductors is described. As inductors in CMOS technology are associated with various problems, it is interesting to examine what performance can be achieved without them. An amplifier with an operating band from 60 MHz to 300 MHz (–3 dB) is built in 0.8 m CMOS. A 3 V supply is used. The measured midband power gain is 30 dB with 50 resistive source and load impedance. As linearity is important for many modern modulation schemes, the amplifier is designed to be as linear as possible. The measured third order intercept point is 23 dBm and the 1 dB compression point is 10 dBm, both referred to the output. The output is single ended to avoid an off-chip differential to single ended transformer.     

Methods and Procedures for Computer Based Handling of Components Reliability Data at FTL (The Swedish Military Electronics Laboratory)

In order to turn reliability prediction into a readily available tool, a system for computerized handling of failure rates was developed at FTL. This system, which is named RPP-1 (Reliability Program One) is presently covering data of electronic and electromechanical components. From a given list of components and data on stresses and working conditions, the failure rates are automatically searched, processed, and pooled in an assessment for an equipment. To make this possible, a number of decisions and judgements had to be taken regarding codes, formulas, models, bank structure, application factors, etc. This paper gives a summary of the FTL solutions for those basic questions. The system?actually a system of subprograms?has been developed at the Swedish Military Electronics Laboratory. The project was headed by the the author of this paper.     

MatLab program for precision calibration of optical tweezers

Optical tweezers are used as force transducers in many types of experiments. The force they exert in a given experiment is known only after a calibration. Computer codes that calibrate optical tweezers with high precision and reliability in the (x,y)-plane orthogonal to the laser beam axis were written in MatLab (MathWorks Inc.) and are presented here. The calibration is based on the power spectrum of the Brownian motion of a dielectric bead trapped in the tweezers. Precision is achieved by accounting for a number of factors that affect this power spectrum. First, cross-talk between channels in 2D position measurements is tested for, and eliminated if detected. Then, the Lorentzian power spectrum that results from the Einstein-Ornstein-Uhlenbeck theory, is fitted to the low-frequency part of the experimental spectrum in order to obtain an initial guess for parameters to be fitted. Finally, a more complete theory is fitted, a theory that optionally accounts for the frequency dependence of the hydrodynamic drag force and hydrodynamic interaction with a nearby cover slip, for effects of finite sampling frequency (aliasing), for effects of anti-aliasing filters in the data acquisition electronics, and for unintended “virtual” filtering caused by the position detection system. Each of these effects can be left out or included as the user prefers, with user-defined parameters. Several tests are applied to the experimental data during calibration to ensure that the data comply with the theory used for their interpretation: Independence of x- and y-coordinates, Hooke's law, exponential distribution of power spectral values, uncorrelated Gaussian scatter of residual values. Results are given with statistical errors and covariance matrix.

Program summary

Title of program: tweezercalibCatalogue identifier: ADTVProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland.Program Summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTVComputer for which the program is designed and others on which it has been tested: General computer running MatLab (MathWorks Inc.).Programming language used: MatLab (MathWorks Inc.). Uses “Optimization Toolbox” and “Statistics Toolbox”.Memory required to execute with typical data: Of order 4 times the size of the data file.High speed storage required: NoneNo. of lines in distributed program, including test data, etc.: 133 183No. of bytes in distributed program, including test data, etc.: 1 043 674Distribution format: tar gzip fileNature of physical problem: Calibrate optical tweezers with precision by fitting theory to experimental power spectrum of position of bead doing Brownian motion in incompressible fluid, possibly near microscope cover slip, while trapped in optical tweezers. Thereby determine spring constant of optical trap and conversion factor for arbitrary-units-to-nanometers for detection system.Method of solution: Elimination of cross-talk between quadrant photo-diode's output channels for positions (optional). Check that distribution of recorded positions agrees with Boltzmann distribution of bead in harmonic trap. Data compression and noise reduction by blocking method applied to power spectrum. Full accounting for hydrodynamic effects: Frequency-dependent drag force and interaction with nearby cover slip (optional). Full accounting for electronic filters (optional), for “virtual filtering” caused by detection system (optional). Full accounting for aliasing caused by finite sampling rate (optional). Standard non-linear least-squares fitting. Statistical support for fit is given, with several plots suitable for inspection of consistency and quality of data and fit.Restrictions on the complexity of the problem: Data should be positions of bead doing Brownian motion while held by optical tweezers. For high precision in final results, data should be time series measured over a long time, with sufficiently high experimental sampling rate: The sampling rate should be well above the characteristic frequency of the trap, the so-called corner frequency. Thus, the sampling frequency should typically be larger than 10 kHz. The Fast Fourier Transform applied requires the time series to contain 2ⁿ data points, and long measurement time is obtained with n>12-15. Finally, the optics should be set to ensure a harmonic trapping potential in the range of positions visited by the bead. The fitting procedure checks for harmonic potential.Typical running time: (Tens of) minutesUnusual features of the program: NoneReferences: The theoretical underpinnings for the procedure are found in [K. Berg-Sørensen, H. Flyvbjerg, Rev. Sci. Instrum. 75 (3) (2004) 594].