Versuch einer philosophie der mathematik, verbunden mit einer kritik der aufstellungen Hegel's über den zweck und die natur der höheren analysis,

Mode of access: Internet.

Neue Grundmittel und Erfindungen zur Analysis, Algebra, Functionsrechnung und zugehörigen Geometrie sowie Principien zur mathematischen Reform nebst einer Anleitung zum Studiren und Lehren der Mathematik.

"Transradicale Algebra und entsprechende Lösung der allgemeinen auch überviergradigen Gleichungen," vol. 2.

The philosophy of arithmetic as developed from the three fundamental processes of synthesis, analysis and comparison, containing also a history of arithmetic.

Mode of access: Internet.

Encyclopaedia of pure mathematics.

Articles reprinted from Encyclopaedia metropolitana.

Notes on functional analysis.

"These notes ... are intended only for the convenience of the students in mathematics 515-516 and are not intended to be considered as a text on the subject matter."

Mathematical analysis for business decisions by James E. Howell and Daniel Teichroew.

Mode of access: Internet.

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

Mode of access: Internet.

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

Mode of access: Internet.

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.

A systematic review and meta-analysis of Northern Hemisphere season of birth studies in schizophrenia

Based on the epidemiological finding that individuals with schizophrenia tend to be born in winter/spring when compared to the general population, we examined (1) the strength and timing of this effect in Northern Hemisphere sites, and (2) the correlation between the season of birth effect size and latitude. Studies were located via electronic data sources, published citations, and letters to authors. Inclusion criteria were that studies specify the diagnostic criteria used, that studies specify the counts of schizophrenia and general population births for each month, and that subjects and the general population be drawn from the same birth years and catchment area. We extracted data from eight studies based on 126,196 patients with schizophrenia and 86,605,807 general population births and drawn from 27 Northern Hemisphere sites. Comparing winter/spring versus summer/autumn births, we found a significant excess for winter/spring births (pooled odds ratio = 1.07; 95% confidence interval 1.05, 1.08; population attributable risk = 3.3%). There was a small but significant positive correlation between the odds ratios for the season of birth comparison and latitude (r = 0.271, p < 0.005). Furthermore, the shape of the seasonality in schizophrenia births varied by latitude band. These variations may encourage researchers to generate candidate seasonally fluctuating exposures.

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.

Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

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.

Systematic review of cholinergic drugs for neuroleptic-induced tardive dyskinesia: a meta-analysis of randomized controlled trials

The authors evaluated the efficacy of cholinergic drugs in the treatment of neuroleptic-induced tardive dyskinesia (TD) by a systematic review of the literature on the following agents: choline, lecithin, physostigmine, tacrine, 7-methoxyacridine, ipidacrine, galantamine, donepezil, rivastigmine, eptastigmine, metrifonate, arecoline, RS 86, xanomeline, cevimeline, deanol, and meclofenoxate. All relevant randomized controlled trials, without any language or year limitations, were obtained from the Cochrane Schizophrenia Group's Register of Trials. Trials were classified according to their methodological quality. For binary and continuous data, relative risks (RR) and weighted or standardized mean differences (SMD) were calculated, respectively. Eleven trials with a total of 261 randomized patients were included in the meta-analysis. Cholinergic drugs showed a minor trend for improvement of tardive dyskinesia symptoms, but results were not statistically significant (RR 0.84, 95% confidence interval (CI) 0.68 to 1.04, p=0.11). Despite an extensive search of the literature, eligible data for the meta-analysis were few and no results reached statistical significance. In conclusion, we found no evidence to support administration of the old cholinergic agents lecithin, deanol, and meclofenoxate to patients with tardive dyskinesia. In addition, two trials were found on novel cholinergic Alzheimer drugs in tardive dyskinesia, one of which was ongoing. Further investigation of the clinical effects of novel cholinergic agents in tardive dyskinesia is warranted. (C) 2004 Elsevier Inc. All rights reserved.