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  • 1
    Electronic Resource
    Electronic Resource
    Correction: Maximum Likelihood Estimation Using Price Data of the Derivative Contract (Mathematical Finance 1994, 4/2, 155–167) (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 10 (2000), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00105
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  • 2
    Electronic Resource
    Electronic Resource
    No Arbitrage in Discrete Time Under Portfolio Constraints (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 11 (2001), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In frictionless securities markets, the characterization of the no-arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental theorem of asset pricing. In the presence of convex constraints on the trading strategies, we extend this theorem under a closedness condition and a nondegeneracy assumption. We then provide connections with the superreplication problem solved in Föllmer and Kramkov (1997).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00117
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  • 3
    Electronic Resource
    Electronic Resource
    A Note on the Boyle–Vorst Discrete-Time Option Pricing Model with Transactions Costs (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 11 (2001), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Working in a binomial framework, Boyle and Vorst (1992) derived self-financing strategies perfectly replicating the final payoffs to long positions in European call and put options, assuming proportional transactions costs on trades in the stocks. The initial cost of such a strategy yields, by an arbitrage argument, an upper bound for the option price. A lower bound for the option price is obtained by replicating a short position. However, for short positions, Boyle and Vorst had to impose three additional conditions. Our aim in this paper is to remove Boyle and Vorst's conditions for the replication of short calls and puts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00120
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  • 4
    Electronic Resource
    Electronic Resource
    Louis Bachelier on the Centenary of Théorie de la Spéculation[We would l] (2000)
    Boston, USA and Oxford, UK : Blackwell Publishers Ltd
    Mathematical finance 10 (2000), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00098
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  • 5
    Electronic Resource
    Electronic Resource
    Bounds on Derivative Prices in an Intertemporal Setting with Proportional Transaction Costs and Multiple Securities (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 11 (2001), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The observed discrepancies of derivative prices from their theoretical, arbitrage-free values are examined in the presence of transaction costs. Analytic upper and lower bounds on the reservation write and purchase prices, respectively, are obtained when an investor's preferences exhibit constant relative risk aversion between zero and one. The economy consists of multiple primary securities with stationary returns, a constant rate of interest, and any number of American or European derivatives with, possibly, path-dependent arbitrary payoffs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00118
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  • 6
    Electronic Resource
    Electronic Resource
    Pricing of New Securities in an Incomplete Market: the Catch 22 of No-Arbitrage Pricing (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 11 (2001), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: There are two distinctly different approaches to the valuation of a new security in an incomplete market. The first approach takes the prices of the existing securities as fixed and uses no-arbitrage arguments to derive the set of equivalent martingale measures that are consistent with the initial prices of the traded securities. The price of the new security is then obtained by appealing to certain criteria or on the basis of some preference assumption. The second method prices the new security within a general equilibrium framework. This paper clarifies the distinction between the two approaches and provides a simple proof that the introduction of the new security will typically change the prices of all the existing securities. We are left with the paradox that a genuinely new derivative security is not redundant, but the dominant pricing paradigm in derivative security pricing is the no-arbitrage approach, which requires the redundancy of the security. Given the widespread practice of using the no-arbitrage approach to price (or bound the price of) a new security, we also comment on some justifications for this approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00115
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  • 7
    Electronic Resource
    Electronic Resource
    Robust Hedging of Barrier Options (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 11 (2001), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion.We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00116
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  • 8
    Electronic Resource
    Electronic Resource
    A Fundamental Theorem of Asset Pricing for Large Financial Markets[The result] (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 10 (2000), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We formulate the notion of “asymptotic free lunch” which is closely related to the condition “free lunch” of Kreps (1981) and allows us to state and prove a fairly general version of the fundamental theorem of asset pricing in the context of a large financial market as introduced by Kabanov and Kramkov (1994). In a large financial market one considers a sequence (Sn)n=1∞ of stochastic stock price processes based on a sequence (Ωn, Fn, (Ftn)t∈In, Pn)n=1∞ of filtered probability spaces. Under the assumption that for all n∈ N there exists an equivalent sigma-martingale measure for Sn, we prove that there exists a bicontiguous sequence of equivalent sigma-martingale measures if and only if there is no asymptotic free lunch (Theorem 1.1). Moreover we present an example showing that it is not possible to improve Theorem 1.1 by replacing “no asymptotic free lunch” by some weaker condition such as “no asymptotic free lunch with bounded” or “vanishing risk.”
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00103
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  • 9
    Electronic Resource
    Electronic Resource
    Editorial (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00057
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  • 10
    Electronic Resource
    Electronic Resource
    ‘Count us in!’ (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00060
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  • 11
    Electronic Resource
    Electronic Resource
    Correlation: From Picture to Formula (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Correlation is introduced intuitively early in the school curriculum by considering patterns in scatter diagrams. Later on, various formulae are used for calculating correlation coefficients. This article suggests ways in which the formulae can be related to the scatter diagrams.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00058
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  • 12
    Electronic Resource
    Electronic Resource
    Lewis Carroll’s Obtuse Problem (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Carroll’s apparently impeccable solution to one of his probability problems is shown to answer another problem that is based on reasonable assumptions. His original assumptions, however, are self contradictory, hence entailing paradoxical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00059
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  • 13
    Electronic Resource
    Electronic Resource
    Musical Means: Using Songs in Teaching Statistics (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Songs offer fresh motivations for probability and statistics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00062
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  • 14
    Electronic Resource
    Electronic Resource
    Some Misconceptions about Attribute Sampling Plans (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article explores some common potential misconceptions about attribute sampling plans. Use of the operating characteristic curve easily enables the misconceptions to be overcome.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00064
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  • 15
    Electronic Resource
    Electronic Resource
    Quartiles for Discrete Data (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Different methods for finding quartiles for discrete data that are available in the literature are examined in the light of a desirable property that quartiles divide the ordered sample observations into four segments having the same number of observations in each segment. A set of formulae that satisfy this property is proposed and illustrated with examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00063
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  • 16
    Electronic Resource
    Electronic Resource
    A Cautionary Note Concerning the Cox and Stuart Test (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A homework assignment led to the observation that the Cox and Stuart test is not symmetric under the transposition of the two variables. Examples of this feature are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00061
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  • 17
    Electronic Resource
    Electronic Resource
    Beer Tasting and the Problem of Coincidences (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes a matching problem. Given k unlabelled items and k labels, how hard is it to correctly match the labels to the items? The problem is an example of a very old one known as the problem of coincidences, which was originally motivated by a game played in the 18th century.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00065
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  • 18
    Electronic Resource
    Electronic Resource
    Book Review (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Book reviewed:Larry Morgan Statistics Handbook for the TI-83
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00066
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  • 19
    Electronic Resource
    Electronic Resource
    Index to Volume 23 (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00067
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  • 20
    Electronic Resource
    Electronic Resource
    Green Statistics (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Environmental statistics is an exciting and rapidly growing area of statistical application. It requires complex new approaches and methods to be developed, to enable study of the crucial environmental problems we face: whether climate change, passive smoking, industrial pollution or forest fires. For the classroom, environmental statistics can bring some reality and immediacy to our teaching.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00047
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  • 21
    Electronic Resource
    Electronic Resource
    A Role for Statistics in International Cricket (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The Duckworth/Lewis method for adjusting scores in rain-interrupted one-day cricket matches is in current use throughout the world. This article outlines how it works and how it came to be adopted by the cricket authorities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00048
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  • 22
    Electronic Resource
    Electronic Resource
    Eliciting Honesty: How to Tell the Truth with Statistics (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This paper describes and illustrates several models of randomized response sampling, a survey technique for eliciting truthful answers to sensitive questions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00049
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  • 23
    Electronic Resource
    Electronic Resource
    An Introduction to the Bootstrap (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article presents bootstrap methods for estimation, using simple arguments. Minitab macros for implementing these methods are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00050
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  • 24
    Electronic Resource
    Electronic Resource
    Generating Multivariate Normal Data in Excel (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article gives further information about generating multivariate Normal data, including a single-cell Microsoft Excel formula to undertake a Choleski decomposition. References are also made to the bivariate case and the ‘common elements’ approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00052
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  • 25
    Electronic Resource
    Electronic Resource
    Correlations May Surprise (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This short note gives some counter-intuitive correlations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00053
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  • 26
    Electronic Resource
    Electronic Resource
    The World of Chance (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes ‘The World of Chance’, an unconventional statistics course taught at the University of Canberra since 1998, modelled on the Chance courses devised at Dartmouth College. Statistical concepts are introduced via a mixture of lectures, class discussions of news stories, and activities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00054
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  • 27
    Electronic Resource
    Electronic Resource
    Once Upon a Time – Including an Unlikely Tale of Shocking Increase in Deaths as Electricity Sales Rise (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Several data sets displaying seasonality provide examples for time series analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00051
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  • 28
    Electronic Resource
    Electronic Resource
    News & Notes 64 (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.t01-1-00055
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  • 29
    Electronic Resource
    Electronic Resource
    Dotplots and Stemplots in Excel (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article shows how to construct dotplots and stemplots using Microsoft Excel 97.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00035
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  • 30
    Electronic Resource
    Electronic Resource
    Exploring a Queueing Problem Through Human Simulation (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A classroom activity where the students actively simulate different queueing systems is described. Analysis of the waiting times gives insight into the structure of queueing systems and the issues to be considered in comparing them.
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    URL: http://dx.doi.org/10.1111/1467-9639.00036
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  • 31
    Electronic Resource
    Electronic Resource
    Generating Multivariate Normal Pseudo Random Data (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article gives a matrix-based method for generating multivariate Normal data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00037
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  • 32
    Electronic Resource
    Electronic Resource
    Letter to the Editor (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00038
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  • 33
    Electronic Resource
    Electronic Resource
    Learning About the Normal Distribution With a Graphics Calculator (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes how a graphics calculator can be used by students who are learning about the Normal distribution. It also discusses the implications of replacing the use of statistical tables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00039
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  • 34
    Electronic Resource
    Electronic Resource
    A New Least-Squares Regression Model (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes simple apparatus for classroom demonstration of fitting a least-squares regression line.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00040
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  • 35
    Electronic Resource
    Electronic Resource
    Ups and Downs on the Roads (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Road casualty data provide examples for charts
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9639.00041
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  • 36
    Electronic Resource
    Electronic Resource
    The Toothless Bathing Beauty and the t-test (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A simple and amusing class experiment is used to introduce many ideas of descriptive and inferential statistics.
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    URL: http://dx.doi.org/10.1111/1467-9639.00042
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  • 37
    Electronic Resource
    Electronic Resource
    How Many Excellent Grades Should Be Tolerated? (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes an example that can be used to convey the ideas of testing hypotheses.
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    Letter to the Editor (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    News & Notes (2001)
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    Investigating Randomness via Simulation Using the TI-83 (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 23 (2001), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Most students do not have a good grasp of the consequences of randomness. Simulating random phenomena with unexpected outcomes sparks student interest and discussion when presenting probability topics in class. TI-83 programs for simulating selected random phenomena are available from the author.
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    CensusAtSchool 2000 (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article covers the development of an ambitious Internet-based project to conduct a simple census of the schoolchildren of England and Wales linked to the 2001 UK National Census.
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    Gilberts Sine Distribution (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The sine distribution introduced by the astronomer G.K. Gilbert in 1892 is revived as an interesting example of an elementary continuous distribution suitable for teaching purposes.
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    Thou Shalt Not Sit with Statisticians (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A widely-used but never-sourced quotation about statisticians is tracked down.
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    Do the Lengths of Pebbles on Hastings Beach Follow a Normal Distribution? (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes a practical activity involving seven 16- to 17-year-old students, a trainee teacher and the author.
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    The Case Against Histograms (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A homework assignment used to show students that histograms can be misleading is presented.
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    Intransitive Dice Revisited (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Intransitive dice were discussed in a previous article, following a competition in the journal. A further interesting result is presented here.
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    Two-Way Charts: Messages for Teacher Professional Development (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Two anecdotes, one from a primary classroom and one from a professional development (PD) workshop, involve the use or possible use of two-way charts. From these stories some recommendations are made for teacher PD.
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    Learning Statistics on the Web – DISCUSS (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    Notes: This article discusses the use of the Internet in teaching and learning statistics and describes how interactive spreadsheets can be integrated with Web-based resources.
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    News & Notes (2000)
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    Blackwell Publishers (2000)
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article abstracts Blackwell Publishers role asa publisher of both statistics and education andour life long goal to extend scholarlycommunication.
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    On Simulation and the Teaching of Statistics (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The use of simulation as an instructional tool can promote a deep conceptual understanding of statistics and lead to misunderstandings. Teachers need to be aware of the misconceptions that can arise as a result of simulation and carefully structure classroom activities so as to derive the benefits of this powerful instructional tool.
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    Storks Deliver Babies (p= 0.008) (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article shows that a highly statisticallysignificant correlation exists between storkpopulations and human birth rates across Europe.While storks may not deliver babies, unthinkinginterpretation of correlation and p-values cancertainly deliver unreliable conclusions.
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    The Big Ticket: How Not to Design a Game Show (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article analyses a television game show andsuggests improvements.
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    Letter to the Editor (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    Using Probability Intervals to Evaluate Long-Term Gambling Success (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Simple probability calculations show some of thedangers of gambling.
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    Assessment of Student Performance in Statistics (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes assessment and scoringmethods that have been used successfully ingraduate-level statistics teaching.
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    Six Billion Characters in Search of an Author (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: An introduction to searching the Internet isfollowed by some examples relating to humanpopulation issues.
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    Bar and Pie Charts: Ideas for the Classroom (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article gives some ideas for the creation ofbar charts and pie charts, focusing onrepresentations of frequencies and proportions.
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    Pictograms in Excel (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes how pictograms can beconstructed using Microsoft Excel.
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    Two-Way Interactions — They're Top of the Pops (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A helpful example of interaction in two-wayanalysis of variance is described.
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    News & Notes (2000)
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    On Simulating Realizations of Correlated Random Variables (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Simulation of correlated observations from athree-dimensional Normal distribution requiressome preliminary mathematics but then turns outto be easy in Microsoft Excel.
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    Book Reviews (2000)
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Book reviewed:Donald Bligh, Intellect
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    The Royal Statistical Society Centre For Statistical Education (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: We present our vision for the Centre’s role in raising statistical standards in the new millennium, particularly in relation to schools.
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    Intransitive Dice (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: In a recent issue of Teaching Statistics, an intransitive dice competition was published. In this article some further interesting results about such dice are presented.
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    A Statistics Field Trip? (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Ideas for statistical investigations can be found in all sorts of places, even on holiday.
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    More Statistical Nuggets with a Graphics Calculator (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article follows on from the one in the previous issue concerning exploration of the graphics calculator.
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    The Monty Hall Matrix (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Teaching statistics 22 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A general procedure for solving the ‘Monty Hall problem’ is demonstrated using probability matrices, and an n-dimensional extension is presented.
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    Letter to the Editor (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    How Many Rs are there in Statistics? (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The basic principles involved in the collection and analysis of data in a regression situation are discussed.
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    Amazing Graphs (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A cautionary tale about bad habits in graphical displays.
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    Data Have No Meaning when Separated from their Context (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: It is argued that many statisticians teach their subject without much concern about the context in which their methods will be used. This issue is illustrated by the analysis of data on cashier fraud at a supermarket. Here different contexts lead to different questions and different modes of analysis.
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    Book Reviews (2000)
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    Topics: Mathematics
    Notes: Book reviewed:Alan Graham and Barrie Galpin Calculator Maths
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    News & Notes (2000)
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    Correction: Pricing Options with Curved Boundaries (Mathematical Finance 1992, 2, 275–297) (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 10 (2000), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
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    Laguerre Series for Asian and Other Options[The author] (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 10 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper has four goals: (a) relate ladder height distributions to option values; (b) show how Laguerre expansions may be used in the computation of densities, distribution functions, and option prices; (c) derive some new results on the integral of geometric Brownian motion over a finite interval; and (d) apply the preceding results to the determination of the distribution of the integral of geometric Brownian motion and the computation of Asian option values. The usual fixed-strike options on the average are treated, as well as options with payoffs expressed in terms of one over the average of the underlying security, which this author calls “reciprocal Asian options.” In all cases the underlying asset is represented by geometric Brownian motion, the averages are performed continuously, and the options are of European type.
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    Leland's Approach to Option Pricing: The Evolution of a Discontinuity (2001)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 11 (2001), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A claim of Leland (1985) states that in the presence of transaction costs a call option on a stock S, described by geometric Brownian motion, can be perfectly hedged using Black–Scholes delta hedging with a modified volatility. Recently Kabanov and Safarian (1997) disproved this claim, giving an explicit (up to an integral) expression of the limiting hedging error, which appears to be strictly negative and depends on the path of the stock price only via the stock price at expiry ST. We prove in this paper that the limiting hedging error, considered as a function of ST, exhibits a removable discontinuity at the exercise price. Furthermore, we provide a quantitative result describing the evolution of the discontinuity: Hedging errors, plotted over the price at expiry, show a peak near the exercise price. We determine the rate at which that peak becomes narrower (producing the discontinuity in the limit) as the lengths of the revision intervals shrink.
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    Generic Existence and Robust Nonexistence of Numéraires in Finite Dimensional Securities Markets[We are gra] (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
    Mathematical finance 10 (2000), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A numéraire is a portfolio that, if prices and dividends are denominated in its units, admits an equivalent martingale measure that transforms all gains processes into martingales. We first supply a necessary and sufficient condition for the generic existence of numéraires in a finite dimensional setting. We then characterize the arbitrage-free prices and dividends for which the absence of numéraires survives any small perturbation preserving no arbitrage. Finally, we identify the cases when any small, but otherwise arbitrary, perturbation of prices and dividends preserves either the existence of numéraires, or their nonexistence under no arbitrage.
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    URL: http://dx.doi.org/10.1111/1467-9965.00102
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    Relationship between ion distribution and membrane potential during a steady state (1960)
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    Bulletin of mathematical biology 22 (1960), S. 323-349 
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    Topics: Biology , Mathematics
    Notes: Abstract Equations were derived showing the relationship between the membrane potential and the quantities which influence it under steady state conditions. Essentially, the membrane potential is caused by the valence and concentration of the non-permeating ions. The permeating ions can modify the membrane potential by altering the relative concentration of the non-permeating ions with respect to the concentration of the permeating ions. For muscle, the sodium cations act as the non-permeating ions in the extracellular environment by the maintenance of some type of active metabolic process and large anions act as the non-permeating ions in the intracellular environment. Both of these non-permeating ions contribute about equally to the maintenance of the resting membrane potential. When the active metabolic process for sodium extrusion breaks down or when acids are added, the membrane potential should decrease. Water should enter the cell when the sodium metabolic process is diminished; water should leave the cell when acids are added. When acid is added, it is expected that the cations potassium and sodium will leave the cell with little or no shift of the chloride ions.
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    Life, information theory, probability, and physics (1960)
    Springer
    Bulletin of mathematical biology 22 (1960), S. 351-364 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract A purely information-theoretical approach to the problem of self-replication of elementary living units implies that pure chance is the determining factor in the formation of the first living unit. The probability of such a spontaneous formation can be calculated from the minimum amount of information which an organism must possess in order to replicate itself. An estimation of this amount of information is made here by two different methods. First by a “paper and pencil experiment” which indicates the minimum amount of information needed on a printed page in order that with given tools the page could be reproduced. Second—by an analytical consideration of some hypothetical molecular mechanisms. A general method for handling such problems is suggested. On the basis of estimated information contents it is shown that under most favorable conditions the probability of a spontaneous generation by pure chance during the lifetime of the earth is vanishingly small. It is concluded that dynamic factors, which may reduce tremendously the information content, must play a role in the genesis of life on earth.
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    Some remarks on molecular biology (1960)
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    Bulletin of mathematical biology 22 (1960), S. 365-370 
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    Topics: Biology , Mathematics
    Notes: Abstract The binding energy of a very long molecular chain, composed of different classes of molecules, depends in general on the order of the molecules. It is shown that under very general conditions there exists for a givenbrutto chemical composition of a chain, a class of chains which is characterized by a total binding energy which is equal to the total binding energy of any other prescribed chain of different composition within the limits of unsharpness of the energy level. This establishes a criterion formapping of a class of configurations of long chain molecules on another class. To the extent that a mapping constitutes a generalized code those results contribute to the theory of molecular codes. Applying to our results the results of a previous paper (1959,Bull. Math. Biophysics,21, 309–326), we arrive at the conclusion that the self-replication of a living molecule may be the property not of a particular structure but of classes of structures.
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    On the utilization of food by planktophage fishes (1960)
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    Bulletin of mathematical biology 22 (1960), S. 371-389 
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    Topics: Biology , Mathematics
    Notes: Abstract Making some plausible assumptions about the over-all mechanism of food catching and consumption by fishes and evaluating in the light of those assumptions some available experimental data, it is possible to calculate from those data the variation of several important factors with the concentration of food. The factors considered are: total rate of metabolism, total diurnal energy expenditure in the process of feeding, average number of hours per day during which the fish feeds, average length of path traveled by a fish per day, and the so-called “energetic coefficient of growth.” A possible relation with the work of N. Rashevsky (Bull. Math. Biophysics,20, 299–308, 1959) is discussed.
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    Symposium on Mathematical Theories of Biological Phenomena (1960)
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    Bulletin of mathematical biology 22 (1960), S. 425-425 
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    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02476724
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    On the theory of indicator-dilution methods under varying blood-flow conditions (1960)
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    Bulletin of mathematical biology 22 (1960), S. 417-424 
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    Topics: Biology , Mathematics
    Notes: Abstract The theory of measurement of flow and volume by indicator dilution techniques is given in conditions of time-variable flow rates. It is shown that the usual Hamilton (1932,Am. J. Physiol.,99, 534–551) methods can be misleading if the flow changes at a rate of close to that of the transport function.
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    An hypothesis of freese and the DNA-protein coding problem (1961)
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    Bulletin of mathematical biology 23 (1961), S. 305-318 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Freese’s Hypothesis states that a single specific alteration in the sequence of nucleotides of an information-bearing DNA molecule results in a specific mutational effect. Within the framework of the DNA-protein coding problem developed elsewhere, and assuming the quasi-ergodicity of the general coding process, it is shown that Freese’s Hypothesis allows us to derive expressions for the length of the smallest mutable DNA molecule and to obtain a bound for the maximal number of allelic molecules of fixed length. To illustrate these ideas, calculations are carried out on appropriate data from bacternophage and man, and the results are shown to differ by a factor of 10 (modulo the rather crude approximations used). It is further shown that, if ρ(N) and ϱ(N) are respectively the number of information-bearing words of lengthN in a given code and the number of words of lengthN, then the number lim ρ(N)/ϱ(N) depends sensitively on the parameter ∈ which specifiesN→∞ the given code. The implications of this result for the spontaneous aggregation of a sufficient number of information-bearing words to characterize an organism are discussed.
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    Post-and predoctoral fellowships in mathematical biology (1961)
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    Bulletin of mathematical biology 23 (1961), S. 319-319 
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    Topics: Biology , Mathematics
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    The perfect learner (1961)
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    Bulletin of mathematical biology 23 (1961), S. 321-335 
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    Topics: Biology , Mathematics
    Notes: Abstract As a “base line” of memorization performance, the behavior of a “perfect learner” is considered. He is characterized by a perfect memory and by the ability to choose the best search procedure in problems where the correct response from a given repertoire is to be found to each of several stimuli under the condition of “right” and “wroing” promptings by the experimenter. Expected learning curves are derived for the case of disjoint response repertoires associated with the stimuli under cyclic and random presentation of the stimuli and for the case of a single response repertoire (a one-to-one matching problem) under cyclic presentation.
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    A method for the computation of aortic distensibility in the living human patient and its use for the determination of the aortic effects of aging, drugs, and exercise (1961)
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    Bulletin of mathematical biology 23 (1961), S. 337-353 
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    Topics: Biology , Mathematics
    Notes: Abstract Detailed equations are given for the computation of aortic distensibility in the intact living human patient from measurements of systolic and diastolic arterial pressures, heart rate and cardiac output. From these equations, the aortic characteristics of a large series of normal men of different ages were computed. Comparing these results with measurements on excised aortas, a more pronounced trend toward increasing aortic stiffness with increasing age is evident in living than in dead aortas. Nor-epinephrine and exercise apparently cause the living aortas to constrict but to become more distensible. The same change occurs after 30 minutes of high spinal anesthesia. The ganglionic blocking agents hexamethonium, pentamethonium, and tetraethylammonium usually cause the living aorta to become stiffer, presumably due to dilatation. The aortas of patients with pulmonary disease usually react in different fashion to exercise or tetraethylammonium. The increased aortic distensibility that occurs with the hypertension induced by nor-epinephrine or exercise acts as a compensatory mechanism by decreasing systolic pressure.
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    Dimensional analysis in mathematical biology I. General discussion (1961)
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    Bulletin of mathematical biology 23 (1961), S. 355-376 
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    Topics: Biology , Mathematics
    Notes: Abstract Dimensional analysis is discussed from the viewpoint of its basic group properties and shown to be an algebraic Abelian group that is useful for analysis of physical measurements. The application of the method to various types of equations and the formulation of previously unclassified dimensions are discussed. Functional dimensional analysis is applied to the problems of cell size and biomass proliferation; future applications are also noted. A number of dimensionless terms have been formulated for cellular physiochemical phenomena. They apparently represent the first systematic study of biological dimensionless numbers recorded in the literature. A dimensionless proliferation law is suggested. A brief analysis of the physical dimensionality associated with information measures is carried out. Entropy and “information” are shown to be completely different in their dimensional meaning; other informational measures of possible interest in biology are proposed. The dimensional coding and computor analysis of biomathematical equations is suggested.
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    A minimal principle in biomechanics (1961)
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    Bulletin of mathematical biology 23 (1961), S. 377-391 
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    Topics: Biology , Mathematics
    Notes: Abstract Expenditure of energy under several simultaneous forms (mechanical, chemical, etc.) is associated with all muscular activity. The energy is directly related to what is commonly called exertion or effort. This paper defines “muscular effort” quantitatively in terms of some of the elements of the dynamics of the human (and animal) body. It postulates that in all likelihood the individual will, consciously or otherwise, determine his motion (or his posture, if at rest) in such a manner as to reduce his total muscular effort to a minimum consistent with imposed conditions, or “constraints”. The principle, formulated in mathematical terms, is sufficient to ascribe to the moments at all body joints—a matter generally of free choice on the part of the individual—their most likely magnitudes. It therefore renders the equations of human (and animal) motion determinate within this context. The paper also describes briefly an iteration method for the solution of these equations, once they have been made determinate. A simple illustrative application of the principle is included.
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    On the role of chemical systems in the microphysical aspects of primary genetic mechanisms (1961)
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    Bulletin of mathematical biology 23 (1961), S. 393-403 
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    Topics: Biology , Mathematics
    Notes: Abstract It is pointed out that two fundamentally different views of primary genetic processes occur in the literature which are frequently confused. The first is a true communication-theoretic view, which regards the genetic apparatus as containing a real information-source and a transducer which converts that information to useful form. The second view is generally expressed as a template scheme based on the Watson-Crick model; it is shown that in this model there is actually no such thing as genetic information in a communication-theoretic sense. Both views are then discussed on the basis of microphysical principles developed in previous work of the author (Bull. Math. Biophysics,22, 227–255, 1960) in an attempt to find which approach is in closer accord with the biological facts. It is shown that, if the communication-theoretic view is correct, then the information-bearing object must act as a “catalyst,” but it is pointed out that the type of catalysis involved must be of a fundamentally different nature than that occurring in familiar enzyme-catalyzed reactions. On the basis of general considerations of irreversible changes in microphysical measuring systems, it is shown that any type of template must suffer a gradual and irreversible denaturation, which seems to make it unlikely that a template could play a primary role in fundamental genetic processes.
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    On imitative behavior. II. Time course of change from one behavior to another (1961)
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    Bulletin of mathematical biology 23 (1961), S. 405-411 
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    Topics: Biology , Mathematics
    Notes: Abstract The theory developed in previous papers and based on distribution curves of definite form is generalized to any form of unimodel distributions. The time course of the change from one behavior to another is discussed and a general theorem about the time course is established.
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    Abstract mathematical molecular biology (1961)
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    Bulletin of mathematical biology 23 (1961), S. 417-417 
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    Training program in computer use for biomedical scientists (1963)
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    Bulletin of mathematical biology 25 (1963), S. 471-471 
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    Reflexes et centres analyseurs dans les microstructures isotropes (1963)
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    Bulletin of mathematical biology 25 (1963), S. 421-469 
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    Notes: Résumé Nous appliquons le modèle de neurone introduit dans un article antérieur à l’étude d’une microstructure isotrope. La stabilité de cette microstructure implique l’existence d’une régulation d’activité que le principe de construction adéquate permet de définir entièrement. Nous aboutissons à une conception stratifiée du cerveau. Un réseau de neurones spécialisés exercerait, grâce à certains médiateurs chimiques, une action diffuse qui modulerait les propriétés du réseau localisé classique. Les lois de Pavlov peuvent être retrouvées à partir des propriétés de la microstructure et de celles de la régulation. La microstructure isotrope peut également fonctionner comme analyseur. Un certain nombre de temps caractéristiques apparaissent alors, qui semblent jouer un grand rôle en psychologie.
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    Tissue blood flow and the sympathomimetic amines (1964)
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    Bulletin of mathematical biology 26 (1964), S. 1-7 
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    Notes: Abstract In the arteries, blood flow and blood pressure are pulsatile in nature (Roston, 1962a; Roston 1962b). The patterns of blood movement and mural distension in the arteries are important because they may be associated with life-threatening degenerative changes in the arterial walls. As the vascular channels narrow, the pulsation decreases. At the level of the capillaries, almost no pulsation exists (Best and Taylor, 1961). The tissues are affected by the direct flow in the capillaries and not by the pulsation in the arteries. Thus, such quantities as pulse pressure, systolic pressure, and diastolic pressure which characterize blood movement in the arteries are not important as far as the tissues are concerned. Rather, the average pressure and flow in the capillaries are the quantities significant for tissue blood flow. The present study analyzes the local blood circulation in a typical tissue. Logical extension of this analysis results in insights into the physiological behavior of the circulation which integrate a considerable body of experimental data.
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    A multidimensional birth process and its application to some problems in the dynamics of biological populations (1966)
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    Bulletin of mathematical biology 28 (1966), S. 333-345 
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    Notes: Abstract This paper is a sequel to a paper by the author entitled “Restricted Transition Probabilities and Their Applications to Some Problems in the Dynamics of Biological Populations” (Bull. Math. Biophysics, 1966,28, 315–331). The paper is divided into two parts. In part one some aspects of the maximum size attained by the population during a finite time interval are studied for the case the stochastic process underlying the evolution of the population is a birth process. Two interesting by-products emerge from the study presented in part one; namely a combinatorial method of finding solutions to the Kolmogorov differential equations in special cases, and secondly, a set of criteria for the optimum allocation of genotypes in the host population of a host-pathogen system. The optimum allocation of genotypes in the host population is a problem of practical importance in controlling plant pathogens. In part two the theory of restricted transition probabilities developed in the companion paper is applied in finding the distribution of the time to the appearance of the first mutation for the case of a two dimensional birth process. The distribution of the time to the appearance of the first mutation is of importance in understanding the role mutation plays in the evolution of a population, particularly in the pathogen population of a host-pathogen system.
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    The motion of the left ventricle. I (1966)
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    Bulletin of mathematical biology 28 (1966), S. 355-362 
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    Notes: Abstract The complex arrangement of the muscle fibers in the ventricular wall and the nonsymmetric contraction and expansion of the ventricle preclude the writing of a differential equation of motion for the ventricle as a whole. We can, however, describe the motion of the ventricle by describing the motion of the dimensional parameters length and diameter; the radius, circumference, cross-sectional area, and volume following naturally from these. The ventricle is assumed to be an ellipsoid of revolution and the dimensional parameters to be periodic functions of time. Each of the parameters is expressed as a Fourier series.
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    Comparaison des modeles de neurone de Hodgkin-Huxley et de Nelson (1966)
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    Bulletin of mathematical biology 28 (1966), S. 347-354 
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    Notes: Abstract Le modèle de Nelson peut-être considéré comme une approximation du modèle de Hodgkin-Huxley. Moins précis, il est plus maniable. Le modèle de Nelson peut également être considéré comme une généralisation du modèle de Hodgkin-Huxley. En effet, il introduit des liaisons synaptiques localisées ou diffusantes, et un processus de facilitation. Le mécanisme des liaisons synaptiques ne se traduit pas facilement dans le langage de Hodgkin-Huxley. Par contre, le processus de facilitation s'interprète facilement. Nelson's model can be taken as an approximation of Hodgkin-Huxley's model. Its precision is lesser, but it is more usable. Nelson's model can also be taken as a generalization of Hodgkin-Huxley's one; for it introduces localized or diffusing synaptic connexions and a facilitating process. The mechanism of synaptic connexions cannot be easily translated into Hodgkin-Huxley's language. On the contrary, the facilitating process is easily interpreted.
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    The theory of the left ventricular aneurysm (1966)
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    Bulletin of mathematical biology 28 (1966), S. 363-370 
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    Notes: Abstract A spherical model for the human left ventricle with two different types of aneurysms, circular and rectangular-square, is proposed and meaningful relations are derived between the parameters of the aneurysms and ventricle. Such ventricular parameters as stroke volume, end-diastolic volume, and end-systolic volume are given normal human values to compute values for end-systolic radius and percentage shortening of muscle for various sized circular and rectangular-square aneurysms.
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