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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.
    Type of Medium: Electronic Resource
    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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    URL: http://dx.doi.org/10.1111/1467-9639.00043
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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)
    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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    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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    ISSN: 1467-9639
    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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    ISSN: 1467-9639
    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
    Teaching statistics 22 (2000), S. 0 
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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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    ISSN: 1467-9639
    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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    ISSN: 1467-9639
    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
    Teaching statistics 22 (2000), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    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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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    Blackwell Publishers (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 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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    ISSN: 1467-9639
    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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    ISSN: 1467-9639
    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
    Teaching statistics 22 (2000), S. 0 
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    ISSN: 1467-9639
    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
    Teaching statistics 22 (2000), S. 0 
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    ISSN: 1467-9639
    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
    Teaching statistics 22 (2000), S. 0 
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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
    Teaching statistics 22 (2000), S. 0 
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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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    ISSN: 1467-9639
    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)
    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
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    On Simulating Realizations of Correlated Random Variables (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: 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)
    Oxford, UK and Boston, USA : Blackwell Publishers Ltd
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    ISSN: 1467-9639
    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
    Teaching statistics 22 (2000), S. 0 
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    ISSN: 1467-9639
    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
    Teaching statistics 22 (2000), S. 0 
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    ISSN: 1467-9639
    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
    Teaching statistics 22 (2000), S. 0 
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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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    ISSN: 1467-9639
    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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    ISSN: 1467-9639
    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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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    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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    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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    Topics: Biology , Mathematics
    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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    ISSN: 1522-9602
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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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    A note on crime control (1966)
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    Bulletin of mathematical biology 28 (1966), S. 375-378 
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    Notes: Abstract The Volterra theory of two competing populations is extended to the contemporary social problem of crime control. Domains of stability for the time dependence of the numbers in the criminal and enforcement groups are exposed by a numerical example. Both augmentation and reduction of enforcement can produce a stable system. Average values of the ratio of members in each group show great sensitivity to the control policies adopted by the remaining sector of the total population.
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    Interactions in enzymatic reactions (1966)
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    Bulletin of mathematical biology 28 (1966), S. 379-390 
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    Notes: Abstract The paper deals with interactions of substances via an enzymatic reaction (Bull. Math. Biophysics,25, 141–154, 1963). The substances are the activators, inhibitors and/or substrates of the reaction. Due to the bimolecularity of the processes in the reaction, the quantitative relation between the steady state amount of complexes and the amounts of the substances assumes a typical form. In multiple enzymatic reactions this form is more complicated, though basically similar. Because the substances may influence the steady state amounts of the complexes in opposite directions, the compensation and blocking effects are the properties of enzymatic reactions. The substances with the same direction of influence may potentiate each other. In the enzymatic reaction here considered, the potentiation is always non-negative.
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    Decay of cell synchronization: Solutions of the cell-growth equation (1966)
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    Bulletin of mathematical biology 28 (1966), S. 391-409 
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    Topics: Biology , Mathematics
    Notes: Abstract Growth-rate functions in analytic form have been obtained for cell cultures in which the doubling times follow the Gaussian and Poisson distributions. The growth-rate functions are calculated by using Laplace transforms to solve an integral equation previously presented. Oscillatory solutions result if a substantial fraction of the cells in a culture are synchronized to divide at some particular time. The synchrony and, hence, the oscillatory character of the growth-rate function eventually disappear because of the non-zero variance of the doubling-time distribution. If their variances are sufficiently small, the Gaussian and Poisson doubling-time distributions lead to growth-rate functions that become identical in the limit of large time.
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    On the derivation of a mean growth equation for cell cultures (1966)
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    Bulletin of mathematical biology 28 (1966), S. 411-416 
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    Notes: Abstract IfN(t) is the expected number of cells in a culture at timet, $$\dot N(t)$$ the corresponding time derivative, andf(t−τ)dt the probability that a cell of aget−τ at timet will divide in the succeeding time intervaldt, then according to Hirsch and Engelberg (this issue) there obtains the integral equation $$\dot N(t) = 2\int_{ - \infty }^t {f(t - \tau )\dot N(\tau )d\tau }$$ for describing the dynamics of the cell population. It is the purpose of this note to give two alternative derivations of this equation, one based on the age density equation of Von Foerster, and the other based on a generalized form of the Harris-Bellman equation describing the first moment of an age dependent, branching process. In addition, a probability model is posed from which the Von Foerster equation and, hence, the Hirsch-Engelberg equation readily follows.
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    A mathematical theory of enamel solubility and the onset of dental caries: I. The kinetics of dissolution of powdered enamel in acid buffer (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 417-432 
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    ISSN: 1522-9602
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    Notes: Abstract A model of the dissolution kinetics of powdered enamel is developed based on the kinetic rate termq, $$q = K'H - k'C \cdot P_1$$ , whereH=[H +],C=[Ca ++] andP 1=[HPO 4 = ]. The differential equations describing the rate of mineral dissolution (and the linearly related rate of appearance of calcium and phosphate in solution) have been derived and solved for three basic cases: (1) when thepH of the solution and surface area of the enamel are considered constant, (2) when thepH is assumed constant, but the reduction in surface area during dissolution is considered, and (3) when the rise ofpH resulting from the buffering effect of the dissolved enamel is considered along with the change in surface area. Analytical solutions have been obtained for cases (1) and (2), while a numerical solution has been found for case (3). Data from a study on enamel dissolution are presented that agree with the theory of case (3), and it is noted that apH rise as large as 0.5 can occur, as has been shown elsewhere in the literature.
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    Reward and punishment in learning with possible reference to punishment for crime (1966)
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    Bulletin of mathematical biology 28 (1966), S. 477-481 
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    Notes: Abstract On the basis of Landahl's theory of two-choice learning it is shown that application of punishment for wrong responses, without giving award for correct ones, does not lead to complete learning, no matter how many trials are used. If initially a “wrong response” was learned, then an attempt to inhibit it by punishment alone will in a class of cases lead only to a 50% suppression of that wrong response. Possible connection with the problem of effectiveness of punishment as a deterrent for crime is mentioned.
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    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1966)
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    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    Cooperative specific adsorption of iona at charged sites in an electric field (1966)
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    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    Operations research around the world meetings (1966)
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    Bulletin of mathematical biology 28 (1966), S. 485-485 
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    Dimensional anlaysis and the equations of electrophoresis (1966)
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    Bulletin of mathematical biology 28 (1966), S. 501-510 
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    Notes: Abstract A set of characteristic parameters is given for electrophoresis accompanied by diffusion, followed by a method of simplification of the transport equation. The concept of electrophoretic similarity is introduced in connection with the presentation of solutions and the final section contains some dimensional considerations of the potential equation.
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    Categories of (ℓ, ℛ)-systems (1966)
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    Bulletin of mathematical biology 28 (1966), S. 511-517 
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    Notes: Abstract We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.
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    The origin of lift forces in fluttering flight (1966)
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    Bulletin of mathematical biology 28 (1966), S. 487-500 
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    Topics: Biology , Mathematics
    Notes: Abstract A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.
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    Evoked potentials arising from neural population elements excited at different times on a warped surface (1966)
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    Bulletin of mathematical biology 28 (1966), S. 519-536 
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    Notes: Abstract Certain types of cortical electrical events are non-propagated so that the associated electric fields must have standing wave characteristics. However, cortical electric events typically are generated by neurone populations which cannot be activated simultaneously on impulse driving. Hence the sum of the standing wave fields due to asynchronous activation of adjoining regions of cortical neurones must give the appearance of a traveling wave. Analysis of cortical waveforms is further complicated by curvature in cortical surfaces. A model is presented that shows the effects of curvature and time lag in activation on the form of the potential at points in space around a laminar array of elements simulating a population of cortical neurones. The results are compared with waveforms evoked by single-shock stimulation of the prepyriform cortex in cats.
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    A continuity equation for cell populations (1966)
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    Bulletin of mathematical biology 28 (1966), S. 545-554 
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    Notes: Abstract A continuity equation for cell-number density in a population of cells is derived, and a system of equations for eliminating parameters between the general solution and the initial distribution obtained.
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    The behavior of the weakening and failing myocardium (1966)
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    Bulletin of mathematical biology 28 (1966), S. 537-544 
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    Notes: Abstract Use of an electrical model of the left ventricle of the heart and the arterial system permits analysis of the changes which take place as the capacity of the myocardium for generation of force decreases. The model is simple in structure, and its construction and practical testing would not be difficult. It demonstrates that, as the heart muscle weakens, the peak of intracardiac force occurs later in systole, and the difference between the intracardiac pressure and the aortic pressure in the second half of systole is much greater than for the normal heart. The feedback mechanisms which are proposed to affect myocardial contractility would affect this compensation for cardiac weakening. Indices to categorize the behavior of the normal, compensated though weakened, and decompensated myocardium are proposed.
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    The frequency distribution of chromosome constituents in cells with chromosome-number dispersion (1966)
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    Bulletin of mathematical biology 28 (1966), S. 555-566 
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    Notes: Abstract The frequency distribution in a population of cells of the quantityCD (defined as the amount of some chromosomal substance in a cell which containsC chromosomes) is calculated using the distribution in the population of the amount per chromosome,D, and the distribution of chromosome number,C.
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    Calculation of rate of synthesis of chromosomal DNA in cells with chromosome-number dispersion (1966)
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    Bulletin of mathematical biology 28 (1966), S. 567-574 
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    Notes: Abstract The rate of chromosomal DNA synthesis in an exponentially growing population of cells having chromosome-number dispersion is calculated using DNA histogram data, chromosome-number distribution data, and the assumptions that the synthesis rate is constant and DNA double exactly.
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    Estimation of rate of synthesis of chromosomal DNA in ehrlich ascites tumor cells (1966)
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    Bulletin of mathematical biology 28 (1966), S. 575-584 
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    Notes: Abstract An estimate is made of the rate coefficient for linear DNA synthesis with exact doubling in an exponentially growing population of Ehrlich ascites tumor cells having chromosome-number dispersion. Comparison of calculated and experimental results suggest that the assumptions used in the calculation are tenable, but further experimental evidence is needed to prove this.
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