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6997 results in Mathematical modeling and methods

Page 20 of 350

  • AN OPTIMAL LINEAR FILTER FOR ESTIMATION OF RANDOM FUNCTIONS IN HILBERT SPACE

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  • PHIL HOWLETT, ANATOLI TOROKHTI
  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 3 / July 2020
    Published online by Cambridge University Press:
    07 January 2021, pp. 274-301
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  • Let $\boldsymbol{f}$ be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space H, and let $\boldsymbol{g}$ be an associated square-integrable, zero-mean, random vector with realizations which are not observable in a Hilbert space K. We seek an optimal filter in the form of a closed linear operator X acting on the observable realizations of a proximate vector $\boldsymbol{f}_{\epsilon } \approx \boldsymbol{f}$ that provides the best estimate $\widehat{\boldsymbol{g}}_{\epsilon} = X \boldsymbol{f}_{\epsilon}$ of the vector $\boldsymbol{g}$. We assume the required covariance operators are known. The results are illustrated with a typical example.

  • ANZ VOLUME 62 ISSUE 2 COVER AND FRONT MATTER

  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 2 / April 2020
    Published online by Cambridge University Press:
    22 December 2020, pp. f1-f2
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  • ANZ VOLUME 62 ISSUE 2 COVER AND BACK MATTER

  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 2 / April 2020
    Published online by Cambridge University Press:
    22 December 2020, pp. b1-b8
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  • MODELLING HUMAN CARRYING CAPACITY AS A FUNCTION OF FOOD AVAILABILITY

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  • DINY ZULKARNAEN, MARIANITO R. RODRIGO
  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 3 / July 2020
    Published online by Cambridge University Press:
    18 December 2020, pp. 318-333
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  • We assume that human carrying capacity is determined by food availability. We propose three classes of human population dynamical models of logistic type, where the carrying capacity is a function of the food production index. We also employ an integration-based parameter estimation technique to derive explicit formulas for the model parameters. Using actual population and food production index data, numerical simulations of our models suggest that an increase in food availability implies an increase in carrying capacity, but the carrying capacity is “self-limiting” and does not increase indefinitely.

Page 20 of 350