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Evolutionary Convergence To Ideal Free Dispersal Strategies And Coexistence, Richard Gejji, Yuan Lou, Daniel Munther, Justin Peyton
Evolutionary Convergence To Ideal Free Dispersal Strategies And Coexistence, Richard Gejji, Yuan Lou, Daniel Munther, Justin Peyton
Mathematics and Statistics Faculty Publications
We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy …
Residues And Tame Symbols On Toroidal Varieties, Ivan Soprunov
Residues And Tame Symbols On Toroidal Varieties, Ivan Soprunov
Mathematics and Statistics Faculty Publications
We introduce a new approach to the study of a system of algebraic equations in (C) whose Newton polytopes have sufficiently general relative positions. Our method is based on the theory of Parshin’s residues and tame symbols on toroidal varieties. It provides a uniform algebraic explanation of the recent result of Khovanskii on the product of the roots of such systems and the Gel’fond–Khovanskii result on the sum of the values of a Laurent polynomial over the roots of such systems, and extends them to the case of an algebraically closed field of arbitrary characteristic.
Approximation For The Expectation Of A Function Of The Sample Mean, Rasul A. Khan
Approximation For The Expectation Of A Function Of The Sample Mean, Rasul A. Khan
Mathematics and Statistics Faculty Publications
Let X¯ n be the mean of a random sample of size n from a distribution with mean μ and variance σ2. Under some conditions it is shown that Ef(X¯ n ) = f(μ) + (σ2/2n) f″(μ) + O(n −2), and var(f(X¯ n )) = (σ2/n) (f′(μ))2 + O(n −2), where f is a continuous function with a suitable growth condition. This complements a result of Lehmann [(1991). Theory of Point Estimation. Wadsworth, California] and Cramér [(1946). Mathematical Methods of Statistics. Princeton University Press, Princeton, N.J.] for wider application. An illustrative example is given to show an application where the …
Asymptotic And Numerical Solutions For Diffusion Models For Compounded Risk Reserves With Dividend Payments, Sally S. L. Shao, C. L. Chang
Asymptotic And Numerical Solutions For Diffusion Models For Compounded Risk Reserves With Dividend Payments, Sally S. L. Shao, C. L. Chang
Mathematics and Statistics Faculty Publications
We study a family of diffusion models for compounded risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models in which the dividend payments are paid from the risk reserves. After defining the process of conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient of the convection term. Based on the behavior of the total income flow, asymptotic and numerical methods are used to solve the …