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Limited Evidence for Depth Specialism in Isolated Seamount Reef Predators. [PDF]

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Cresswell BJ   +7 more
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Asymptotic Behaviour of Nonoscillatory Equations

Canadian Journal of Mathematics, 1983
For nonlinear equations of the formIthere has been considerable interest in determining the asymptotic forms of nonoscillatory solutions. We assume r(t) is continuous and positive on [0, ∞), and f(t, x) is continuous on [0, ∞) × R, and f(t, x) ≥ 0 for x ≠ 0. For n = 2, equation (I) was studied by Kusano and Naito [3], who found necessary and sufficient
Edelson, Allan L., Perri, Emilia
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ASYMPTOTIC BEHAVIOUR OF VISCOELASTIC WAVES

The Quarterly Journal of Mechanics and Applied Mathematics, 1988
In one-dimensional pulse propagation in a linearly viscoelastic material, at sufficiently large distances from the source the pulse may approach a constant shape. For all viscoelastic materials for which this occurs, we determine the asymptotic shape of the signal and its speed. The signal width is determined implicitly.
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Stability and Asymptotic Behaviour

2014
The focus of this chapter is threefold in theme. Firstly, the topic of stability of equilibria will be investigated in the context of an autonomous differential equation \( \dot{x} = f\left( x \right) \) with an equilibrium at 0 (i.e. f(0) = 0). Loosely speaking, this topic addresses the following question: in forwards time, do solutions which start ...
Hartmut Logemann, Eugene P. Ryan
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ASYMPTOTIC BEHAVIOUR OF DISCRETE LINEAR PROCESSES

Journal of Time Series Analysis, 1985
Abstract. We consider the linear process Yn(ω) =ΣAk(ω) ·Xn‐k (ω) on a probability space (Ω, P) and ask for sufficient conditions in order to get a limit theorem for (Yk) if the corresponding limit theorem for (Xk) is true.
Stadtmüller, U., Trautner, R.
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Asymptotic behaviour of the partition function

Sbornik: Mathematics, 2000
For given integers \(m\) and \(d, 2\leq m\leq d\), the author studies the ``partition function \(b_{m,d}\) of order \(d\) with base \(m\)'', \[ b_{m,d}(n) := \#\Bigl\{ (a_0, a_1, \dots); \quad n = \sum_k a_k\cdot m^k, \text{ where } a_k\in \{0,1,\dots,d-1\},\;k\geq 0 \Bigr\}, \] and the partition function of order \(\infty\), \[ b_{m,\infty}(n) = \lim_{
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Asymptotic behaviour in convection–diffusion processes

Nonlinear Analysis: Theory, Methods & Applications, 1999
The Cauchy problem for the equation \[ u_t=(u^m)_{xx}+(u^n)_x \] is studied for \(m>1\) and \(n\geq m+1\). It is shown that for \(n> m+1\) the solution behaves (as \(t\to\infty\)) like the Barenblatt solution of the porous medium equation having the same mass. If \(n=m+1\) then the behavior is asymptotically selfsimilar.
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Asymptotic behaviour of neural networks

AIP Conference Proceedings, 1998
A new method is presented for analysing the global stability properties of neural networks. An efficient and numerically robust procedure is developed for estimating regions of asymptotic stability. The method combines Liapunov theory, simulation in reverse time and some topological properties of the true stability region.
M. Loccufier, E. Noldus
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