By Zhifu Xie (auth.), Bourama Toni, Keith Williamson, Nasser Ghariban, Dawit Haile, Zhifu Xie (eds.)

This quantity includes the invited contributions from talks brought within the Fall 2011 sequence of the Seminar on Mathematical Sciences and purposes 2011 at Virginia country college. members to this quantity, who're top researchers of their fields, current their paintings in the way to generate actual interdisciplinary interplay. therefore all articles therein are selective, self-contained, and are pedagogically uncovered and support to foster pupil curiosity in technological know-how, expertise, engineering and arithmetic and to stimulate graduate and undergraduate study and collaboration among researchers in several areas.

This paintings is acceptable for either scholars and researchers in quite a few interdisciplinary fields specifically, arithmetic because it applies to engineering, physical-chemistry, nanotechnology, lifestyles sciences, laptop technology, finance, economics, and online game theory.

**Read or Download Bridging Mathematics, Statistics, Engineering and Technology: Contributions from the Fall 2011 Seminar on Mathematical Sciences and Applications PDF**

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**Example text**

T∈R 26 T. Diagana ⎛ Now ⎜ A(t) = ⎜ ⎝ 0 1 ⎞ ⎟ ⎟ ⎠ −a(t) −b(t) which yields Pt (λ ) = det(A(t) − λ IR2 ) = λ 2 + b(t)λ + a(t) for all t ∈ R. Let D(t) = b2 (t) − 4a(t) for all t ∈ R. 6) yields either D(t) > 0 or D(t) < 0 for all t ∈ R. 6) hold, then eigenvalues of A(t) are given by λ1 (t) = −b(t) + b2 (t) − 4a(t) −b(t) − and λ2 (t) = 2 b2 (t) − 4a(t) . 2 It is then easy to see that λ1 (t), λ2 (t) < 0 for all t ∈ R. 6) hold, then eigenvalues of A(t) are given by λ1 (t) = −b(t) + i 4a(t) − b2(t) −b(t) − i 4a(t) − b2(t) and λ2 (t) = .

Bezandry where Γ u(n) := n−1 n−1 r=0 s=r ∑ ∏ γs f (r, u(r)), is the representation of the solution of Eq. 4). It is clear that Γ is well defined. Now, let u, v ∈ AP(Z+ , L1 (Ω ; R+ )) having the same property as X defined in the Beverton–Holt equation. One can easily see that E |Γ u(n) − Γ v(n)| ≤ n−1 n−1 r=0 s=r ∑ ∏ E |γs | E | f (r, u(r)) − f (r, v(r))| , and hence letting β = sup E[γn ] we obtain n∈Z+ sup E |Γ u(n) − Γ v(n)| ≤ n∈Z+ μβ 1−β sup E |u(n) − v(n)|. n∈Z+ μβ < 1. 4). Obviously, Γ is a contraction whenever References 1.

The following definitions of doubly weighted pseudo-almost automorphy are due to Diagana [5, 6]. 4. Let μ ∈ U∞ and ν ∈ U∞ . A function f ∈ C(R, Rn ) is called doubly weighted pseudo-almost automorphic if it can be expressed as f = g + φ , where g ∈ AA(Rn ) and φ ∈ PAP0 (Rn , μ , ν ). The collection of such functions will be denoted by PAP(Rn , μ , ν ). 5. Let μ , ν ∈ U∞ . A function f ∈ C(R × Rm , Rn ) is called doubly weighted pseudo-almost automorphic if it can be expressed as F = G + Φ , where G ∈ AA(Rm , Rn ) and Φ ∈ PAP0 (Rm , Rn , μ , ν ).