Dini Derivatives Clause Samples

Dini Derivatives. Consider the nonautonomous system y˙ = f (t, y), (2.1) where D ⊂ Rm is a domain and f : R × D → Rm. Let V (t, y) : R × D → R be a continuous function satisfying a local Lipschitz condition for y, uniformly with respect to t. Then we define D+V (t, y) = lim sup V (t + τ, y + τ f (t, y)) − V (t, y) . τ→0+ τ The function D+V is called the upper Dini derivative of V along the trajectory of (2.1). Suppose that for an initial condition y(0) = y0, (2.1) has a solution y(t) defined on an interval [0, η) and let D+V (t, y(t)) be the upper Dini derivative of V (t, y(t)) with respect to t, i.e., D+V (t, y(t)) = lim sup V (t + τ, y(t + τ)) − V (t, y(t)) . τ→0+ τ Let t∗ ∈ [0, η) and put y(t∗) = y∗. Then one has that (see [33]) D+V (t∗, y(t∗)) = D+V (t∗, y∗).
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Dini Derivatives. Consider the nonautonomous system
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Related to Dini Derivatives

  • Derivatives Where a term is defined herein, a capitalized derivative of such term shall have a corresponding meaning unless the context otherwise requires.

  • UNMODIFIED DERIVATIVES Substances created by the RECIPIENT which constitute an unmodified functional subunit or product expressed by the ORIGINAL MATERIAL. Some examples include: subclones of unmodified cell lines, purified or fractionated subsets of the ORIGINAL MATERIAL, proteins expressed by DNA/RNA supplied by the PROVIDER, or monoclonal antibodies secreted by a hybridoma cell line.

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