Sentence examples for a time scale where from inspiring English sources

where is a time scale,, where is right dense and is left dense.

We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations on a time scale, where,.

The study of fractional -calculus in [1] serves as a bridge between the fractional -calculus in the literature and the fractional -calculus on a time scale, where, and.

We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations on a time scale, where is a quotient of odd positive integers with, and real-valued positive rd-continuous functions defined on.

We consider the pair of second-order dynamic equations, (r(t)(xΔ) γ )Δ + p(t)x γ (t) = 0 and (r(t)(xΔ) γ )Δ + p(t)x γσ (t) = 0, on a time scale, where γ > 0 is a quotient of odd positive integers.

This paper is concerned with oscillations of the second-order delay nonlinear dynamic equation ( a ( t ) ( x Δ ( t ) ) α ) Δ + q ( t ) x β ( τ ( t ) ) = 0 on a time scale, where a and q are real-valued rd-continuous positive functions on, α and β are ratios of odd positive integers, τ : T → T, τ ( t ) ≤ t, ∀ t ∈ T, and lim t → ∞ τ ( t ) = ∞.

Now we consider the second-order delay nonlinear dynamic equation ( a ( t ) ( x Δ ( t ) ) α ) Δ + q ( t ) x β ( τ ( t ) ) = 0 (1.1). on an arbitrary time scale, where a and q are real-valued rd-continuous positive functions defined on ; α and β > 0 are ratios of odd positive integers; τ : T → T, τ ( t ) ≤ t, ∀ t ∈ T and lim t → ∞ τ ( t ) = ∞.

In this article, we want to become familiar with some of the dynamic equations that arise in context of solving the Schrödinger equation on a suitable time scale where the expression time scale is in the context of this article related to the spatial variables.

Throughout this paper we have presented time on a screening time scale, where 1 is the first year of the screening programme.

We also accept that we are combing results of tests over a wide time scale, where the accuracy of the technique may have improved.

This means that the hazard process is defined on the time since some starting point, e.g. the beginning of some disease, in contrast to a gap time scale where the hazard process restarts after each event.