Sentence examples for by using the almost from inspiring English sources

The main purpose of this paper is, by establishing some dynamic inequalities on time scales, to discuss the permanence of system (1.3) and, by using the almost periodic functional hull theory on time scales, to establish criteria for the existence and uniqueness of globally attractive almost periodic solutions of system (1.3).

Assuming strong monotonicity, pseudo almost automorphy and other appropriate conditions of the operators (A t)) and Stepanov-like pseudo almost automorphy of the forced term (f(t)), we obtain the Stepanov-like pseudo almost automorphy of the solution to the evolution equation by using the almost automorphic component equation method.

For the preliminary work which has investigated the permanence, the existence and uniqueness of globally attractive almost periodic solutions to almost periodic systems governed by differential or difference equations by using the almost periodic functional hull theory, we refer the reader to [26 30].

Further, for realizing the almost passive Hamiltonian system, parallel compensation scheme is given by using the proposed almost passive condition.

The locally Lipschitz case is treated in the same manner as done in the proof of Theorem 2 (1) by stopping the process at time τ U, (2) by using the Lipschitz continuity of f and g in the ball of radius U and (3) by a truncation argument and using the almost sure boundedness of the solutions extending the convergence to the locally Lipschitz case.

(Mr. Bush also distinguished himself by using the word "not" almost 17 times per 1,000 words -- more than any previous president -- which Mr. Winter says is a measure of "activity inhibition," typically high in people who have given up alcohol or do not drink).

The aim of this paper is, by using the properties of almost periodic functions and constructing a suitable Lyapunov functional, to obtain sufficient conditions for the existence of a unique globally attractive positive almost periodic solution of system (1.1).

Based on the theory of calculus on time scales, by using the properties of almost periodic functions and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained.

(IV) By using the relations between asymptotically almost periodic function and the almost periodic functions.

Motivated by the existing nice studies and the above considerations, a main novelty of the present paper is that we develop a new class of almost periodic time scales called Hausdorff almost periodic time scales by using the Hausdorff distance and define almost periodic functions on these new time scales.

For isotropic plates, the frequency-response curves for large-amplitude vibrations obtained by using the three theories are almost coincident.