Sentence examples for beginning we give from inspiring English sources

At the very beginning, we give the following remark.

In the beginning, we give the following lemma which is cited from Lemma 3 in [37], and we shall need it in the proof of the energy norm estimate.

In this section, we present a convergence theorem of the implicit compensated Euler method (1.5) to the SDE with Poisson random measure (1.1) over a finite time interval [ 0, T ] under the Lipschitz conditions and the linear growth conditions, where T is a constant and Δ t = T / N, N ∈ N. At the beginning, we give four lemmas.

To begin, we give an overview of the variation-of-constants formula for linear equations of neutral type.

To begin with, we give an expression of (mathcal{A}).

To begin with, we give the definition of - -concave-convex operators.

To begin with, we give some basic definitions and notations which will be used in the sequel.

To begin with, we give the performance comparison for a variety of algorithms under different SNR conditions.

To begin with, we give some properties of a q-shifting operator ({_{a}Phi}_{q}(m) = qm + 1-q aa) that can be found in [9].

To begin with, we give two examples to illustrate the problem that may happen when conducting these optimizations under macro and small cell networks, in both the downlink and uplink respectively.

To begin with, we give a brief re-statement of the problem.