Sentence examples for define a positive constant from inspiring English sources

We define a positive constant M ¯ as follows: M ¯ = max i ∈ N { sup s ∈ [ − τ i, 0 ] | Y i ( s ) | }.

Before the design procedure, we define a positive constant as follows: tau_{k}=big| h_{k}^big| ^{2},quad k=0,1,2, ldots,n.

To state our first result, we define a positive constant A p by A p : = C 1 p − 1 ( C 1 C 0 ) p − 1 ≥ 1, (2). which is equal to 1 in the case of A ( x, y ) = | y | p − 2 y (i.e., the case of the p-Laplacian) because we can choose C 0 = C 1 = p − 1.

We define a positive constant M as follows: M = max i j ∈ J { sup s ∈ ( − ∞, 0 ] Y i j ( s ) }. Let K be a positive number such that Y i j ( t ) ≤ M < M + 1 = K for all  t ∈ ( − ∞, 0 ], i j ∈ J. (3.11).

Define a positive constant by Gamma_{0}:=max_{tin I} int_{0}^{1} G t, s),ds=frac{beta delta +alpha delta +alpha gamma /2}{rho }. (2.8).

Throughout the present paper, M is defined as a positive constant.

where is a probability density function defined on (see [9, 10]) and induces an invertible operator defined on and there exists a positive constant and such that and.

where D is a positive constant defined in Lemma  2.2.

Let be nonnegative sequences defined on, and let be a positive constant.

end{aligned} By Lemma 3.4 there exist a point (omega_{k+1}inpartial H(z_{k+1},z_{k})) defined as in (15) and a positive constant (C_{2}>0) such that Vert omega_{k+1} Vert leq C_{2} bigl( Vert z_{k+1}-z_{k} Vert + Vert z_{k}-z_{k-1} Vert bigr).

For a positive constant M, define v_{M}(x)=minbigl{ u(x),Mbigr} and choose (v=v_{M}^{kp+1}) ((kge0)) as a test function in (2.1).