Sentence examples for definite respect from inspiring English sources

In this way important consensuses were achieved based on a definite respect for the first principle of ecological security that was set up in the initial meeting of the SEA process.

Stein begins, then, by proposing that one define the relation of 'having become' or 'already definite' with respect to spacetime points.

That is, he proposes that given some choice of spacetime point x, there is at least one distinct point y that has not become, that is not already definite, with respect to x.

A two-place relation schematically written as Rxy will be intended to capture the idea that point y has already become or is definite with respect to point x.

Consider a Lyapunov candidate function defined in the set (bar{Omega}) as begin{aligned} W x) =& operatorname{KL}(Ka, Kx) =& sum_{i=1}^{I} (Kx)_{i} log frac{(Kx)_{i}}{(Ka)_{i}} + (Ka)_{i} - (Kx)_{i} =& sum_{i=1}^{I} int _{(Ka)_{i}}^{(Kx)_{i}} logfrac{y}{(Ka)_{i}}, dy, end{aligned} which is positive definite with respect to the point (a in{mathcal{A}}).

end{aligned} Obviously, F is the mapping derived by system (3), and ((0, 0)) is a fixed point of F. The linear function V(L,I =frac{ 1-m palpha}{ (1-p(1-km)+paL,I =frac{ 1-m palpha}ma) )}L+frac{1-p 1-km-gamma)}I on ([0, N^]times[0, N^]) is continuous and positive definite with respect to ((0, 0)).

Let there exist a neighborhood ({mathcal{O}}(o)), in which the function delta t, x) = 2x^{T} C f t, x) +sum _{k=1}^{n} h_{k}^{T} t, x) C_{d} h_{k} t, x) (11) is negative definite with respect to system (9).

From Eq. (70), it is obvious that (dot{V}_{g}) could be made negative definite with respect to the system errors (varvec{e} = left[ {begin{array}{*{20}c} {varvec{e}_{c}^{text{T}} } & {varvec{varepsilon}_{z}^{text{T}} } & {varvec{e}_{theta }^{text{T}} } end{array} } right]^{text{T}}) by augmenting sufficiently the parameters (c_{i},,,(i = 1,,2,,3)).

Namely, if there exists a neighborhood ({mathcal{O}}(o)), in which the function delta(x) = 2x^{T} C f(x) +h^{T}(x) C_{d} h(x) is positive definite with respect to system (3), then the trivial solution of (3) is unstable on the interval ([0, infty)).

Let there exist a neighborhood ({mathcal{O}}(o)), in which the function delta( x) = x^{T} A^{T} C x +x^{T} C A x + x^{T} H^{T} C_{d} H x (13) is negative definite with respect to system (12).

We also use the diagonal matrix (C_{d}) which has the same elements on the diagonal as C. Let there exist a neighborhood ({mathcal{O}}(o)), in which the function delta(x) = 2x^{T} C f(x) + h^{T}(x) C_{d} h(x) (6) is negative definite with respect to system (3).