Sentence examples for constant preserving from inspiring English sources

Constant preserving: mathfrak{E}[C]=C for (Cin R).

By the convexity (resp. concavity) and constant preserving condition, one can easily obtain Proposition 2.1, which shows that (S^{mathrm{cv}}) (resp. (S^{mathrm{conca}})) has minimal members (resp. maximal members).

Monotonicity: (mathbb{E}[X]geqmathbb{E}[Y]) if (Xgeq Y); Constant preserving: (mathbb{E}[C]=C) for (Cin R); Sub-additivity: (mathbb{E}[X+Y]leqmathbb {E}[X]+mathbb{E}[Y]); Positive homogeneity: (mathbb{E}[lambda X]=lambda mathbb {E}[X]) for (lambdageq0).

A nonlinear expectation ({mathcal{E}}[cdot]) can also be defined as a real functional (mathcal{E} :L^{1}(Omega,mathcal{F},P) longmapsto R) satisfying the following conditions: (A1) constant preserving: (mathcal{E}[c]=c), (forall c in R);   (A2) monotonicity: (mathcal{E} [X] geqmathcal{E} [Y]) if (X geq Y) P-a.s.s

Since (mathcal{E}_{0}) satisfies the constant preserving and convexity conditions, we have begin{aligned} {mathcal{E}_{0} ^{ast}}[X] = & lim_{ lambdarightarrow+infty} lambda{mathcal{E}_{0}}biggl[frac{X}{lambda}biggr] geq& lim_{ lambdarightarrow+infty} -lambda{mathcal{E}_{0}}biggl[ frac{-X}{lambda}biggr] geq& - mathcal{E}_{0} [-X] > & -infty.

monotonicity: (mathfrak{E}[mathfrak{X}]ge mathfrak{E}[ mathfrak{Y}]) if (mathfrak{X}le mathfrak{Y}); constant preserving: (mathfrak{E}[C]=C) for (Cin R); sub-additivity: (mathfrak{E}[mathfrak{X}+mathfrak{Y}]le mathfrak{E}[mathfrak{X}]+mathfrak{E}[mathfrak{Y}]); positive homogeneity: (mathfrak{E}[lambda mathfrak{X}]=lambda mathfrak{E}[mathfrak{X}]) for (lambda geq 0).

The net result is a substantial enhancement in the dielectric constant while preserving low dielectric loss and very high breakdown field.

Furthermore, if each fragment in Fset can only have a constant number of mismatches (one can enforce this in the definition of a fragment), a simple brute force search will compute the optimal split position for each pair in constant time, preserving the running time of O(K).

It is shown that only a constant control preserves the canonical contact form, hence a state feedback necessarily changes the closed-loop contact form.

It is assumed that the duration of slots for the BS RS links and for the RS UE links is constant to preserve interference stationarity between cell clusters.

The approach is not trivial due to the difficulties in preserving constant salts concentration in a solid state, while maintaining the conductive properties of the polymeric layer [ 12].