Sentence examples for decomposition left from inspiring English sources

According to Proposition 2 there exists the decomposition (left( z'+frac{displaystyle 1}{displaystyle x}z+2yzright) left( z=y'+frac{displaystyle 1}{displaystyle x}yright) =0) from which only the special solution (y=frac{displaystyle C}{displaystyle x}) follows.

On the one hand, according to Proposition 1, the counterparty risky contract ((A^{sharp },mathcal {X})) admits the following decomposition left(A^{sharp},mathcal{X} right)=(A,mathcal{X})+left(A^{text{CCR}},0right), (70).

Fire exposure results in gradually increasing damages within exposed laminates: PPS matrix thermal decomposition leaves intra- and inter-laminar voids leading to more or less extensive delamination depending on fire testing conditions.

Also the soil in RO and RT were tilled more than that used for soyabean during temporary bed preparation resulting in a relatively faster decomposition leaving significantly lower levels of C compared to RS. Change of cropping systems from RR to other annual crops such as RT and RO reduced the soil C sequestration to a significant level after 10 years of cultivation.

However, as demonstrated, this ideal picture is not always fulfilled, as TMA fully decomposes and forms an aluminate by losing all its methyl ligands upon deposition on a hydroxide-free Cu2O surface at 473 K. TMA decomposition leaves behind carbon atoms and clusters, and methyl groups attached to the copper surface.

decomposition ( g_{delta left( Bright) Z}left( lambda right) =g_{delta left( Bright) S}left( lambda right) +g_{delta left( Bright) N}left( lambda right) ), see Findley (2012).

We reexpress the MMSE decomposition (delta left( Bright) Z_{t}=delta left( Bright) hat{s}_{t}+delta left( Bright) hat{p}_{t}+delta left( Bright) hat{u}_{t}) (see Sect. 13.1) as begin{aligned} delta left( Bright) Z_{t}=delta _{n}left( Bright) delta _{s}left( Bright) hat{s}_{t}+delta _{s}left( Bright) delta _{n}left( Bright) hat{p}_{t}+delta left( Bright) hat{u}_{t}.

(In terms of modular decomposition used in [ 16] it means that a cograph can be decomposed by modular decomposition without leaving non-trivial non-decomposable prime module).

Dry reforming of methane (DRM) proceeds via CH4 decomposition to leave surface carbon species, followed by their removal with CO2-derived species.

The model focuses on reactors operated in "depletion" mode, a situation where the precursor species have undergone a sequence of gas-phase decomposition reactions leaving only the deposition species to diffuse to and react on the substrate surface, generating the thin film.

It yields the decomposition begin{aligned} left( z'-frac{displaystyle 1}{displaystyle y}z^2- y+x^2y-C zright) big (y'- x^2+1 y^2+Cy=0big y'- x^2+1 y^2+Cy=0big =0