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We analyze the response of the basin to an excess rain field (rain contributing to direct runoff), which is assumed to be variable in space and time; catchment response is supposed to be characterized by the time-invariant distribution of the travel time of water particles within the basin.
The theory is thermodynamics-like because it also invokes the time-invariant distribution of expression levels.
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In this formulation, the instantaneous sap velocity at any point in the radial profile of xylem tissue is defined as the product of a time-invariant sap velocity distribution and a time-varying term which is defined as a stem conductance.
The model is based on the stochastic convective reactive approach and assumes a time-invariant lognormal travel-time distribution of the stream tube ensemble connecting the river and a groundwater observation well.
Considering the time-invariant frequency component, concentrated distribution of the tremor source, and time-invariant amplitude ratios, the scaling bound on the amplitude of the tremor suggests a fixed-source geometry with variable forces that drive the tremor.
Table 2 presents the distribution of time-invariant covariates in the sample and as a function of children's poverty status at baseline.
It was shown that both the grain-size and grain-shape (side) distributions are time-invariant and the linear relationship between the mean radii of individual grains and topological classn was reproduced.
The coefficients in the linear combination depend on time whereas the component distributions are time-invariant.
Using fundamental geometric methods, we have proved the existence of a nonlinear scaling operator which relates constant mean curvature surfaces and time invariant pressure distribution graphs constrained by the Darcy Forchheimer law.
In this case, we can consider that various states of the promoter are at stochastic equilibrium (meaning they have reached a time invariant probability distribution).
This property is fundamental in signal processing, as convolution with a tempered distribution is a linear time-invariant system, and applying the linear time-invariant system measures its impulse response.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com