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In this approach, the MC is used to transform the first order partial differential equations model of such processes into a set of time-delayed ordinary differential equations whose elements are used to generate certain matrices that satisfy linear matrix inequalities that render the proportional integral (PI) control parameters that guarantee the process stability.
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For realistic modeling of such processes these uncertainties have to be considered.
Mathematical modeling of such processes is essential to understand the entire mechanism.
The mathematical models of such processes are called differential systems with impulse effect.
The modeling of such processes requires comprehensive reaction schemes along with kinetic parameters to describe each of these mechanisms.
The modelling of such processes was firstly developed assuming perfect mixing for the whole system as a black box.
As detailed models of such processes turn out to be very complicated, POD is an attractive way to obtain reduced models of low order.
The modelling of such processes is complicate because the mechanisms leading from primary defects (the ones directly created by the process) to secondary ones (arising from the interactions between primary defects themselves and between primary defects and other impurities present in the material) depend, in an unpredictable way, on the microscopic structure of each particular material.
Therefore, modelling of such processes is a real problem which attracts special attention to the research of possible stable configurations and shapes of nanocrystals [30 36].
Therefore mathematical models of such processes include an additional parameter which is called the control or disturbance vector depending on the character of the exterior influences.
The mechanisms underlying the fates of HSCs are still largely unknown, although several descriptive models of such processes have been established.
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