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However, the semantics of these languages are often given only informally or operationally, which makes their analysis and comparison difficult.
The chief advantage of recognising systems as partially coherent is that it makes their analysis more straightforward under conditions previously regarded as non-coherent.
Since many engineering systems are built modularly from interconnections of components, the resulting mathematical models can be arbitrarily complex, which makes their analysis equally challenging.
The complex matrix of these materials makes their analysis challenging for classical elemental analytical techniques with specific and complicated sample pretreatment procedures needed for reliable quantification.
Using the polynomial framework one can show that the class of nested canalyzing functions, or, equivalently, the class of unate cascade functions, forms an algebraic variety which makes their analysis amenable to the use of techniques from algebraic geometry and computational algebra.
The high dimension of the genotype data makes their analysis difficult and time-consuming.
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The answer I suspect is that which has vexed many non-politicians, namely how to make their analysis acceptable to politicians.
Second, they introduce a natural length scale, called the arm length, and use this to make their analysis of launch angle and velocity dimensionless.
The widespread deployment of computing devices that manage and control physical processes in safety critical environments, has made their analysis and verification a very important problem.
Metabolites are small molecules of diverse physico-chemical properties with greatly different abundance levels that make their analysis challenging.
However, the presence of numerous and sequentially diverse families of repetitive elements make their analysis a challenging task.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com