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According to Ramsey, the antinomies of the first group (such as Russell's, or Burali-Forti's) can be avoided by referring to a universe of mathematical objects which is structured into types of individuals, functions of individuals, functions of functions of individuals, etc.
In interpreting this sentence we can take 'Mary' to be of type i, but we can also take it to be of type <>, that is, the type of a propositional function on propositional functions of individuals.
Two kinds of functions, then, can be of the second order: (1) functions of first-order functions of individuals, of r-type /1)/1, and (2) functions of r-type /2, such as our example xˆ has all the qualities that great generals have.
The molecular basis of gene regulation by dietary protein intake is an important field of research for studying regulation of physiological functions of individuals living under condition of restricted, imbalanced, or excessive food intake.
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We construct a Lyapunov function from the sum of nonlinearly-weighted Lyapunov functions of individual subsystems.
Nevertheless, we are only beginning to understand the functions of individual desmosomal proteins during development.
The identification of small molecules displaying different selectivity patterns against a protein target is a prerequisite to interfere with functions of individual members of protein families [1].
The availability of closed form expressions for the Green's functions (or, equivalently, transfer functions) of individual elements facilitates the analysis of these systems.
The special sauce of Workflow is that it enables users to dip into specific "deep linked" functions of individual apps and connect those actions together into a string of seamless, invisible commands.
Predictions were calculated from the concentration response functions of individual s-triazines by applying the concepts of concentration addition and independent action (response addition) alternatively.
Relating these population-level patterns to the computational functions of individual neurons is a major focus of current research in neurophysiology.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com