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A variable n is bound if it is in the scope of at least n binders (λ); otherwise it is free. The binding site for a variable n is the nth binder it is in the scope of, starting from the innermost binder. The most primitive operation on λ-terms is substitution: replacing free variables in a term with
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality.
When substituting for a data point, it is known as "unit imputation"; when substituting for a component of a data point, it is known as "item imputation". There are three main problems that missing data causes: missing data can introduce a substantial amount of bias , make the handling and analysis of the data more arduous , and create ...
Advice on the application of change of variable to PDEs is given by mathematician J. Michael Steele: [1] "There is nothing particularly difficult about changing variables and transforming one equation to another, but there is an element of tedium and complexity that slows us down.
A substitution σ is called a linear substitution if tσ is a linear term for some (and hence every) linear term t containing precisely the variables of σ ' s domain, i.e. with vars(t) = dom(σ). A substitution σ is called a flat substitution if xσ is a variable for every variable x. A substitution σ is called a renaming substitution if it ...
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