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Laravel 3 was released in February 2012 with a set of new features including the cmd command-line interface (CLI) named Artisan, built-in support for more database management systems, database migrations as a form of version control for database layouts, support for handling events, and a packaging system called Bundles. An increase of Laravel ...
Not only are uninitialized variables a frequent cause of bugs, but this kind of bug is particularly serious because it may not be reproducible: for instance, a variable may remain uninitialized only in some branch of the program. In some cases, programs with uninitialized variables may even pass software tests.
Slack variables give an embedding of a polytope into the standard f-orthant, where is the number of constraints (facets of the polytope). This map is one-to-one (slack variables are uniquely determined) but not onto (not all combinations can be realized), and is expressed in terms of the constraints (linear functionals, covectors).
The meaning of binding operators is supplied by the semantics of the language and does not concern us here. Variable binding relates three things: a variable v, a location a for that variable in an expression and a non-leaf node n of the form Q(v, P). Note: we define a location in an expression as a leaf node in the syntax tree.
Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial:
To recover the underlying parameter , we introduce a set of variables Z that is highly correlated with each endogenous component of X but (in our underlying model) is not correlated with e. For simplicity, one might consider X to be a T × 2 matrix composed of a column of constants and one endogenous variable, and Z to be a T × 2 consisting of ...
The variables corresponding to the columns of the identity matrix are called basic variables while the remaining variables are called nonbasic or free variables. If the values of the nonbasic variables are set to 0, then the values of the basic variables are easily obtained as entries in b {\displaystyle \mathbf {b} } and this solution is a ...
Local variables may have a lexical or dynamic scope, though lexical (static) scoping is far more common.In lexical scoping (or lexical scope; also called static scoping or static scope), if a variable name's scope is a certain block, then its scope is the program text of the block definition: within that block's text, the variable name exists, and is bound to the variable's value, but outside ...