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On the other hand, in the expressions evaluated by #expr and #ifexpr, Boolean operators like and, or, and not interpret the numerical value 0 as false and any other number as true. In terms of output, Boolean operations return 1 for a true value and 0 for false (and these are treated as ordinary numbers by the numerical operators).
Database systems usually implicitly create an index on a set of columns declared PRIMARY KEY, and some are capable of using an already-existing index to police this constraint. Many database systems require that both referencing and referenced sets of columns in a FOREIGN KEY constraint are indexed, thus improving performance of inserts ...
In object-oriented computer programming, a null object is an object with no referenced value or with defined neutral (null) behavior.The null object design pattern, which describes the uses of such objects and their behavior (or lack thereof), was first published as "Void Value" [1] and later in the Pattern Languages of Program Design book series as "Null Object".
The indexing expression for a 1-based index would then be ′ +. Hence, the efficiency benefit at run time of zero-based indexing is not inherent, but is an artifact of the decision to represent an array with the address of its first element rather than the address of the fictitious zeroth element.
Consequently, while these databases excel at basic CRUD operations and key-based lookups, their suitability for complex queries involving joins or non-indexed filtering varies depending on the database type—document, key–value, wide-column, or graph—and the specific implementation. [35]
A bar chart can show the comparison of the actual versus the reference amount. [54] Frequency distribution: Shows the number of observations of a particular variable for a given interval, such as the number of years in which the stock market return is between intervals such as 0–10%, 11–20%, etc.
The best measure is the standard deviation of the difference between the portfolio and index returns. Many portfolios are managed to a benchmark, typically an index. Some portfolios, notably index funds , are expected to replicate, before trading and other costs, the returns of an index exactly, while others ' actively manage ' the portfolio by ...
The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns; see the second example below. The information ratio is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns.