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This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.
The unit of angular frequency is the radian per second (rad/s) but, for discrete-time signals, can also be expressed as radians per sampling interval, which is a dimensionless quantity. Angular frequency is frequency multiplied by 2 π.
Dimensionless quantities, or quantities of dimension one, [1] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [ 2 ] [ 3 ] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units .
A frequency distribution shows a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc.
For Brownian walk, Sharpe ratio / is a dimensional quantity and has units /, because the excess return and the volatility are proportional to / and / correspondingly. Kelly criterion is a dimensionless quantity , and, indeed, Kelly fraction μ / σ 2 {\displaystyle \mu /\sigma ^{2}} is the numerical fraction of wealth suggested for the investment.
A quantity of dimension one is historically known as a dimensionless quantity (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is . Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension.
Since the radian is a dimensionless unit in the SI, the radian per second is dimensionally equivalent to the hertz—both can be expressed as reciprocal seconds, s −1. So, context is necessary to specify which kind of quantity is being expressed, angular frequency or ordinary frequency.
Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables.This technique can simplify and parameterize problems where measured units are involved.