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  2. Scale analysis (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Scale_analysis_(mathematics)

    Scale analysis rules as follows: Rule1-First step in scale analysis is to define the domain of extent in which we apply scale analysis. Any scale analysis of a flow region that is not uniquely defined is not valid. Rule2-One equation constitutes an equivalence between the scales of two dominant terms appearing in the equation. For example,

  3. Nondimensionalization - Wikipedia

    en.wikipedia.org/wiki/Nondimensionalization

    Analysis of differential equation models in biology: a case study for clover meristem populations (Application of nondimensionalization to a problem in biology). Course notes for Mathematical Modelling and Industrial Mathematics Jonathan Evans, Department of Mathematical Sciences, University of Bath. (see Chapter 3).

  4. Scale analysis (statistics) - Wikipedia

    en.wikipedia.org/wiki/Scale_analysis_(statistics)

    The item-total correlation approach is a way of identifying a group of questions whose responses can be combined into a single measure or scale. This is a simple approach that works by ensuring that, when considered across a whole population, responses to the questions in the group tend to vary together and, in particular, that responses to no individual question are poorly related to an ...

  5. Dimensionless quantity - Wikipedia

    en.wikipedia.org/wiki/Dimensionless_quantity

    In mathematics, the "number of elements" in a set is termed cardinality. Countable nouns is a related linguistics concept. Counting numbers, such as number of bits, can be compounded with units of frequency (inverse second) to derive units of count rate, such as bits per second. Count data is a related concept in statistics.

  6. Scale (analytical tool) - Wikipedia

    en.wikipedia.org/wiki/Scale_(analytical_tool)

    The scale of analysis encompasses both the analytical choice of how to observe a given system or object of study, and the role of the observer in determining the identity of the system. [ 2 ] [ 3 ] This analytical tool is central to multi-scale analysis (see for example, MuSIASEM , land-use analysis).

  7. Nonparametric statistics - Wikipedia

    en.wikipedia.org/wiki/Nonparametric_statistics

    Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. [1]

  8. Multiple-scale analysis - Wikipedia

    en.wikipedia.org/wiki/Multiple-scale_analysis

    In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values of the independent variables. This is done by introducing fast-scale and slow-scale variables for ...

  9. Helmert transformation - Wikipedia

    en.wikipedia.org/wiki/Helmert_transformation

    μ – scale factor, which is unitless; if it is given in ppm, it must be divided by 1,000,000 and added to 1. R – rotation matrix. Consists of three axes (small [clarification needed] rotations around each of the three coordinate axes) r x, r y, r z. The rotation matrix is an orthogonal matrix. The angles are given in either degrees or radians.