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  2. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗. Similarly, the function has a local minimum point at x ∗, if f(x ∗) ≤ f(x) for all x in X within distance ε of x ∗.

  3. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    In higher dimensions, a critical point of a scalar valued function is a point at which the gradient is zero. The second derivative test can still be used to analyse critical points by considering the eigenvalues of the Hessian matrix of second partial derivatives of the function at the critical point. If all of the eigenvalues are positive ...

  4. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates, their absolute difference. Thus if p {\displaystyle p} and q {\displaystyle q} are two points on the real line, then the distance between them is given by: [ 1 ]

  5. Tukey's range test - Wikipedia

    en.wikipedia.org/wiki/Tukey's_range_test

    Notice that the point estimator and the estimated variance are the same as those for a single pairwise comparison. The only difference between the confidence limits for simultaneous comparisons and those for a single comparison is the multiple of the estimated standard deviation.

  6. Similarity measure - Wikipedia

    en.wikipedia.org/wiki/Similarity_measure

    Similarity between two data points. Image shows the path of calculation when using the Euclidean distance formula. There are many various options available when it comes to finding similarity between two data points, some of which are a combination of other similarity methods.

  7. Duncan's new multiple range test - Wikipedia

    en.wikipedia.org/wiki/Duncan's_new_multiple_range...

    The new multiple range test proposed by Duncan makes use of special protection levels based upon degrees of freedom.Let , = be the protection level for testing the significance of a difference between two means; that is, the probability that a significant difference between two means will not be found if the population means are equal.

  8. Image subtraction - Wikipedia

    en.wikipedia.org/wiki/Image_subtraction

    This is commonly used in fields such as time-domain astronomy (known primarily as difference imaging) to find objects that fluctuate in brightness or move. In automated searches for asteroids or Kuiper belt objects , the target moves and will be in one place in one image, and in another place in a reference image made an hour or day later.

  9. Weierstrass function - Wikipedia

    en.wikipedia.org/wiki/Weierstrass_function

    Rather between any two points no matter how close, the function will not be monotone. The computation of the Hausdorff dimension D {\textstyle D} of the graph of the classical Weierstrass function was an open problem until 2018, while it was generally believed that D = 2 + log b ⁡ ( a ) < 2 {\textstyle D=2+\log _{b}(a)<2} .