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Mission Command, for example, is a command philosophy to which many modern military establishments aspire, and which involves individual judgment and action within the overall framework of the commander's intent. Its assumptions about the value of individual initiative make it more a Theory-Y than a Theory X philosophy. [14]
The degree of dependence between variables X and Y does not depend on the scale on which the variables are expressed. That is, if we are analyzing the relationship between X and Y, most correlation measures are unaffected by transforming X to a + bX and Y to c + dY, where a, b, c, and d are constants (b and d being positive).
For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x 2 + y 2 = 4; the area, the perimeter and the tangent line at any point can be computed from this equation by using integrals and derivatives, in a way that can be applied to any curve.
for all x, y ∈ X, if x ≠ y then xRy or yRx. For example, on the natural numbers, < is connected, while "is a divisor of " is not (e.g. neither 5R7 nor 7R5). Strongly connected for all x, y ∈ X, xRy or yRx. For example, on the natural numbers, ≤ is strongly connected, but < is not. A relation is strongly connected if, and only if, it is ...
The variable y is directly proportional to the variable x with proportionality constant ~0.6. The variable y is inversely proportional to the variable x with proportionality constant 1. In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.
For example, the equations = = form a parametric representation of the unit circle, where t is the parameter: A point (x, y) is on the unit circle if and only if there is a value of t such that these two equations generate that point.
Geometric interpretation of the covariance example. Each cuboid is the axis-aligned bounding box of its point (x, y, f (x, y)), and the X and Y means (magenta point). The covariance is the sum of the volumes of the cuboids in the 1st and 3rd quadrants (red) and in the 2nd and 4th (blue).
If the element y in Y is assigned to x in X by the function f, one says that f maps x to y, and this is commonly written = (). In this notation, x is the argument or variable of the function. A specific element x of X is a value of the variable , and the corresponding element of Y is the value of the function at x , or the image of x under the ...