Search results
Results From The WOW.Com Content Network
For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 .
Lis (Library of Iterative Solvers for linear systems; pronounced lis]) is a scalable parallel software library to solve discretized linear equations and eigenvalue problems that mainly arise from the numerical solution of partial differential equations using iterative methods. [1] [2] [3] Although it is designed for parallel computers, the ...
If a relation is transitive then its transitive extension is itself, that is, if R is a transitive relation then R 1 = R. The transitive extension of R 1 would be denoted by R 2, and continuing in this way, in general, the transitive extension of R i would be R i + 1. The transitive closure of R, denoted by R* or R ∞ is the set union of R, R ...
In mathematics, an inequation is a statement that an inequality holds between two values. [1] [2] It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific inequality relation. Some examples of inequations are: <
Each value of the unknown for which the equation holds is called a solution of the given equation; also stated as satisfying the equation. For example, the equation x 2 − 6 x + 5 = 0 {\displaystyle x^{2}-6x+5=0} has the values x = 1 {\displaystyle x=1} and x = 5 {\displaystyle x=5} as its only solutions.
For example, the natural numbers 2 and 6 have a common factor greater than 1, and 6 and 3 have a common factor greater than 1, but 2 and 3 do not have a common factor greater than 1. The empty relation R (defined so that aRb is never true) on a set X is vacuously symmetric and transitive; however, it is not reflexive (unless X itself is empty).
A correct evaluation order is a numbering : of the objects that form the nodes of the dependency graph so that the following equation holds: () < (,) with ,. This means, if the numbering orders two elements a {\displaystyle a} and b {\displaystyle b} so that a {\displaystyle a} will be evaluated before b {\displaystyle b} , then a ...
Furthermore, equality in the isoperimetric inequality implies both equality in the Wirtinger inequality and also the equality x′(t) + y(t) = 0, which amounts to y(t) = c 1 sin(t – α) and then x(t) = c 1 cos(t – α) + c 2 for arbitrary numbers c 1 and c 2. These equations mean that the image of (x, y) is a round circle in the plane.