Search results
Results from the WOW.Com Content Network
In complex analysis, a branch of mathematics, an isolated singularity is one that has no other singularities close to it. In other words, a complex number z 0 is an isolated singularity of a function f if there exists an open disk D centered at z 0 such that f is holomorphic on D \ {z 0}, that is, on the set obtained from D by taking z 0 out.
The first complete root-isolation procedure results of Sturm's theorem (1829), which expresses the number of real roots in an interval in terms of the number of sign variations of the values of a sequence of polynomials, called Sturm's sequence, at the ends of the interval.
The goal of these steps is usually to isolate the variable one is interested in on one side, a process known as solving the equation for that variable. For example, the equation x − 7 = 4 {\displaystyle x-7=4} can be solved for x {\displaystyle x} by adding 7 to both sides, which isolates x {\displaystyle x} on the left side and results in ...
Vincent was the last author in the 19th century to use his theorem for the isolation of the real roots of a polynomial. The reason for that was the appearance of Sturm's theorem in 1827, which solved the real root isolation problem in polynomial time, by defining the precise number of real roots a polynomial has in a real open interval (a, b).
Holding all other things constant is directly analogous to using a partial derivative in calculus rather than a total derivative, and to running a regression containing multiple variables rather than just one in order to isolate the individual effect of one of the variables. Ceteris paribus is an extension of scientific modeling.
The book by Hemaspaandra and Ogihara has a chapter on the isolation technique, including generalizations. [6] The isolation lemma has been proposed as the basis of a scheme for digital watermarking. [7] There is ongoing work on derandomizing the isolation lemma in specific cases [8] and on using it for identity testing. [9]
If the space X is a metric space, for example a Euclidean space, then an element x of S is an isolated point of S if there exists an open ball around x that contains only finitely many elements of S. A point set that is made up only of isolated points is called a discrete set or discrete point set (see also discrete space).
Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph Fourier [ 1 ] who proposed the method in 1826 and Theodore Motzkin who re-discovered it in 1936.