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The cavity method is an alternative method, often of simpler use than the replica method, for studying disordered mean-field problems. It has been devised to deal with models on locally tree-like graphs. Another alternative method is the supersymmetric method. The use of the supersymmetry method provides a mathematical rigorous alternative to ...
Finite volume method (numerical analysis) Highest averages method (voting systems) Method of exhaustion; Method of infinite descent (number theory) Information bottleneck method; Inverse chain rule method ; Inverse transform sampling method (probability) Iterative method (numerical analysis) Jacobi method (linear algebra) Largest remainder ...
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
In mathematics, Descartes' rule of signs, described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients. The number of positive real roots is at most the number of sign changes in the sequence of the polynomial's coefficients (omitting zero coefficients), and the difference ...
In the following, denotes the number of people in the initial circle, and denotes the count for each step, that is, people are skipped and the -th is executed. The people in the circle are numbered from 1 {\displaystyle 1} to n {\displaystyle n} , the starting position being 1 {\displaystyle 1} and the counting being inclusive .
[1] The stalagmometric method (Ancient Greek: στάλαγμα, romanized: stálagma, lit. 'drop') is one of the most common methods for measuring surface tension . The principle is to measure the weight of drops of a fluid of interest falling from a capillary glass tube , and thereby calculate the surface tension of the fluid.
Similar to the examples described above, we consider x, y, φ to be independent uniform random variables over the ranges 0 ≤ x ≤ a, 0 ≤ y ≤ b, − π / 2 ≤ φ ≤ π / 2 . To solve such a problem, we first compute the probability that the needle crosses no lines, and then we take its complement.
Replace some a i by a variable x in the formulas, and obtain an equation for which a i is a solution. Using Vieta's formulas, show that this implies the existence of a smaller solution, hence a contradiction. Example. Problem #6 at IMO 1988: Let a and b be positive integers such that ab + 1 divides a 2 + b 2. Prove that a 2 + b 2 / ab + 1 ...