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An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion ), the search path of a foraging animal, or the price of a fluctuating ...
A copyright page with the printer's key underlined. This version of the book is the eighteenth printing. The printer's key, also known as the number line, is a line of text printed on a book's copyright page (often the verso of the title page, especially in English-language publishing) used to indicate the print run of the
Rosetta Code is a wiki-based programming chrestomathy website with implementations of common algorithms and solutions to various programming problems in many different programming languages. [ 1 ] [ 2 ] It is named for the Rosetta Stone , which has the same text inscribed on it in three languages, and thus allowed Egyptian hieroglyphs to be ...
The jump on line 50 will always be taken if the jump on line 20 is taken. Therefore, for as long as line 100 is within the reachable range of the jump (or the size of the jump doesn't matter), the jump on line 20 may safely be modified to jump directly to line 100. Another example shows jump threading of 2 partial overlap conditions:
If q = 2, then (a-b) 2 = 2 and there is no integral solution a, b. When q > 2, the equation x 2 + y 2 − qxy − q = 0 defines a hyperbola H and (a,b) represents an integral lattice point on H. If (x,x) is an integral lattice point on H with x > 0, then (since q is integral) one can see that x = 1. This proposition's statement is then true for ...
Many algorithms explicitly fit 0-degree splines to the noisy signal in order to detect steps (including stepwise jump placement methods [2] [8]), but there are other popular algorithms that can also be seen to be spline fitting methods after some transformation, for example total variation denoising.
Core Python Programming is a textbook on the Python programming language, written by Wesley J. Chun. The first edition of the book was released on December 14, 2000. [1] The second edition was released several years later on September 18, 2006. [2] Core Python Programming is mainly targeted at higher education students and IT professionals. [3]
The jump can be iterated into transfinite ordinals: there are jump operators for sets of natural numbers when is an ordinal that has a code in Kleene's (regardless of code, the resulting jumps are the same by a theorem of Spector), [2] in particular the sets 0 (α) for α < ω 1 CK, where ω 1 CK is the Church–Kleene ordinal, are closely ...