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In computability theory, computational complexity theory and proof theory, a fast-growing hierarchy (also called an extended Grzegorczyk hierarchy, or a Schwichtenberg-Wainer hierarchy) [1] is an ordinal-indexed family of rapidly increasing functions f α: N → N (where N is the set of natural numbers {0, 1, ...}, and α ranges up to some large countable ordinal).
The number of cell pairs is proportional to the number of cells which is again proportional to the number of particles . The total cost of finding all pairwise distances within a given cut-off is in O ( N c ) ∈ O ( N ) {\displaystyle {\mathcal {O}}(Nc)\in {\mathcal {O}}(N)} , which is significantly better than computing the O ( N 2 ...
The number of viable cells in a preparation for a transformation reaction may range from 2×10 8 to 10 11; most common methods of E. coli preparation yield around 10 10 viable cells per reaction. The standard plasmids used for determination of transformation efficiency in Escherichia coli are pBR322 or other similarly sized or smaller vectors ...
If x ≠ 0, z = x(1 + ε(y/x)) is a polar decomposition of a dual number z = x + yε, where ε 2 = 0; i.e., ε is nilpotent. In this polar decomposition, the unit circle has been replaced by the line x = 1, the polar angle by the slope y/x, and the radius x is negative in the left half-plane.
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [4] [5] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [6] or they can be used to build a pointer based quadtree.
Jay-Z is accused in a lawsuit of raping a 13-year-old girl with fellow music mogul Sean “Diddy” Combs. The lawsuit was first filed in October but did not list Jay-Z, whose given name is Shawn ...
The extraneous intermediate list structure can be eliminated with the continuation-passing style technique, foldr f z xs == foldl (\ k x-> k. f x) id xs z; similarly, foldl f z xs == foldr (\ x k-> k. flip f x) id xs z ( flip is only needed in languages like Haskell with its flipped order of arguments to the combining function of foldl unlike e ...
This wet dog food is packed with fresh ingredients with real turkey being first in the list. No fillers or by-products here, only natural ingredients like pumpkin, brown rice, apples, peas and ...