The simplest version of the test statistic from this

The simplest version of mechanical cocking device is a hook attached to a belt, drawing the bow by straightening the legs.

This theorem by Henkin is the most directly obtained version of the completeness theorem in its simplest proof.

The simplest version of the paradox is the sentence:

The simplest technique is to lock down the camera and shoot the scene twice, with one " version " of the actor appearing on the left side, and the other on the right side.

One of the stranger ports is also one of the simplest: an instant messenger bot is wrapped around a version of Frotz with the bare minimum of IO functionality creating a bot with which one can play most Z-machine games using an instant messenger client.

The simplest version, stripped of the vivid, and probably misleading, detail added by later chroniclers, has " King Hungus " and his army win a victory aided by Saint Andrew, in gratitude for which the Picts agree to venerate the Saint.

In the simplest version of the Bohr model, the mass of the atomic nucleus is considered to be infinite compared to the mass of the electron, so that the center of mass of the system lies at the barycenter of the nucleus.

The simplest version of the algorithm uses the union-find data structure, which unlike other lowest common ancestor data structures can take more than constant time per operation when the number of pairs of nodes is similar in magnitude to the number of nodes.

Perhaps the simplest version is that any set can be a universe, so long as the object of study is confined to that particular set.

The simplest and most common version of subjective idealism combines subjunctive phenomenalism, the view that statements about physical objects can be translated into subjunctive conditionals about perceptions, with belief in immaterial minds.

The simplest version are two-sided bags, either joined round the edges or foldes and joined along two sides.

The simplest workaround is to load MusicMatch 7. 5 as the DLL files in the older version are compatible with all versions of Windows 7.

The simplest type of cone CVT, the single-cone version, uses a wheel that moves along the slope of the cone, creating the variation between the narrow and wide diameters of the cone.

The simplest product viewers usually require at least 3 versions of an image: a 100x100 thumbnail, a 400x300 medium ' in-page, selected ', and a 1200x900 ' zoomed ' version.

The simplest and probably most common situation of backporting is a fixed security-hole in a newer version of a piece of software.

The simplest version involves having three balls, with two going up simultaneously on either side, followed by one going up in the middle.

The simplest algorithm to find an EMST in two dimensions, given n points, is to actually construct the complete graph on n vertices, which has n ( n-1 )/ 2 edges, compute each edge weight by finding the distance between each pair of points, and then run a standard minimum spanning tree algorithm ( such as the version of Prim's algorithm or Kruskal's algorithm ) on it.

Here we present the simplest version of a divide-and-conquer algorithm, similar to the one originally proposed by Cuppen in 1981.

The algorithm presented here is the simplest version.

In the simplest version of the powerset construction, the set of all states of the DFA is the powerset of, the set of all possible subsets of.

Its simplest combinatorial version is due to Zuk: let be a discrete group generated by a finite subset S, closed under taking inverses and not containing the identity, and define a finite graph with vertices S and an edge between g and h whenever g < sup >− 1 </ sup > h lies in S. If this graph is connected and the smallest non-zero eigenvalue of its Laplacian is greater than ½, then has property ( T ).

The simplest version, type 1, extends the Standard Model by assuming two or more additional right-handed neutrino fields, and the existence of a very large mass scale.

The simplest version of a mirror coating is a single layer of a deposited thin film of a suitable metal, usually prepared by ion beam deposition, sputter deposition or vapor deposition.

Brownian motion is among the simplest of the continuous-time stochastic ( or probabilistic ) processes, and it is a limit of both simpler and more complicated stochastic processes ( see random walk and Donsker's theorem ).

Newman's proof is arguably the simplest known proof of the theorem, although it is non-elementary in the sense that it uses Cauchy's integral theorem from complex analysis.

Because polynomials are among the simplest functions, and because computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation.

In its simplest form, Bell's theorem states:

In this article we consider mainly the simplest kind of spectral theorem, that for a self-adjoint operator on a Hilbert space.

The Cayley – Hamilton theorem always provides a relationship between the powers of A ( though not always the simplest one ), which allows one to simplify expressions involving such powers, and evaluate them without having to compute the power A < sup > n </ sup > or any higher powers of A.

The simplest proofs use just those notions needed to formulate the theorem ( matrices, polynomials with numeric entries, determinants ), but involve technical computations that render somewhat mysterious the fact that they lead precisely to the correct conclusion.

The computation of the homology groups of the product of two spaces involves the tensor product ; but only in the simplest cases, such as a torus, is it directly calculated in that fashion ( see Künneth theorem ).

In mathematics, the rank – nullity theorem of linear algebra, in its simplest form, states that the rank and the nullity of a matrix add up to the number of columns of the matrix.

In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be ( by a slight deformation ) approximated by ones that are piecewise of the simplest kind.

The simplest case is when the coefficient ring for homology is a field F. In this situation, the Künneth theorem ( for singular homology ) states that for any integer k,

A fairly simple proof of the lemma, reminiscent of one of the simplest proofs of Fermat's little theorem, can be obtained by evaluating the product

The assumptions of the simplest version of the theorem are that a group wishes to reach a decision by majority vote.

Thus, although the current standard model of particle physics " in principle " predicts all known non-gravitational phenomena, in practice only a few quantitative results have been derived from the full theory ( e. g., the masses of some of the simplest hadrons ), and these results ( especially the particle masses which are most relevant for low-energy physics ) are less accurate than existing experimental measurements.

As interpreted in contemporary scientific practice, " entities should not be multiplied beyond necessity " advises opting for the simplest theory among a set of competing theories that have a comparable explanatory power, discarding assumptions that do not improve the explanation.

Once these basic steps have been mastered, students begin to practice the simplest temae, typically beginning with O-bon temae ( see above ).

The simplest telephoto designs could consist of one element in each group, but in practice, more than one element is used in each group to correct for various aberrations.

Libation was a central and vital aspect of ancient Greek religion, and one of the simplest and most common forms of religious practice.

As valuable as the annual reports of such organizations as Human Rights Watch or Amnesty International may be, they remain abstract compilations of horrors, not muddy-boot accounts from Third World villages and streets where people chance their lives to practice the simplest of freedoms.