* Unclosed loose string subgroup: Here the pieces of string are not closed, and are not attached to the wire.

His life was shown in the Philippine TV news show Case Unclosed as its 13th episode.

More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language ( the sensitivity of complexity relative to the choice of description language is discussed below ).

It is not hard to see that the minimal description of a string cannot be too much larger than the string itself-the program GenerateFixedString above that outputs s is a fixed amount larger than s.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

* Conical pendulum, a weight ( or bob ) fixed on the end of a string ( or rod ) suspended from a pivot

In some applications, such as substring search, one must compute a hash function h for every k-character substring of a given n-character string t ; where k is a fixed integer, and n is k. The straightforward solution, which is to extract every such substring s of t and compute h ( s ) separately, requires a number of operations proportional to k · n.

The disadvantage is that this design limits the pitch of the instrument because string lengths are more fixed and lighter strings are needed to lift it much more than a tone.

Two pendula with the same period fixed on a string act as pair of coupled oscillators.

A pulse ( physics ) | pulse traveling through a string with fixed endpoints as modeled by the wave equation.

searches for any of a list of fixed strings using the Aho – Corasick string matching algorithm.

The following observations all apply to a string that is infinitely flexible strung between two fixed supports.

Normally, a string of characters such as the words " hello there " is represented using a fixed number of bits per character, as in the ASCII code.

A fixed cutter bit is one where there are no moving parts, but drilling occurs due to percussion or rotation of the drill string.

In computer science, a Procrustean string is a fixed length string into which strings of varying lengths are placed.

Chordophones – sound is primarily produced by the vibration of a string or strings that are stretched between fixed points.

It does not make calculating the displayed width of a string easier except in limited cases, since even with a “ fixed width ” font there may be more than one code point per character position ( combining marks ) or more than one character position per code point ( for example CJK ideographs ).

For many years now Shubb has had available a fifth-string capo, consisting of a narrow metal strip fixed to the side of the neck of the instrument, with a sliding stopper for the string.

* one piece of string, ribbon or similar, which may form a closed loop or which may have other pieces like balls fixed to its end.

( The BBC documentary Dambusters Declassified ( 2010 ) stated that the pronged device was not used due to issues related to vibration and that other methods were employed, including a length of string tied in a loop and pulled back centrally to a fixed point in the manner of a catapult.

There have been two approaches to finding solutions: First, numerically, one can truncate the string field to include only fields with mass less than a fixed bound, a procedure known as " level truncation ".

In any magnetic pickup, a vibrating guitar string, magnetized by a fixed magnet within the pickup induces an alternating voltage across its coil ( s ).

Gene flow will effectively cease when the distinctive mutations characterizing each subgroup become fixed.

In another direction, every normal subgroup of a finite p-group intersects the center nontrivially as may be proved by considering the elements of N which are fixed when G acts on N by conjugation.

Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.

Generally in each subgroup a fixed relation holds between period and absolute magnitude, as well as a relation between period and mean density of the star.

For such a subgroup G, define Fix ( G ) to be the field consisting of all elements of L that are held fixed by all elements of G. Then the maps E Gal ( L / E ) and G Fix ( G ) form an antitone Galois connection.

O ( n, R ) is a subgroup of the Euclidean group E ( n ), the group of isometries of R < sup > n </ sup >; it contains those that leave the origin fixed – O ( n, R ) = E ( n ) ∩ GL ( n, R ).

SO ( n, R ) is a subgroup of E < sup >+</ sup >( n ), which consists of direct isometries, i. e., isometries preserving orientation ; it contains those that leave the origin fixed – SO ( n, R )

We write M < sup > G </ sup > for the subgroup of M consisting of all elements of M that are held fixed by G. This is a left-exact functor, and its right derived functors are the group cohomology functors, typically written as H < sup > i </ sup >( G, M ).

Membership to any given subgroup is also not defined by fixed rules.

In mathematics, a Tarski monster group, named for Alfred Tarski, is an infinite group G, such that every proper subgroup H of G, other than the identity subgroup, is a cyclic group of order a fixed prime number p. A Tarski monster group is necessarily simple.

* The subgroup of elements fixed by is ; in particular, is a closed subgroup.

J < SUB > 1 </ SUB > The subgroup fixed by an outer involution.

In general, it is quite complicated to determine the set of good bases for a fixed subgroup U. To overcome this difficulty, one determines the set of all good bases of all finite

If H is a closed subgroup of G, the pair ( G, H ) is said to have relative property ( T ) of Margulis if there exists an ε > 0 and a compact subset K of G such that whenever a unitary representation of G has an ( ε, K )- invariant unit vector, then it has a non-zero vector fixed by H.

such that G < sub > 0 </ sub > is the fixed point subgroup of W under the action of G, i. e.

More generally, in Lie theory a symmetric space is a homogeneous space G / H for a Lie group G such that the stabilizer H of a point is an open subgroup of the fixed point set of an involution of G. This definition includes ( globally ) Riemannian symmetric spaces and pseudo-Riemannian symmetric spaces as special cases.

Then a symmetric space for G is a homogeneous space G / H where the stabilizer H of a typical point is an open subgroup of the fixed point set of an involution σ of G. Thus σ is an automorphism of G with σ < sup > 2 </ sup > = id < sub > G </ sub > and H is an open subgroup of the set

is an involutive Lie group automorphism such that the isotropy group K is contained between the fixed point group of σ and its identity component ( hence an open subgroup ).

* For any subgroup H of Gal ( E / F ), the corresponding field, usually denoted E < sup > H </ sup >, is the set of those elements of E which are fixed by every automorphism in H.

It is a subgroup of the orthogonal group O ( 3 ), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices.