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Page "Frobenius group" ¶ 19
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Any and irreducible
* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
Any polynomial may be decomposed into the product of a constant by a product of irreducible polynomials.
* Any number constructible out of the integers with roots, addition, and multiplication is therefore an algebraic integer ; but not all algebraic integers are so constructible: in a naïve sense, most roots of irreducible quintics are not.
Any β perpendicular to α ( on the Y axis ) trivially fulfills both with 0, but does not define an irreducible root system.
Any non-zero vector of an irreducible representation is cyclic.
Any complete group variety ( variety here meaning reduced and geometrically irreducible separated scheme of finite type over a field ) is automatically commutative, by an argument involving the action of conjugation on jet spaces of the identity.
Any Hausdorff ( T < sub > 2 </ sub >) space is sober ( the only irreducible subsets being points ), and all
Any finite-dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to Élie Cartan.
* Any submodule of a finitely generated module over a Noetherian ring is an intersection of a finite number of irreducible submodules.
Elliott Sober says that by intelligent design's own arguments, a designer capable of creating irreducible complexity must also be irreducibly complex: " Any mind in nature that designs and builds an irreducibly complex system is itself irreducibly complex " Sober says that this an argument that intelligent design proponents still need to respond to.
Any reduced scheme has a normalization, whose construction we first give for irreducible reduced schemes.

Any and representation
Any form of triangle that we experience will be an imperfect representation of the ideal triangle.
:" Any person who, on or in connection with any goods or services, or any container for goods, uses in commerce any word, term, name, symbol, or device, or any combination thereof, or any false designation of origin, false or misleading description of fact, or false or misleading representation of fact, which
" Any representation by us ", he advised, " will do her more harm than good.
Any process involving virtual particles admits a schematic representation known as a Feynman diagram, which facilitates the understanding of calculations.
Any issues such as, inadequate resolution, latency of the video image, lag in the mechanical and computer processing of the movement and response, and optical distortion due to camera lens and head mounted display lenses, can cause the user ' simulator sickness ' which is exacerbated by the lack of vestibular stimulation with visual representation of motion.
Any perspective representation of a scene that includes parallel lines has one or more vanishing points in a perspective drawing.
Any creature with a representation in its brain would need to interact with the objects that are represented to identify them with the representation.
Any severe disturbance of space representation, spontaneously appearing following bilateral parietal damage, strongly suggests the presence of Bálint's syndrome and should be investigated as such.
Any object can have an ambiguous representation and can be mistakenly categorized into the wrong groups without sufficient memory recognition of an object.
* Constraint 15: Any but the most primitive stability conditions must be susceptible to multidimensional representation, where spatial distance correlates with cognitive distance.
Any representation that a car marketer makes that is required by the AALA is exempt from the Commission ’ s policy.

Any and R
* Any commutative ring R is an algebra over itself, or any subring of R.
* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.
Any subset of R < sup > n </ sup > ( with its subspace topology ) that is homeomorphic to another open subset of R < sup > n </ sup > is itself open.
Brown continued releasing recordings: in 1993, he issued the album, Universal James, which included Brown's final Billboard charted single, " Can't Get Any Harder ", which peaked at # 76 on the US R & B chart and # 59 on the UK chart.
Any formal series with has a composition inverse provided is an invertible element of R. The coefficients are found recursively from the above formula for the coefficients of a composition, equating them with those of the composition identity X ( that is 1 at degree 1 and 0 at every degree greater than 1 ).
* Any positive multiple of the repunit R < sub > n </ sub >< sup >( b )</ sup > contains at least n nonzero digits in base b.
Any binary relation R on a set A can generate a natural partial order on the R-cycle equivalence classes of set A, so that xRy implies ≥.
* The Drug War in Mexico: By Any Other Name it's Terrorism, by Barnard R. Thompson ( MexiData. info )
Any totally ordered set that is not isomorphic to R but satisfies ( 1 ) – ( 4 ) is known as a Suslin line.
Any physical object whose radius R becomes less than or equal to the Schwarzschild radius will undergo gravitational collapse and become a black hole.
* Any ring R can be considered as a one-object preadditive category ; the category of left modules over R is the same as the additive functor category Add ( R, Ab ) ( where Ab denotes the category of abelian groups ), and the category of right R-modules is Add ( R < sup > op </ sup >, Ab ).
Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.
* Any two-sided ideal of a ring R is an R-bimodule.
* Any module over a commutative ring R is automatically a bimodule.
Any proposed inverse R of F ( reconstruction formula, in the lingo ) would have to map to some subset of.
* Any slave who evades capture for 20 days or more is to be publicly whipped for the first offense ; branded with the letter R on the right cheek for the second offense ; and lose one ear if absent for thirty days for the third offense ; and castrated for the fourth offense.
In early June, Banks released the second single off the album, " Any Girl " featuring R & B singer Lloyd.
O. A. R., who grew up in nearby Rockville, Maryland, recorded the live album Any Time Now at the 9: 30 Club on November 23 – 24, 2001.
Any non-singular matrix S of the same size is said to transform A into another symmetric matrix B = SAS < sup > T </ sup >, also of order n, where S < sup > T </ sup > is the transpose of S. If A is the coefficient matrix of some quadratic form of R < sup > n </ sup >, then B is the matrix for the same form after the change of coordinates defined by S.
Lloyd C. Gardner, " Pay Any Price: Lyndon Johnson and the Wars for Vietnam ", Chicago: Ivan R. Dee, 1995.

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