essentially unique वाक्य
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- They can all be represented in an essentially unique way as Seifert fiber spaces : the quotient manifold is a sphere and there are 3 exceptional fibers of orders 2, 3, and 3.
- They can all be represented in an essentially unique way as Seifert fiber spaces : the quotient manifold is a sphere and there are 3 exceptional fibers of orders 2, 3, and 4.
- They can all be represented in an essentially unique way as Seifert fiber spaces : the quotient manifold is a sphere and there are 3 exceptional fibers of orders 2, 3, and 5.
- One alternative proposal that has been developed is the theory of derivators that "-category is canonically triangulated, and moreover mapping cones become essentially unique ( in a precise homotopical sense ).
- A related notion is a universal property, where an object is not only essentially unique, but unique " up to a unique isomorphism " ( meaning that it has trivial automorphism group ).
- On the other hand, there is not an essentially unique group with exactly 4 elements, as there are two non-isomorphic examples : the cyclic group of order 4 and the Klein four group.
- The Caballo Mountains are essentially unique in New Mexico because their section of exposed rocks begins in Precambrian time, and runs through every geological period of the Phanerozoic eon with the exceptions of the Triassic and Jurassic.
- Every closed 3-manifold has a prime decomposition : this means it is the connected sum of prime 3-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).
- Every Boolean algebra " A " has an essentially unique completion, which is a complete Boolean algebra containing " A " such that every element is the supremum of some subset of " A ".
- If the space " X " has a universal cover then that universal cover is essentially unique : if the mappings and are two universal covers of the space " X " then there exists a homeomorphism such that.
- A complete flag on an inner product space has an essentially unique orthonormal basis : it is unique up to multiplying each vector by a unit ( scalar of unit length, like 1,-1, " i " ).
- This folk-revival environment helped the more educated members of the community to obtain an awareness of the value of musical tradition and authenticity, and therefore to resist the growing trend of fashionable Gypsy Music ( a music based on the commercial myth of an essentially unique Gypsy Music spanning from India to Spain ).
- By spectral theory, there is an essentially unique measure ? on the locally compact space " X " and a unitary transformation " U " between " H " 0 and " L " 2 ( " X ", ? ) which carries the operators in \ mathfrak { A } onto the corresponding multiplication operators.
- If an unbiased estimator of g ( \ theta ) exists, then one can prove there is an essentially unique MVUE . Using the Rao Blackwell theorem one can also prove that determining the MVUE is simply a matter of finding a sufficient statistic for the family p _ \ theta, \ theta \ in \ Omega and conditioning " any " unbiased estimator on it.
- Pioneering electronic music experimenters like Leon Theremin, Louis and Bebe Barron, Christopher R . Morgan, and Raymond Scott had built sound-generating devices and systems of varying complexity, and several large electronic synthesizers ( e . g . the RCA Mark II Sound Synthesizer ) had been built before the advent of the Moog, but these were essentially unique, custom-built devices or systems.
- I'm not a master of wiki policy ( or of wine ), but it seems to me that the claims they're marshalling to discount pieces of coverage are extrinsic to notability-- and very intrinsic to the wine enthusiast world . ( The gravity press system that makes them essentially unique in VA, they say, is just a revival of older Greco-Roman techniques.
- In the finite-length situation, decomposition into indecomposables is particularly useful, because of the Krull-Schmidt theorem : every finite-length module can be written as a direct sum of finitely many indecomposable modules, and this decomposition is essentially unique ( meaning that if you have a different decomposition into indecomposable, then the summands of the first decomposition can be paired off with the summands of the second decomposition so that the members of each pair are isomorphic ).
- Maximal compact subgroups of connected Lie groups are usually " not " unique, but they are unique up to conjugation, meaning that given two maximal compact subgroups " K " and " L ", there is an element " g " " " G " such that " gKg " " 1 = " L " hence a maximal compact subgroup is essentially unique, and people often speak of " the " maximal compact subgroup.
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