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[2006.14701] Efficient triangulations and boundary slopes
For a compact, irreducible, ∂ -irreducible, an-annular bounded 3-manifold M ≠ B3, then any triangulation T of M can be modified to an ideal triangulation T∗ of M∘. …
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Efficient triangulations and boundary slopes
For a compact, orientable, irreducible, ∂-irreducible, and an-annular 3-manifold, it is shown there are only finitely many boundary slopes for incompressible and …
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[PDF] Irreducible Complexity Revisited | Semantic Scholar
This essay wants to revisit Behe's concept of irreducible complexity and indicate why the problem he has raised is, if anything, still more vexing for Darwinism than when he first raised it. Michael Behe's concept of irreducible complexity, and in particular his use of this concept to critique Darwinism, continues to come under heavy fire from the biological …
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Do Not Crush List
Oral Medications That Should Not Be Crushed - January 2024 Update. Although crushing pills can make taking pills easier, and may even be necessary for some (e.g., those with a feeding tube), it is important to be mindful of which solid oral medications should not be crushed before consumption as it may alter their intended effects due to …
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1.3: Irreducible Representations and Character Tables
No headers. Similarity transformations yield irreducible representations, Γ i, which lead to the useful tool in group theory – the character table.The general strategy for determining Γ i is as follows: A, B and C are matrix representations of symmetry operations of an arbitrary basis set (i.e., elements on which symmetry operations are performed). ). There is some …
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Irreducible Matrix -- from Wolfram MathWorld
A square matrix which is not reducible is said to be irreducible. TOPICS Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
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Efficient triangulations and boundary slopes
1. Introduction. In [8] it is shown that for M ≠ B 3, a compact, orientable, irreducible, ∂–irreducible, and an-annular 3-manifold with non-empty boundary, any triangulation T of M can be modified by crushing along a closed normal surface (possibly not connected) in T to an ideal triangulation T ⁎ of the interior of M, M ∘.The ideal …
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Irreducible Definition & Meaning
The meaning of IRREDUCIBLE is impossible to transform into or restore to a desired or simpler condition; specifically : incapable of being factored into polynomials of lower degree with coefficients in some given field (such as the rational numbers) or integral domain (such as the integers). How to use irreducible in a sentence.
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arXiv:2006.14701v1 [math.GT] 25 Jun 2020
1. Introduction In [6] it is shown that for M 6= B3, a compact, irreducible, ∂–irreducible, and an-annular 3-manifold with non-empty boundary, any triangulation T of M can be …
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Irreducible Element -- from Wolfram MathWorld
An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an element a is irreducible if the only possible decompositions of a into the product of two factors are of the form a=u^(-1)·ua, where u^(-1) is the multiplicative inverse of u. The …
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commutative algebra
In any commutative ring with unity, prime ideals are proper (by definition), irreducible, and radical. As noted in comments and answers above, the converse is true: proper, irreducible, and radical ideals are prime.
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Investigation of Pore Characteristics and Irreducible Water …
An irreducible water saturation model was established based on fractal theory and the capillary bundle model. The factors affecting the irreducible water saturation were fractal dimension, maximum connected pore throat radius, minimum pore throat radius, and thickness of the water film. The calculation results are closer to the …
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A New Approach to Crushing 3-Manifold Triangulations
Conversely, it is shown that for a compact, irreducible, boundary-irreducible, and an-annular 3-manifold, any triangulation can be modified to an annular …
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What is the meaning of an "irreducible representation"?
$begingroup$ You can't mean both. A "representation" of a group is a special kind of homomorphism whose domain is the group. A "representative" of a group would be an element of the group (under some kind of equivalence relation). There is a very standard, clear, definition of "irreducible representation" for any group, and I don't …
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Irreducible
Something irreducible is as simple, basic, or straightforward as it possibly can be.
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Irreducible Polynomial -- from Wolfram MathWorld
Irreducible Polynomial -- from Wolfram MathWorld
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Irreducible Fear of the Sublime | Occulta Veritas
Irreducible Fear of the Sublime by Occulta Veritas, released 19 July 2024 1. The Mirror Stage 2. The Sacred Horizons of Totality 3. Metonimia 4. S(Ⱥ) 5. Bound to Incompleteness 6. Irreducible Fear of the Sublime _____ Released via I, Voidhanger Records, this album is my personal attempt to find beauty in the bleakness of the …
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Irreducible Complexity
Irreducible Complexity. Irreducible complexity is a term coined by Michael Behe, who defines it as follows. Irreducible complexity is just a fancy phrase I use to mean a single system which is composed of several interacting parts, and where the removal of any one of the parts causes the system to cease functioning.
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A New Approach to Crushing 3-Manifold Triangulations
a new treatment that reduces the crushing process to a sequential combination of three "atomic" operations on a cell decomposition, all of which are simple to analyse. As an …
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Irreducible polynomials
Thus f(x) is irreducible. Note that we can apply Eisenstein to the polynomial x2 2 with the prime p= 2 to conclude that x2 2 is irreducible over Q. Here is a more interesting example: Example 17.10. Let f(x) = 2x7 415x6 + 60x5 18x 9x3 + 45x2 3x+ 6: Then f(x) is irreducible over Q. We apply Eisenstein with p= 3.
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In Defense of Evolution | NOVA | PBS
Irreducible complexity is a term that was first used on behalf of the intelligent-design movement by Michael Behe, a biochemist at Lehigh University. What Behe observed is that living cells are ...
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IRREDUCIBLE definition and meaning | Collins English …
3 meanings: 1. not able to be reduced or lessened 2. not able to be brought to a simpler or reduced form 3. mathematics a. (of.... Click for more definitions.
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The Evolutionary Origins of Irreducible Complexity
The Intelligent Design argument from Irreducible Complexity (IC) Since this post, and those that will follow it, depend on an accurate representation of the argument for irreducible complexity (IC), I will take some time to clarify exactly how Michael Behe, the biochemist and Intelligent Design (ID) proponent who has most extensively developed …
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A NEW APPROACH TO CRUSHING
In detail: the crushing procedure eliminates unwanted normal spheres and discs from a triangulation by cutting the manifold open along them, collapsing the result- ing spheres …
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algebraic topology
Definition 1: We say M M is irreducible if given any smoothly embedded submanifold S S of M M with S ≅S2 S ≅ S 2, there exists a smoothly embedded …
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Efficient triangulations and boundary slopes
Suppose M ≠ B 3 is a compact, orientable, irreducible, ∂-irreducible, and an-annular 3–manifold with nonempty boundary. Then there is an algorithm that will …
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Breaking down irreducible complexity
There has been more than a little science tearing down Irreducible Complexity. Every example in Michael Behe's book "Darwin's Black Box" has been pretty well settled, although not to his satisfaction. During the Dover Trial he [Behe] faced over 50 scientific publications that dealt with his examples and proved that they are not ...
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What is an irreducible matrix?
So, a matrix is called irreducible if it is not permutation-similar to any block-triangular matrix. Share. Cite. Follow edited Apr 5, 2019 at 23:28. answered Apr 5, 2019 at 23:23. user1551 user1551. 142k 10 10 gold badges 129 129 …
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0-EFFICIENT TRIANGULATIONS OF 3-MANIFOLDS
a 0-efficient triangulation is irreducible, not RP3 and the triangulation has precisely one-vertex or the manifold is S 3 and the triangulation has precisely two vertices.
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How do you see a Markov chain is irreducible?
Some of the existing answers seem to be incorrect to me. As cited in Stochastic Processes by J. Medhi (page 79, edition 4), a Markov chain is irreducible if it does not contain any proper 'closed' subset other than the state space.. So if in your transition probability matrix, there is a subset of states such that you cannot 'reach' (or access) any other states …
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Irreducible Complexity
Criticism. The concept of irreducible complexity has been widely debated and criticized by the scientific community. Critics argue that Behe's definition is flawed because it assumes that all components of a system must have originated for the specific purpose of that system, disregarding the possibility that components could have been co-opted from …
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Irreducible elements in the ring of formal power series
$begingroup$ @hiren_garai: Yes; fixed. The point is you were doing the "is irreducible" wrong. Every element can always be written as a product with one factor a unit. The key to an irreducible element is that that's the only way they can be written as a product. $endgroup$ – Arturo Magidin
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Irreducible Ring -- from Wolfram MathWorld
A ring in which the zero ideal is an irreducible ideal. Every integral domain R is irreducible since if I and J are two nonzero ideals of R, and a in I, b in J are nonzero elements, then ab is a nonzero element of I intersection J, …
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Efficient triangulations and boundary slopes
For a compact, orientable, irreducible, ∂-irreducible, and an-annular 3-manifold, it is shown there are only finitely many boundary slopes for incompressible and ∂-incompressible surfaces of a bounded Euler characteristic.We use normal surface theory and the inverse relationship of crushing a triangulation along a normal surface [8] and …
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abstract algebra
$begingroup$ Incidentally, if a polynomial is irreducible in the algebraic closure of every prime field, then it is irreducible. (This is only interesting when one has a polynomial of multiple variables :)). This can be proved via an application of model theory: note that the statement "a given polynomial over $mathbb{Z}$ is irreducible in some …
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