With the reduction of the Marne salient we could look forward to the concentration of our divisions in our own zone.
"Kelly Miller's History of the World War for Human Rights" by Kelly Miller
With the reduction of the Marne salient, we could look forward to the concentration of our divisions in our own zone.
"Winning a Cause" by John Gilbert Thompson and Inez Bigwood
This sort of separation takes place at one of the two reduction divisions.
"A Critique of the Theory of Evolution" by Thomas Hunt Morgan
Quite naturally, he did not take kindly to the reduction of his corps from four to three divisions.
"The Story of the Great War, Volume VIII (of VIII)" by various
During the tetrad division in the basidium nuclear reduction occurs.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3" by Various
Reduction division, 41, 42.
"Being Well-Born" by Michael F. Guyer
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Consider a p-adic local ﬁeld F (i.e. a ﬁnite ﬁeld extension of Qp ) and the connected reductive groups G and G′ over F of multiplicative groups of the matrix algebra Matn (F ) and a central division algebra D over F of degree n.
Characteristic polynomials of central simple algebras
At the other end, when M is a linear structure, such as a reduct of an ordered vector space over an ordered division ring, then every deﬁnable set is semi-linear.
Definable groups as homomorphic images of semilinear and field-definable groups
Both reduction steps are similar in nature, although the second one is much more subtle; they consist of dividing D into three regions, of which only the middle one is affected by the coplactic operation, and showing that U and V have a similar division.
Some bijective correspondences involving domino tableaux
The reduction steps included bias subtraction and division by normalized twilight ﬂat- ﬁeld images.
Near-Infrared photometry of carbon stars in the Sagittarius dwarf irregular galaxy and DDO 210
Then C ′ also has good reduction, and so C ′ [p∞ ]0 /O → C [p∞ ]0 /O is an epimorphism of p-divisible groups over Spec O.
Elliptic Curves of Odd Modular Degree
A(Q) if A has good reduction at all primes above p. (Recall that the prime-to-p division hul l of Γ0 in A(Q) is the group of all x ∈ A(Q) such that there exists n ∈ Z \ pZ with nx ∈ Γ0 .) On the other hand, by Remark 2.13, if A is deﬁned over Q, then Γ is of inﬁnite rank.
Relations among modular points on elliptic curves
The maintainability of the simulator has increased caused by the division into components and the reduction in complexity, but mostly by the speciﬁcation of the architecture and system design.
Software (Re-)Engineering with PSF II: from architecture to implementation
According to, we say that the m-adic ﬁltration is essential ly divisible with respect to the minimal reduction xR if, whenever u ∈ v(xR), then there is an a ∈ xR with v(a) = u and ord(a) = vord(u).
Associated graded rings of one-dimensional analytically irreducible rings II
The m-adic ﬁltration is essential ly divisible if there exists a minimal reduction xR such that it is essentially divisible with respect to xR.
Associated graded rings of one-dimensional analytically irreducible rings II
So, if we choose for the maximal ideal of R a monomial minimal reduction, by Proposition 1.2 we have that the m-adic ﬁltration is essentially divisible with respect to such a reduction.
Associated graded rings of one-dimensional analytically irreducible rings II
By what we observed above, the m-adic ﬁltration is essentially divisible with respect to the minimal reduction t6R.
Associated graded rings of one-dimensional analytically irreducible rings II
According to, we say that the m-adic ﬁltration is essential ly divisible with respect to the minimal reduction xR if, whenever u ∈ v(xR), then there is an a ∈ xR with v(a) = u and ord(a) = vord(u).
Associated graded rings of one-dimensional analytically irreducible rings II
The m-adic ﬁltration is essential ly divisible if there exists a minimal reduction xR such that it is essentially divisible with respect to xR.
Associated graded rings of one-dimensional analytically irreducible rings II
So, if we choose for the maximal ideal of R a monomial minimal reduction, by Proposition 1.2 we have that the m-adic ﬁltration is essentially divisible with respect to such a reduction.
Associated graded rings of one-dimensional analytically irreducible rings II
By what we observed above, the m-adic ﬁltration is essentially divisible with respect to the minimal reduction t6R.
Associated graded rings of one-dimensional analytically irreducible rings II
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