Philips Entertainment Lighting has introduced the successor to the CD-R Lamps for Optical Purposes.
The new CD-R , Philips Optical Lamps – Entertainment Lighting is not only an update but also contains improvements for the user.
CD&R to Become Majority Owner of Wilsonart International.
Debevoise, Latham Advise as CD&R Exchanges Vows with David's Bridal.
The CDR-882 uses high-quality IDE CD-R drives mounted in a steel 2U rack-mounting chassis to ensure reliable, glitch-free recording, even in unfavorable environments such as live concerts.
The CDR-882 is compatible with all types of CD-R media, both low- and high-speed (up to 52x).
American Handgunne r 2010 CD-Rom Digital Edition.
Handy digital-image burner for working with multiple memory card formats, or when a computer with a CD-R drive is not available.
These concepts immediately come to mind when listening to Grouper 's new double-album, Violet Replacement, available as a limited edition CD-R package and as digital downloads.
Jesse Krakow Minor Music Theme Song none none CD-R 2012.
Jesse Krakow Minor Music Theme Song none None CD-R 2012.
Jesse Krakow Minor Music Theme Song CD-R 2012.
Jesse Krakow Minor Music Theme Song CD-R Theme Song 2012.
I purchased an inexpensive CD-R/RW drive and installed it.
How CD- ROMs Are Made CD- ROMs are made by "burning" a blank CD-R disc and sending it to a media manufacturer, which creates a master disc that is used to stamp out the required quantity.
***
This is equivalent to the condition that for any RG-module N we have Exti RG (M , N ) = 0 for i ≥ n + 1. A group G has cohomological dimension cd(G) ≤ n over R if the trivial RG-module R has cohomological dimension ≤ n.
Survey on Classifying Spaces for Families of Subgroups
From the choice of x follows that dim R/(a′ + b′) = d − 1, dim R/a′ = dim R/a − 1 > d − 1 and dim R/b′ = dim R/b − 1 > d − 1; hence by induction we have s := cd(R, a′ ∩ b′ ) ≥ n − d.
Groebner deformations, connectedness and cohomological dimension
Then cd(R, a ∩ b) ≥ min{c(R), sdim R − 1} − dim R/(a + b) Proof.
Groebner deformations, connectedness and cohomological dimension
So cd(R/℘, ((a ∩ b) + ℘)/℘) ≥ c(R) − d, and using the Independence Theorem ([3, Theorem 4.2.1]) cd(R, a ∩ b) ≥ cd(R/℘, ((a ∩ b) + ℘)/℘) ≥ c(R) − d.
Groebner deformations, connectedness and cohomological dimension
Then d ≥ dim R/℘i − cd(R/℘i , ((a + ℘i ) ∩ (b + ℘i ))/℘i ) − 1.
Groebner deformations, connectedness and cohomological dimension
But cd(R/℘i , ((a + ℘i ) ∩ (b + ℘i ))/℘i ) = cd(R/℘i , ((a ∩ b) + ℘i )/℘i ) ≤ cd(R, a ∩ b), and obviously dim R/℘i ≥ sdim R, hence d ≥ sdim R − 1 − cd(R, a ∩ b).
Groebner deformations, connectedness and cohomological dimension
Proposition 1.5 implies c = dim R/(J + K) ≥ min{c(R), sdim R − 1} − cd(R, J ∩ K) and since √a = J ∩ K the theorem is proved.
Groebner deformations, connectedness and cohomological dimension
In particular, if cd(R, a) ≤ d − 2 the punctured spectrum Spec(R/a) \ {m} of R/a is connected.
Groebner deformations, connectedness and cohomological dimension
That is, if R is a complete equidimensional ring of dimension d and if c(R/b) ≥ d − cd(R, b) − 1 holds for all ideals b ⊆ R, then taking b = 0 it follows that R is connected in codimension 1.
Groebner deformations, connectedness and cohomological dimension
M /aM ) ≥ min{c(M ), sdim M − 1} − cd(M , a), by the following argument: we can consider the complete local ring S := R/(0 :R M ).
Groebner deformations, connectedness and cohomological dimension
In particular if R is a Cohen-Macaulay local ring then c(R/a) ≥ r − cd(R, a) − 1.
Groebner deformations, connectedness and cohomological dimension
Therefore, since, by the Flat Base Change Theorem, cd(Rm , aRm ) ≤ cd(R, a), we have c(R/a) ≥ c(R) − cd(R, a) − 1.
Groebner deformations, connectedness and cohomological dimension
Let k be a ﬁeld, R a k -algebra ﬁnitely generated positively graded on Z and M a Z-graded ﬁnitely generated R-module; then, if a is graded, c(M /aM ) ≥ c(M ) − cd(M , a) − 1.
Groebner deformations, connectedness and cohomological dimension
We recall that the cohomological dimension of a noetherian scheme X , written cd(X ), is the smallest integer r ≥ 0 such that: H i (X, F ) = 0 for all i > r and for all quasi-coherent sheaves F on X (the reader can see for several results about the cohomological dimension of algebraic varieties).
Groebner deformations, connectedness and cohomological dimension
If cd(U ) ≤ r, then c(Z ) ≥ c(X ) − r − 2, where the inequality is strict if X is reducible.
Groebner deformations, connectedness and cohomological dimension
***