Báo cáo toán học: "K0 of Exchange Rings with Stable Range 1" pps

... the class of generalized abelian rings (for short, GA- rings) introduced in [10] is a proper subclass of the class of WGA -rings. We will prov e that, for an exchange ring R with stable range 1, ... e 0 R. Vietnam Journal of Mathematics 34:2 (2006) 171–178 K 0 of Exchange Rings with Stable Range 1 * Xinmin Lu 1,2 and Hourong Qin 2 1 Faculty of Science, Jiangxi...

Ngày tải lên: 06/08/2014, 05:20

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Ngày tải lên: 05/08/2014, 15:21

... +1, so that all of the prime factors of m are certainly ≤ m ≤ √ 2z + √ z +1. But then, all of the prime factors of m belong to S J (as we saw in the first paragraph of this proof), and so m belongs ... proof of Theorem 2 Corollary 2. Fix the real number z ≥ ( √ 2 − 1) 2 . Suppose that the product of some subset of the integers in I =[ √ 2z − √ z, √ 2z + √ z +1], equals N times...

Ngày tải lên: 07/08/2014, 06:22

... sphere, then without loss of generality V 2 =(0, 0,c  ). Conversely, every triangle with (0, 4, 2), (0, 0,c  ) ∈V tiles the sphere. Proof: The proof of the first part is similar to that of Proposition ... tilings are “nearly edge-to-edge”. 4 Proof of Theorem 1 The proof of Theorem 1 breaks up naturally into a sequence of propositions, dealing separately with each possible V 1...

Ngày tải lên: 07/08/2014, 13:21

... neighborhood of a (0, 5, 1) vertex Proposition 3 If the configuration of Figure 4b appears in a tiling of the sphere with triangle T 6 , this configuration must extend to that of Figure 5b. Proof: By ... the configuration of Figure 4b appears in a tiling of the sphere with the triangle T 6 , it must extend to the configuration of Figure 8c. Proof: We first show that the hypotenus...

Ngày tải lên: 07/08/2014, 13:21

... 1940’s, of whether such tilings exist with tiles of arbitrarily small diameter. None of the tiles exhibited in this sequence of papers offers any improvement on the (90 ◦ , 60 ◦ , 36 ◦ ) triangle, with ... introduced the idea of the vertex signature V T of a triangle T with angles (α, β, γ), defined to be the set of triples {(a, b, c) : aα + bβ + cγ = 360 ◦ }. Such a vector...

Ngày tải lên: 07/08/2014, 15:22

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Ngày tải lên: 05/08/2014, 15:20

... then can use that 4 points of a spherical subset of such a set determine the support of that subset. We give some examples, with condensed or omitted proofs. The proofs of the following three theorems ... that with p =0: all points are on k round sets and k(s − 1) <t. In Figure 1 we see examples (with S the set of all circles and lines) of a 12-set with R(6, 4), a 10-set...

Ngày tải lên: 07/08/2014, 13:21

... definition of the quantum yield as follows: # of emitted photons # of absorbed photons Φ ≡ , (3) the number of emitted photons indicates the multiplication of the quantum yield and the number of ... quantity of Aβ peptides is directly proportionate to that of the tagged fluorochrome, the photocurrents generated by p-FET are a function of the amount of Aβ peptides s...

Ngày tải lên: 20/06/2014, 20:20

... the increase of the mean free path for t he excitation of plasma with decreasing pressure, resulting in a decreased amount of atomic hydrogen emission to greatly lower the etching of the sp 2 carbon ... films decreased with decreasing pressure. The reason is due to the great reduction of H a emission to lower the etching of sp 2 carbon phase, resulting from the increase of m...

Ngày tải lên: 20/06/2014, 20:20