Infrared Spectra of {Y3}[Mgy M 2-y](M 3-ySiy)O12 Garnets (M=Al3+, Fe 3+, Ga3+, y=0. 0 to 2. 0)

The Fe 3 O 4 origin of the ‘ ‘ Biphase ” reconstruction on a - Fe 2 O 3 ( 0 0 0 1 )

0039-6028/$ see front matter 2009 Elsevier B.V. A doi:10.1016/j.susc.2009.06.006 * Corresponding author. Address: Department of neering, Northwestern University, 2220 N Campus Dr E-mail address: [email protected] (L.D. M The so-called Biphase termination on a-Fe2O3 has been widely accepted to be a structure with a 40 Å unit supercell composed of coexisting islands of Fe1 xO and a-Fe2O3. ...

2 3 1 1 1 0 0 0 0 1 1 1 2 3 1 2 3 1 3 2 2 3 Adjacency matrix Adjacency list

Graphs and Digraphs: A graph G = (V,E) is a structure that represents a discrete set V objects, called vertices or nodes, and a set of pairwise relations E between these objects, called edges. Edges may be directed from one vertex to another or may be undirected. The term “graph” means an undirected graph, and directed graphs are often called digraphs (see Fig. 1). Graphs and digraphs provide a...

3 2 1 0 4 3 2

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F 0 1 2 3 2 N ? 2 2 N ? 1 0 0 0 0 0 0 0 1 1 2 2 2 2 2

13 Proof: R private (f) C private (f) since in any protocol the parties send at least one bit per round. On the other hand, for every privately computable function f the bound R private (f) is achieved by the protocol A f. In any round of this protocol the parties send a message with size at most n. (Note that in steps (2a) and (2b) of A f we may save one bit per round by omitting the most sign...