{"title":"Notation","authors":"D. Lind, B. Marcus","doi":"10.1111/j.1399-6576.1966.tb00345.x","DOIUrl":"https://doi.org/10.1111/j.1399-6576.1966.tb00345.x","url":null,"abstract":"a, b, c Typical symbols from an alphabet 1 A Transposed matrix 39 A > 0 Positive matrix 100 A 0 Nonnegative matrix 100 A B Matrix inequality 100 A > B Strict matrix inequality 100 A≈∼B Elementary equivalence 226 A ≈ B Strong shift equivalence 227 A ∼ B Shift equivalence 235 A Alphabet 1 A k-blocks over A 2 A Full shift over A 2 AG, A(G) Adjacency matrix of graph G 35 AG Symbolic adjacency matrix 65 adjA Adjugate of A 113 B(X) Language of X 9 Bn(X) n-blocks in X 9 βN Higher block map 12 BF (A) Bowen–Franks group 248 BFp(A) Generalized Bowen–Franks group 250 Cf Companion matrix of f 373 Ck(u) Cylinder set using block u 179 χA(t) Characteristic polynomial of A 100 (∆ A ,∆ A , δ A ) Dimension triple of A 252 dφ Degree of sliding block code φ 303 d φ Minimal number of pre-image symbols 304 E(G), E Edge set of graph 33 EI Edges with initial state I 34 E Edges with terminal state J 34 e, f, g Typical edges of a graph 33 〈E〉Q Rational vector space generated by E 397 〈E〉R R-ideal generated by E 417 F Set of forbidden blocks 5 FX(w) Follower set of a word 72 FG(I) Follower set of a state 78 fλ Minimal polynomial of λ 370 fΛ Polynomial associated to list Λ 385 [[φ]] Topological full group 476 (∂Φ, Φ) Graph homomorphism 34 G Graph 33 G Transposed graph 39 G(A), GA Graph with adjacency matrix A 35 G ∼= H Graph isomorphism 34 G[N] Higher edge graph 42 G Higher power graph 45 G= (G,L) Labeled graph 64 GX Minimal presentation of sofic shift 83 G1 ×G2 Product of graphs 87","PeriodicalId":384023,"journal":{"name":"Scientific Parallel Computing","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129206090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Parallel Performance","authors":"M. Iskandarani","doi":"10.2307/j.ctv1ddcxfs.6","DOIUrl":"https://doi.org/10.2307/j.ctv1ddcxfs.6","url":null,"abstract":"We multiplied random univariate polynomials with 8192 terms. Typical problems run 5x faster with 4 cores on a Core i7 CPU.","PeriodicalId":384023,"journal":{"name":"Scientific Parallel Computing","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116621471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"High Performance Fortran","authors":"Kwai Lam Wong","doi":"10.2307/j.ctv1ddcxfs.13","DOIUrl":"https://doi.org/10.2307/j.ctv1ddcxfs.13","url":null,"abstract":"High Performance Fortran is an informal standard for extensions to Fortran 90 to assist its implementation on parallel architectures, particularly for data-parallel computation. Among other things, it includes directives for expressing data distribution across multiple memories, and concurrent execution features. This paper provides an informal introduction to the main features of HPF.","PeriodicalId":384023,"journal":{"name":"Scientific Parallel Computing","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130275692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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